2023Activity reportProjectTeamSYCOMORES
RNSR: 202124119E Research center Inria Centre at the University of Lille
 In partnership with:Université de Lille, CNRS
 Team name: Symbolic analysis and Componentbased design for Modular RealTime Embedded Systems
 In collaboration with:Centre de Recherche en Informatique, Signal et Automatique de Lille
 Domain:Algorithmics, Programming, Software and Architecture
 Theme:Embedded and Realtime Systems
Keywords
Computer Science and Digital Science
 A2.1.9. Synchronous languages
 A2.3.1. Embedded systems
 A2.3.3. Realtime systems
 A2.4.1. Analysis
 A2.4.3. Proofs
 A2.6.1. Operating systems
 A7.2. Logic in Computer Science
Other Research Topics and Application Domains
 B6.6. Embedded systems
1 Team members, visitors, external collaborators
Research Scientists
 Patrick Baillot [CNRS, Senior Researcher, HDR]
 Raphaël Monat [INRIA, Researcher]
 Vlad Rusu [INRIA, Researcher, HDR]
Faculty Members
 Giuseppe Lipari [Team leader, UNIV LILLE, Professor, HDR]
 Clément Ballabriga [UNIV LILLE, Associate Professor, until Sep 2023, Currently on leave]
 Julien Forget [UNIV LILLE, Associate Professor, HDR]
PostDoctoral Fellow
 Leandro Moreira Gomes [UNIV LILLE, from Sep 2023, ATER]
PhD Students
 Chiara Daini [INRIA, from Jul 2023]
 Nordine Feddal [INRIA]
 Sandro Grebant [UNIV LILLE, until Nov 2023]
 Victor Sannier [UNIV LILLE, from Sep 2023]
 Ikram Senoussaoui [UNIV LILLE, ATER]
Interns and Apprentices
 Pierre Goutagny [ENS DE LYON, Intern, from Oct 2023]
Administrative Assistant
 Nathalie Bonte [INRIA]
External Collaborator
 Aymeric Fromherz [Inria Paris]
2 Overall objectives
The SYCOMORES projectteam aims at developing a framework for the design and the analysis of embedded realtime systems based on symbolic analysis of parametric components.
To reduce the complexity, we will use a modular approach to the design, development and analysis of ERTS. In particular, we will decline modularity along several directions (Figure 1):
 a componentbased design and development methodology; a ERTS system is decomposed in generic, configurable and reusable components that can be combined and instantiated in the final system;
 parametric specification of inputs, configurations and properties; a component is characterised by its interface that will be specified using parameters whose concrete values are unknown at design time;
 symbolic analysis of components; by using symbolic techniques, the properties of a component will be proved correct at design time even when parameters have unknown values.
Finally, we will propose composition operators to integrate a set of components into a larger component, or into a complete system. The operators will allow to (partially or totally) instantiate parameters and connect component interfaces guaranteeing their compatibility and preserving their properties.
To this end, we will investigate several challenging problems at three different levels of abstraction, as shown in Figure 2. At the application level, we will focus on multirate dataflow programming languages like Scade 14, Simulink 28, or in our case Prelude29, as they are widely used in safetycritical domains like avionics and automotive. We want to tackle the notions of component, parametric interfaces and contracts in the ERTS context. We will investigate modular code generation (compilation) of a synchronous component (as opposed to a synchronous program) with realtime constraints. In the long term, we would like to prove the semantic preservation of properties of the program during compilation by using interactive proof systems.
The compiler will produce the component implementation as a set of concurrent realtime tasks with their scheduling parameters. At this level, we will work on parametric and modular worstcase execution time (WCET) analysis of tasks' code, and symbolic schedulability analysis of the components' tasks. We will also work on analysis of the correctness of system integration, and safe dynamic replacement/upgrade of components.
At the lowest level, we will work on the scheduler implementation in the Operating System. We will propose a hierarchical scheduling architecture, in order to provide temporal isolation to realtime components. We will formally prove the scheduler properties by using modular proof techniques in the Coq proof assistat 34, and we will provide a correctby construction implementation of the scheduler by using code generation techniques from a Coq program specification.
As a crosscutting activity, since safety will be a prime concern in our project, we will rely on formal methods throughout the project: synchronous programming languages, abstract interpretation, symbolic analyses and proof techniques. Our research objectives will be tightly coupled to ensure the safety of the final framework.
For instance, our tools and techniques will share proof facts (e.g. timing analysis is correct only if schedulability analysis and WCET analysis are both correct), models (e.g. the schedulability analysis, programming language and WCET analysis must share the same task model), and results (e.g. the WCET and schedulability results will impact the program design).
3 Research program
We detail the objectives by categorising them according to 3 major research axes. Within each axis, we distinguish Short Term (13 years) and Medium Term (24 years) objectives, and we describe how we will achieve them. We also detail how the objectives are related to one another. Finally, we present our Long Term (4+ years) objectives.
3.1 Axis 1: Design and implementation of RTcomponents
In this research axis we will focus on the programming of RTcomponents. We will cover programming aspects at different levels of the development process, from highlevel design, to lowlevel implementation on distributed heterogeneous embedded platforms.
3.1.1 Short term
(A1.S1) Synchronous languages
We will continue working on synchronous programming languages for generating correctbyconstruction code. In particular, one of the objectives of the ANR projet CORTEVA (which is coordinated by G. Lipari, started in Jan. 2018, and will last for 48 months) is to extend the synchronous language Prelude29 to address systems with extremely variable execution time.
The language is being extended (its semantics and its compilation) with constructs to dynamically change the behaviour of a subset of the system based on rare events, like the occurrence of a large execution time of a task. The proposed extensions will guarantee that the system will respect correctness properties even in the presence of such rare events.
Dependencies: We rely on Parametric WCET to detect the occurence of large execution times (A2.S1).
(A1.S2) Scheduling of complex task models
