We