Modern hardware platforms consist of heterogeneous processors with a large degree of parallelism. For example, the NVIDIA Jetson AGX Xavier chipthat is used in modern ADAS systems in the automotive domain, comprises 2 DLAs (Deep Learning Accelerators), 1 integrated GPU (Graphical Processing Unit), and 8 ARM 57 processing cores. Efficiently programming ERTS for such hardware is not easy, as the complexity of the interaction between software and hardware resources makes it difficult to predict performance. Building predictable realtime applications on these platforms requires appropriate programming models. In the recent literature, many graphbased task models have been proposed to exploit the parallelism of such architectures 33, 18. Such models are neither based on components, nor are they parametric. It is our intention to investigate the possibility to apply componentbased techniques to such complex task models.
3.1.2 Medium term
(A1.M1) Parametric scheduling analysis of RealTime components.
Analyzing the schedulability of a system under variations of the task parameters is a complex problem: the complexity of the analysis grows exponentially with the size of the system, and it explodes for mediumtolarge sized systems.
The problem can be decomposed by analysing the schedulability of smaller realtime components under variation of some parameters. The idea is to follow a Resource Reservation strategy, where components are assigned and guaranteed a fraction of the system resources. In this way, the temporal behaviour of one component is isolated from the interference of other components.
First, we will introduce the notion of parametric interface for a component modelled as a multirate dataflow program. The interface will specify the temporal properties and constraints on the input/outputs of a component: periodicity and deadline constraints, dimension of the buffer for communicating with other components, and communication protocols.
To analyse the schedulability of a components under the hypothesis of variation of its parameters (the ones specified in the interface as well as the WCET of the tasks), we will extend the sensitivity analysis techniques, first proposed by Bini et al. 20, 19 to more complex task models and to hierarchical scheduling systems. The objective is to find the range of the parameters for which the component is schedulable.
(A1.M2) Predictable communication costs.
ERTS are increasingly being built using multicore hardware. This transition is however still significantly delayed by the difficulty to provide safe and tight timing guarantees. Indeed, even though multicore architectures enable the simultaneous parallel execution of programs on different cores, these programs are not completely independent. They have to be synchronized at some point to exchange data and they also share some common resources, such as peripherals, communication bus and (parts of the) memory. Synchronizations and shared resource contentions cause hardtopredict interferences and timing overheads, which significantly increase the complexity of timing analyzes (WCET and scheduling).
One solution for mitigating these overheads, and making them more predictable, consists in relying on multiphase task models that decouple communication phases from computation phases 31, 23. This greatly simplifies WCET analysis of computation phases, and also makes it possible to schedule communication phases so as to reduce their interference.
Memory architectures based on local addressable memories (scratchpads), instead of caches, are also being proposed 24, 30, to avoid the hardtopredict timing effects of cache consistency mechanisms (which are used to speedup access to the main shared memory).
We plan to integrate these two approaches in our project, since predictability is a major concern. The Prelude compiler will be extended to provide multiphase task code generation, to be executed on scratchpadbased memory architectures. We will also develop the corresponding schedulability analysis method. Our objective is to devise our development framework such that the programmer abstracts from the implementation of communication mechanisms related on the target OS and hardware. This will enable the programmer to seamlessly transition between different architectures (unicore/multicore, cachebased/scratchpadbased).
3.2 Axis 2: Static Analysis of RT components
In this research axis, we will design static program analysis techniques for RT components at the binary level. While these techniques will mainly focus on WCET analysis, some results will also be reused to analyze security properties instead.
3.2.1 Short Term
(A2.S1) Symbolic WCET analysis.
We will work towards improving static analysis techniques for WorstCase Execution Time Analysis. In particular, we will extend the Parametric WCET method 17 with more powerful symbolic capabilities. Currently, Parametric WCET can represent the WCET of a function as a formula in a number of parameters (e.g. input data). It does however suffer from two important limitations. First, it cannot represent relations between distinct parameters. We will extend the Parametric WCET by abstract interpretation of binary code to detect linear relations between distinct parameters in the code, by using techniques similar to 16. Second, it struggles to represent program properties that relate instructions of the program that are not close to one another, such as for instance infeasible execution paths 32. We are currently extending this work to enable the representation of properties related to such global execution contexts.
3.2.2 Medium Term
(A2.M1) Modular WCET analysis
Traditional WCET analysis is performed on a whole program. This approach is limited by two factors: first, performance concerns (analysis time tends to grow faster than the analyzed program size), and second, the analysis requires access to the complete program (including libraries, etc.). A modular and composable WCET analysis approach would reduce the analysis time, and enable the integration of thirdparty library or system calls in the analysis process.
To this end, we will extend our polyhedrabased abstract interpretation 16 to support interprocedural analysis, based on function summaries 22, describing relations between the inputs and outputs of the function. This will enable us to compute WCETrelated functional properties, such as e.g. loop bounds, in a composable way.
This work on composable analysis will lead to a full composable WCET analysis, by integrating it in our symbolic WCET computation framework 17.
Dependencies: To achieve this objective, we will need the advanced parameter handling techniques of S2.
(A2.M2) Security analysis of binary code
Program analysis of ERTS has historically focused mainly on safety, i.e. ensuring the absence of system failures. However, in recent years ERTS have become increasingly more connected to other computer systems through communication networks. This makes ERTS more vulnerable to external attacks, as illustrated by various reports of hacks of highly computerized modern cars. This results in an increased need for analyses that focus on ensuring the security of ERTS, i.e. ensuring there is no vulnerability to external malevolent computer attacks.
Our work on abstract interpretation of binary code 16 enables to detect linear relations between the datalocations accessed by a binary program (registers, memory addresses and their contents). While this work was initially targeted for WCET analysis, we plan to apply the developped techniques to the security domain as well. In particular, we will analyze security properties specific to the binary structure (e.g. unauthorized accesses to specific memory sections) and study the discovery of potential security threats in closedsource software (to detect malwares).
3.3 Axis 3: Proof of RT Components
The formal proof activity in the project will focus on compositional techniques for proving RT components of operating systems. Our plan is to focus mainly on RT schedulers.
3.3.1 Short term
(A3.S1) A proof methodology for a standard scheduling policy
We shall start with the standard scheduling policy EDF (Earliest Deadline First) and develop a proof methodology for it, which we shall later adapt to more advanced policies. The methodology incorporates a formal notion refinement as a means to master complexity and to smoothly descend from abstract definitions down to executable schedulers.
First, we are planning to model EDF at an abstract level in Coq. We shall formally prove at this level the schedulability property: under adequate hypotheses any given set of periodic hard realtime tasks can be scheduled, such that each task completes before its deadline. Since in the short term we shall only deal with strictly periodic, hard realtime tasks (reading data from sensors, performing some computation and sending the results to actuators), one only needs to consider the schedulability on finite executions, whose length equals the hyperperiod: the least common multiplier of the task's periods. As a result, we expect that induction, well supported by Coq, will be the appropriate proof technique for this stage of the project.
Then, we shall refine the abstract EDF scheduling policy into a scheduling algorithm written in Coq's input language Gallina, a purely functional language, and shall prove again by induction that the algorithm preserves the already established properties of the policy.
Next, our plan is to further refine these functional algorithms into imperative Gallina programs, in order to get a step closer to executable code1. Imperative programs in purely functional languages such as Gallina are traditionally written using monads e.g., state monads, which enable variable assignments in functional code. For doing this we shall benefit from the experience of our colleagues in the 2XS team, our closest collaborators within the CRIStAL laboratory. They have been developing a minimalistic OS kernel called Pip 35 in imperative Gallina using the statemonad technology and have directly proved properties of the kernel in Coq. Unlike them, we do not prove properties directly on the monadic code, but shall prove a refinement step (from functional to imperative) ensuring that schedulability holds on the imperative scheduler.
The final step is translating the imperative Gallina scheduler to executable code. For this we shall use a translator also developped by the 2XS team, which essentially maps wordforword imperartive Gallina programs to C programs with appropriate primitives that, after compilation of the C code, turn our schedulers into executable programs within Pip.
3.3.2 Medium term
In the medium term we are planning to make progress on two directions: the RT components being proved and the proof techniques.
(A3.M1) More advanced schedulers and other RT components
Once the validation of the proof/refinement methodology on the EDF example is complete, we are planning to progressively generalise it to other schedulers. The next likely candidate is the Grub scheduler, developped by Giuseppe Lipari 15, 26, which generalises EDF and makes it possible to mix periodic tasks (hard realtime) with sporadic tasks (soft realtime). The algorithm guarantees that the deadlines of the hard realtime tasks are met, while for the soft realtime ones a certain quality of service is guaranteed.
We are also planning to formally verify existing resource reservation hierarchical schedulers 27 by extending the proof/refinement approach with compositional features that exploit the componentbased nature of the considered applications.
Depending on the availability of human resources, we would also like to formally verify other RT components, such as interruption multiplexers, memory managers, or synchronisation mechanisms.
(A3.M2) More advanced proof techniques
We expect that different verification techniques will be necessary to prove these more advanced schedulers. The EDF scheduler can be proved correct by considering its behaviour over a limited period of time, which as explained above can be dealt with using induction. However, Grub also has to schedule sporadic tasks that, by definition, do not repeat themselves periodically. Without a periodic repetition the behaviour cannot be studied over a finite interval, infinite executions have to be considered. Hence, we are planning to use coinduction, the natural technique for defining and reasoning about infinite objects. As stated in the Preliminaries we already have experience with coinduction, especially, with improving the way it is dealt with in Coq to make it better suited for use in nontrivial applications. We are planning to continue doing this both for corecursive program definitions (e.g., reactive systems, including schedulers, are such programs) and for coinductive reasoning techniques.
3.4 Long term
In the long term, we will integrate the elements studied during the medium term phase, in order to provide a seamless framework that goes from highlevel design to final implementation. Translations will be automated and proved correct. These objectives are transverse by nature, so all members of the projectteam will participate. Since these objectives focus on integration of our previous results, they are related to all of our short and medium term objectives.
(L1) Integrated framework
During the medium term phase, we will develop bricks that contribute to the design and analysis of ERTS. In the long term phase, we will integrate these bricks into a complete framework. This will raise several research topics.
First, we will have to evaluate the impact of scheduling on WCET analysis. Though this topic has already been studied before, our symbolic approach to both problems will raise new opportunities and challenges.
Second, we will evaluate the scalability of the approach with respect to realistic and complex realtime programs. In particular, the advent of powerful heterogeneous hardware platform permits to exploit their large scale parallelism. It is then important to check the suitability and the expressiveness of our framework with respect to these new powerful platforms.
(L2) Proving semantics preservation
In our framework, an ERTS is first specified with a highlevel dataflow semantics (in Prelude). Then, it undergoes translations to produce the final program (in C) embedded on the hardware platform. One of our long term objectives is to prove that the complete translation process, from Preludeto C, is semanticspreserving.
There exists previous work and techniques for the formal verification of compilers such as CompCert 25 (from C code to binary code) and the Lustre verified compiler 21. However, these works focus on the preservation of the functional semantics (computing the correct values). A major novelty of our work will be to focus on the preservation of the temporal semantics (computing values at the correct time) as well. As far as we know, proving the preservation of temporal semantics was previously explored in theoretical models (e.g. timed automata, or Petri nets), but not in programming languages and compilers. It is an ambitious challenge, because it connects compilation with scheduling and WCET analysis.
(L3) Corecursionpreserving compilation and coinductive verification techniques
An alternative view of reactive programs (such as Prelude programs) is that of corecursive transformers from infinite flows of inputs to infinite flows of outputs. We envisage an enhanced compilation chain that, in addition to what is planned in L2, enables the tracing of corecursion down to the executable code. Since corecursive calls typically compile to lowlevel instructions such as loops or jumps, such a tracing mechanism would enable recognising the corecursive calls at the lowlevel. This, in turn, would enable the formal reasoning about lowlevel corecursive programs, using coinductive techniques that we shall develop in A3. We note that schedulers can also be expressed as corecursive programs, hence the verification boils down to compositionally verifying compositions of corecursive programs. It is, again, an ambitious challenge at every step, since corercursive programs are notoriously difficult to define, compose, and verify. This envisaged works depends on progress in essentially all the objectives enumerated above.
(L4) Dynamic update of components
ERTS may evolve over time, in particular, one component may be upgraded while the system is operational. In the traditional development process of critical software, once the system has been developed, tested and certified, it is not possible to change it anymore, with the only exception of correcting a critical bug. Dynamic updates are not possible since they would require to recertify the whole system.
In the long term, we would like to apply our component based development process to the problem of guaranteeing the correctness of dynamic updates. This means that the system must be able to evolve over time, during operation, without jeopardizing the guarantee on existing properties.
Given the large complexity of the formal methods we will use for offline analysis, it is unthinkable to apply the same type of analysis online. One possibility is to separate the analysis into two distinct parts: an offline part which may be complex and does most of the work; and an online part which is much simpler but relies on the offline computation. Alternatively, it is possible to offload part of the analysis to the cloud, where there is abundance of computational resources.
4 Application domains
The long term research we propose to pursue in this project will advance the current development practice for embedded realtime critical systems.
First, it will impact the design and development of critical software for domains like avionics, automotive, train, etc. It is well known that developing safetycritical software is a long and costly process, where each error could endanger human life. It has been estimated that the cost to certify 30K lines of DAL A code is around 2M$ if the code has been developed by experienced programmers, and it jumps to 8M$ if the code has been produced by nonexperienced ones.
The avionic industry is slowly adopting formal methods to reduce the cost by reducing (or, in certain cases, eliminating altogether) testing and improve confidence in the methodology. Our integrated framework (L1) will greatly reduce the development cost of safetycritical software because it will automatise many of the steps in the design and development methodology. For example, the use of semantic preserving transformations (L2, L3) will enhance the confidence in the correctness of the generated code, reducing the need for extensive testing, thus further reducing cost.
Other critical domains, like automotive, have not yet fully adopted safetycritical standard methodologies like in the avionic domain, mainly for cost reasons. Our framework will lower the cost of developing safety critical software, thus improving the safety of critical software in a wider range of domains.
Finally, thanks to the research in (L4), it will be possible to update a software component online without performing a complete analysis of the system, while the system is operational. An example of futuristic application will be the possibility to update one software subsystem of an autonomous vehicle while the vehicle is running, without compromising its functionality.
5 Social and environmental responsibility
Raphaël Monat takes part in the genderequality commission of the lab, and attended some meetings of the sustainable development group.
6 Highlights of the year
Julien Forget defended his Habilitation à Diriger les Recherches on "Programming and analysis of critical realtime systems", June 12, 2023.
6.1 Awards
In Fall 2023, Raphaël Monat participated to the Software Verification Competition (SVComp) by submitting the Mopsa static analyzer he is codeveloping. Mopsa earned a gold medal in the SoftwareSystems category. There were 22 competing tools in this category.
6.2 PhD graduation
Two PhD students of the team graduated in 2023.
Sandro Grebant defended his thesis titled "Efficient treebased symbolic WCET computation" on the 7th of November 2023 at the University of Lille. Sandro was cosupervised by Julien Forget and Giuseppe Lipari
Ikram Senoussaoui defended her thesis titled "Processor and memory coscheduling of embedded realtime applications on multicore platforms" on the 14th of Decembre 2023 at the University of Lille. She was cosupervised by Giuseppe Lipari , Benahoua Kamel from the University of Oran 1, and HoussamEddine Zahaf from the University of Nantes.
7 New software, platforms, open data
7.1 New software
7.1.1 otawa

Keywords:
Static analysis, WCET

Functional Description:
Otawa is an open source static analysis tool developed and maintained by the TRACES team at the University of Toulouse and codeveloped by the team SYCOMORES at Inria lille NordEurope. Specifically, SYCOMORES has developed two plugins for OTAWA: Polymalys, for polyhedrabased analysis and loop bound estimation, and WSymb, a Control Flow Tree extractor and symbolic WCET evaluator.
 URL:

Contact:
Clement Ballabriga

Partner:
Université de Toulouse
7.1.2 prelude

Keywords:
Synchorous language, Real time

Functional Description:
Prelude is a synchronous dataflow language with realtime constraints, designed by Julien Forget. Prelude programs are compiled into mulithread C code. The language and its compiler are developed in collaboration with ONERA Toulouse. Prelude is currently being extended to support adaptive applications.
 URL:

Contact:
Julien Forget
7.1.3 ptask

Keywords:
Real time, Library

Functional Description:
PTASK is a library for programming realtime systems in Linux. It serves as the target RTOS API in the SYCOMORES project. The PTASK library is authored by Giuseppe Lipari. It has been initially developed to support teaching realtime systems at the Scuola Sant’Anna. It has later been extended with additional capabilities and it is being used as target for design tools such as CPAL19 from RTaW20 and by other companies.
 URL:

Contact:
Giuseppe Lipari
7.1.4 Catala

Keywords:
Domain specific, Programming language, Law

Functional Description:
Catala is a domainspecific programming language designed for deriving correctbyconstruction implementations from legislative texts. Its specificity is that it allows direct translation from the text of the law using a literate programming style, that aims to foster interdisciplinary dialogue between lawyers and software developers. By enjoying a formal specification and a prooforiented design, Catala also opens the way for formal verification of programs implementing legislative specifications.
 URL:
 Publications:

Contact:
Denis Merigoux

Participants:
Denis Merigoux, Louis Gesbert, Aymeric Fromherz, Alain Delaet–Tixeuil, Raphael Monat

Partner:
Université PanthéonSorbonne
7.1.5 datescalc

Keywords:
Law, Programming language

Functional Description:
A date calculation library with a welldefined semantics
 URL:

Contact:
Raphael Monat
7.1.6 Mopsa

Keywords:
Formal methods, Static analysis, Abstraction

Functional Description:
Mopsa is an opensource static analysis platform relying on abstract interpretation. It provides a novel way to combine abstract domains, in order to offer extensibility and cooperation between them, which is especially beneficial when relational numerical domains are used. It is able to analyze C, Python, and programs mixing these two languages. Mopsa was originally developed at LIP6, Sorbonne Université following an ERC Consolidator Grant award to Antoine Miné. It is now partially developed at Inria.
 URL:

Contact:
Antoine Miné

Partner:
Sorbonne Université
7.1.7 Haddock

Keywords:
Partial function, (Co)Recursive Function, Coq

Functional Description:
A Coq library for defining and reasoning about partial (co)recursive functions.
 URL:

Contact:
Vlad Rusu

Partners:
Université de Lille, CNRS, Université de Bucarest
8 New results
8.1 Mopsa at the Software Verification Competition
Mopsa is a multilanguage static analysis platform relying on abstract interpretation. It is able to analyze C, Python, and programs mixing these two languages
In Fall 2023, Raphaël Monat participated to the Software Verification Competition (SVComp) by submitting the Mopsa static analyzer he is codeveloping. Mopsa earned a gold medal in the SoftwareSystems category; this category aims at "representing verification tasks from real software systems". There were 22 competing tools.
This is our second participation, our first participation is described in 5.
Participants: Raphaël Monat.
8.2 Contentionfree scheduling of AECR dag tasks on partitioned multicore platforms
This work is based on the thesis of Ikram Senoussaoui. She is supervised by Giuseppe Lipari, Kamel Benahoua (University of Oran 1) and Houssam Zahaf (University of Nantes).
Commercialofftheshelf (COTS) platforms feature several cores that share and contend for memory resources. In realtime system applications, it is of paramount importance to correctly estimate tight upper bounds to the delays due to memory contention. However, without proper support from the hardware (e.g. a realtime bus scheduler), it is difficult to estimate such upper bounds.
We aim at avoiding contention for a set of tasks on a hardware multicore architecture, where each core has its private scratchpad memory and all cores share access to the main memory. By avoiding contention, we make multicore programming predictable again.
We propose a new task model, AECRdag (Acquisition, Execution, Communication Restitution – Directed Acyclice Graph), where a periodic or sporadic task is models by a set of subtask nodes and communication between then, organised as a DAG. The model captures the parallelism of the task and it makes explicit the communication between the subtasks.
Then, we propose a methodology based on Integer Linear Programming, for allocating the subtasks on the cores using partitioned preemptive EDF, so to reduce the cost of communication between subtasks allocated to different cores. Then, we propose a method based on Evolutionary Programming, that allocates the intermediated deadlines to the subtasks so to respect the precedence constraints and the endtoend deadline.
This work has been presented in the last chapter of the thesis of Ikram Senoussaoui. It has also been submitted to the Journal of Systems Architectures where it is now under major revision.
Participants: Giuseppe Lipari, Ikram Senoussaoui.
8.3 Bunched Fuzz: Sensitivity for Vector Metrics
Program sensitivity measures the distance between the outputs of a program when run on two related inputs. This notion, which plays a key role in areas such as differential privacy and optimization, has been the focus of several program analysis techniques introduced in recent years. Among the most successful ones, we can highlight type systems inspired by linear logic, as pioneered by Reed and Pierce in the Fuzz functional programming language. In Fuzz, each type is equipped with its own notion of distance, and sensitivity analysis boils down to type checking. In particular, Fuzz features two product types, corresponding to two different notions of distance: the tensor product combines the distances of each component by adding them, while the with product takes their maximum.
In 10 with colleagues from Boston University we proposed an extension of Fuzz where product types are generalized to arbitrary ${L}^{p}$ distances, metrics that are often used in privacy and optimization. The original Fuzz products, tensor and with, correspond to the special cases ${L}^{1}$ and ${L}^{\infty}$. To support the handling of such products, we extend the Fuzz type system with bunches—as in the logic of bunched implications—where the distances of different groups of variables can be combined using different ${L}^{p}$ distances. We show that our extension can be used to reason naturally about quantitative properties of probabilistic programs.
Participants: Patrick Baillot.
8.4 Formal Definitions and Proofs for Partial (Co)Recursive Functions
Participants: Vlad Rusu.
Partial functions are a key concept in programming. Without partiality a programming language has limited expressiveness  it is not Turingcomplete, hence, some programs cannot be written. In functional programming languages, partiality mostly originates from the nontermination of recursive functions. Corecursive functions are another source of partiality: here, the issue is not nontermination, but the inability to produce arbitrary large, finite approximations of a theoretically infinite output.
Partial functions have been formally studied in the branch of theoretical computer science called domain theory. In this paper we propose to step up the level of formality by using the Coq proof assistant. The main difficulty is that Coq requires all functions to be total, since partiality would break the soundness of its underlying logic. In 12 (currently submitted to a journal) we propose practical solutions for this issue, as well as other issues that appear when one attempts to define and reason about partial (co)recursive functions in a total functional language such as that of the Coq proof assistant.
Our solutions have been implemented in an opensource Coq library 7.1.7. We present several examples of partial recursive and corecursive functions defined with our approach. For the functions that are actually total, a coinductive proof technique enables users to prove the totality.
8.5 While Loops in Coq
Participants: Vlad Rusu.
While loops are present in virtually all imperative programming languages. They are important both for practical reasons (performing a number of iterations not known in advance) and theoretical reasons (achieving Turing completeness). In 9 we propose an approach for incorporating while loops in an imperative language shallowly embedded in the Coq proof assistant. The main difficulty is that proving the termination of while loops is nontrivial, or impossible in the case of nontermination, whereas Coq only accepts programs endowed with termination proofs. Our solution is based on a new, general method for defining possibly nonterminating recursive functions in Coq. We illustrate the approach by proving termination and partial correctness of a program on linked lists. The development is available here.
8.6 WCET analysis with procedure arguments as parameters
In 8 we present a methodology for obtaining the WCET of a program procedure as a function of the its arguments. The methodology extends a previous method for symbolic WCET to the case of conditional statements (ifthenelse). Then, a new technique based on abstract interpretation has been developed to 1) detect the arguments in the function code, 2) compute a symbolic expression of the WCET based on the arguments. Finally, a compiler generates efficient Ccode for evaluating the formula at runtime, thus enabling the use for this technique for adaptive scheduling. The resulting methodology has been tested on several benchmarks from the literature, proving its efficiency and tightness.
This work is part of the thesis of Sandro Grebant. He was supervised by Julien Forget and Giuseppe Lipari, and he defended succesfully in November 2023.
Participants: Sandro Grebant, Julien Forget, Clément Ballabriga, Giuseppe Lipari.
8.7 Static Analysis of Functional Programs Handling Recursive Algebraic Data Types
In 11, we describe a static value analyzer by abstract interpretation for a typed firstorder functional language, which is a safe and automatic approach to guarantee the absence of errors at runtime. Based on relational abstract domains and realizing summaries of recursive fields of algebraic types, this approach allows to analyze recursive functions manipulating recursive algebraic types and to infer in an abstract domain their inputoutput relationship. An implementation is underway on the MOPSA multilanguage analysis platform and successfully analyzes short programs of a few lines. This work thus paves the way towards accurate and relational value analysis based on abstract interpretation for functional languages of higher order than ML.
Participants: Raphaël Monat.
9 Partnerships and cooperations
9.1 International research visitors
Horatiu Cheval

Status:
PhD student

Institution of origin:
University of Bucharest

Country:
Romania

Dates:
410 Sept. 2023

Context of the visit:
During Horatiu's visit we initiated the collaboration that resulted in the (currently, submitted) paper 12.

Mobility program/type of mobility:
funded by the EuroProofNet COST action
Participants: Vlad Rusu.
9.2 European initiatives
9.2.1 Other european programs/initiatives
COST Action EuroProofNet: all relevant information is here. This action funded the visit of Horatiu Cheval, PhD student at Univ. Bucharest, Romania.
9.3 National initiatives
Raphaël Monat is coPI of an Inria Exploratory Action called AVoCat, aiming at exploring Automatic Verification of Catala programs. The project is shared with Aymeric Fromherz at Inria Paris.
Participants: Raphaël Monat.
10 Dissemination
10.1 Promoting scientific activities
10.1.1 Scientific events: organisation
Chair of conference program committees
Julien Forget has been cochair of the ECRTS'23 Artifact Evaluation committee.
Member of the conference program committees
Patrick Baillot has been member of the PC of the conference FoSSaCS 2023 and since 2023 of the steering committee of the conference FSCD.
Julien Forget has been PC member for ECRTS'23 and DATE'23.
Raphaël Monat has been a PC member of SOAP'23, SVComp 2024 and JFLA 2024.
Vlad Rusu had been PC member for FROM 2023 and Tacas 2024.
10.1.2 Journal
Member of the editorial boards
Giuseppe Lipari is member of the editorial board of RealTime System Journal.
10.1.3 Invited talks
Vlad Rusu gave an invited talk at the tenth congress of Romanian mathematicians (July 2023, Pitesti, Romania).
Giuseppe Lipari gave an invited talk "Parametric WCET" at the University of Nantes during his visit on September 2929.
10.1.4 Scientific expertise
From october to december 2023, Giuseppe Lipari has served as member of the HCERES commitee for the evaluation of the LIP6 laboratory of the Sorbonne University in Paris.
10.1.5 Research administration
Patrick Baillot is Délégué Scientifique at CNRS Sciences Informatiques, since September 2022 (40% of his work time).
10.1.6 Hiring committees
Raphaël Monat has been a jury for oral examinations to enter Écoles Normales Supérieures.
Vlad Rusu was a member of the hiring committee of researchers for Inria Lille (CRCN/ISFP).
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
Giuseppe Lipari is responsible for the "IoT and Cybersecurity" specialty of the Master in Computer Science of the University of Lille. The Masters' courses of this specialty are taught in English. The specialty is also part of the Graduate Programme "Information and Knowledge Society" of the University of Lille.
Giuseppe Lipari has taught the following courses at the University of Lille in the academic year 20222023:
 Programmation de Systemes (Resp., L3, 3 ECTS, 180 students) and Programmation de Systemes + (Resp., L3, 3 ECTS, 80 students)
 Embedded System Design (Resp., M1, 6 ECTS, 25 students)
 Operating System 1 (M1, 3 ECTS, 25 students)
 Operating Systems 2 (Resp., M1, 3 ECTS, 75 students)
 Advanced Object Oriented Programming (Resp., M1, 3 ECTS, 75 students)
 Advanced Operating Systems (Resp., M2, 3 ECTS, 30 students)
 RealTime Systems (Resp., M2, 3 ECTS, 15 students)
Moreover, Giuseppe Lipari has supervised several internships and memoirs of M2, for a total service of 338.5 hours (eqTD) in 20222023.
Julien Forget has taught the following courses at the University of Lille in the academic year 20222023:
 Structured programming (Resp., Ing3, 48h, 50 students)
 Operating Systems (Ing3, 16h, 12 students)
 Operating Systems (Resp., Ing3, 16h, 50 students)$\times 2$
 Objectoriented Programming (Ing4, 10h, 12 students)
 Theoretical Computing (Resp., Ing4, 22h, 24 students)
 Data structures (Resp., Ing3, 12h, 24 students)
 Programming project (Ing3, 22h, 12 students)
 An Introduction to Research (Ing4, 6h, 50 students)
Overall, the teaching activities of Julien Forget amount to a total service of 245 hours (eqTD) in 20222023.
Vlad Rusu has taught a cours on Formal Methods for Embedded Systems (M2) at the "Internet of Things and Cybersecurity" specialty of the Master in Computer Science at the University of Lille (M2, 12 hours)
Vlad Rusu gave a oneday course on introduction to the Coq proof assistant at an autumn school (September 2024, Bucharest, Romania).
Raphaël Monat has taught a course on "Compilation des Logiciels" at the Master in Computer Science of the University of Lille (M1, 3 ECTS, 24 hours).
10.2.2 Supervision
Master2 internship of Victor Sannier , apriljuly 2023, supervised by Patrick Baillot .
10.2.3 Juries
Julien Forget was examiner for the defense of Basile Pesin's Ph.D. (PSL/ENS) on "Verified compilation of a synchronous dataflow language with state machines".
Julien Forget was examiner for the defense of Rémi Meunier's Ph.D. (U. Toulouse) on "Prédiction du temps d'exécution d'applications dans des architectures multicœur".
Giuseppe Lipari was reviewer of the thesis of Gabriele Ara at Scuola Superiore Sant'Anna of Pise, whose defense was succesfully completed on the 16th of June 2023. He was also president of the jury for Clément Boin at the University of Lille on the 18th of December 2023. He was also president of the jury of Lorenzo Canonne at the University of Lille on the 19th of December 2023.
11 Scientific production
11.1 Major publications
 1 inproceedingsWCET analysis with procedure arguments as parameters.RTNS 2023: The 31st International Conference on RealTime Networks and SystemsDortmund, GermanyACM2023, 1122HALDOI
 2 inproceedingsWhile Loops in Coq.Electronic Proceedings in Theoretical Computer Science7th Symposium on Working Formal Methods (FROM 2023)389Bucarest, RomaniaSeptember 2023, 96  109HALDOI
 3 inproceedingsBunched Fuzz: Sensitivity for Vector Metrics.ESOP 2023  European Symposium on ProgrammingProceedings of ESOP 2023 (European Symposium on Programming)Paris, FranceSpringerApril 2023HALDOI
11.2 Publications of the year
International journals
Invited conferences
 5 inproceedingsMopsaC: Modular Domains and Relational Abstract Interpretation for C Programs (Competition Contribution).Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2023)13994Lecture Notes in Computer ScienceParis, FranceSpringer, ChamApril 2023, 565570HALDOIback to text
International peerreviewed conferences
 6 inproceedingsOn Basic Feasible Functionals and the Interpretation Method.Lecture Notes in Computer ScienceInternational Conference on Foundations of Software Science and Computation StructuresLuxembourg City, LuxembourgSpringerApril 2024HAL
 7 inproceedingsNew challenges in adaptive realtime systems with parametric WCET.RTSOPS 2023  12th International RealTime Scheduling Open Problems SeminarVienne, AustriaJuly 2023HAL
 8 inproceedingsWCET analysis with procedure arguments as parameters.RTNS 2023: The 31st International Conference on RealTime Networks and SystemsDortmund, GermanyACM2023, 1122HALDOIback to text
 9 inproceedingsWhile Loops in Coq.Electronic Proceedings in Theoretical Computer Science7th Symposium on Working Formal Methods (FROM 2023)389Bucarest, RomaniaSeptember 2023, 96  109HALDOIback to text
 10 inproceedingsBunched Fuzz: Sensitivity for Vector Metrics.ESOP 2023  European Symposium on ProgrammingProceedings of ESOP 2023 (European Symposium on Programming)Paris, FranceSpringerApril 2023HALDOIback to text
National peerreviewed Conferences
 11 inproceedingsAnalyse statique de valeurs par interprétation abstraite de programmes fonctionnels manipulant des types algébriques récursifs.Journées Francophones des Langages ApplicatifsJFLA 2023  34èmes Journées Francophones des Langages ApplicatifsPrazsurArly, FranceJanuary 2023, 211242HALback to text
Reports & preprints
 12 miscFormal Definitions and Proofs for Partial (Co)Recursive Functions.December 2023HALback to textback to text
 13 miscBiGKAT: an algebraic framework for relational verification of probabilistic programs.March 2023HAL
11.3 Cited publications
 14 miscSCADE Suite.2018back to text
 15 articleResource Reservations for General Purpose Applications.IEEE Trans. Ind. Informatics512009, 1221URL: https://doi.org/10.1109/TII.2009.2013633DOIback to text
 16 inproceedingsStatic Analysis Of Binary Code With Memory Indirections Using Polyhedra.International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI'19)Lisbon, Portugal1 2019HALback to textback to textback to text
 17 articleSymbolic WCET Computation.ACM Transactions on Embedded Computing Systems (TECS)172December 2017, 126HALDOIback to textback to text
 18 inproceedingsResourceEfficient Execution of Conditional Parallel RealTime Tasks.EuroPar 2018: Parallel ProcessingChamSpringer International Publishing2018, 218231back to text
 19 articleThe space of EDF deadlines: the exact region and a convex approximation.RealTime Systems4112009, 2751back to text
 20 articleSensitivity analysis for fixedpriority realtime systems.RealTime Systems39132008, 530back to text
 21 inproceedingsA formally verified compiler for Lustre.ACM SIGPLAN Notices526ACM2017, 586601back to text
 22 inproceedingsDisjunctive relational abstract interpretation for interprocedural program analysis.International Conference on Verification, Model Checking, and Abstract InterpretationSpringer2019, 136159back to text
 23 inproceedingsPredictable flight management system implementation on a multicore processor.Embedded Real Time Software (ERTS'14)2014back to text
 24 inproceedingsCommunication Centric Design in Complex Automotive Embedded Systems.29th Euromicro Conference on RealTime Systems (ECRTS 2017)Dubrovnik, Croatia2017back to text
 25 miscThe CompCert C verified compiler.2018back to text
 26 inproceedingsGreedy reclamation of unused bandwidth in constantbandwidth servers.12th Euromicro Conference on RealTime Systems (ECRTS 2000), 1921 June 2000, Stockholm, Sweden, ProceedingsIEEE Computer Society2000, 193200URL: https://doi.org/10.1109/EMRTS.2000.854007DOIback to text
 27 inproceedingsResource Partitioning among RealTime Applications.Proc. 15th Euromicro Conf. RealTime SystemsIEEE Computer Society2003, 151158DOIback to text
 28 miscSimulink.2018back to text
 29 articleMultitask implementation of multiperiodic synchronous programs.Discrete Event Dynamic Systems2132011, 307338back to textback to text
 30 inproceedingsAutomated generation of timepredictable executables on multicore.RTNS 2018October 2018back to text
 31 inproceedingsA predictable execution model for COTSbased embedded systems.RealTime and Embedded Technology and Applications Symposium (RTAS)IEEE2011back to text
 32 inproceedingsA general approach for expressing infeasibility in implicit path enumeration technique.2014 International Conference on Embedded Software (EMSOFT)IEEE2014, 19back to text
 33 articleParallel RealTime Scheduling of DAGs.IEEE Transactions on Parallel and Distributed Systems251212 2014, 32423252DOIback to text
 34 miscThe Coq proof assistant reference manual.2021back to text
 35 miscThe Pip protokernel.2018back to text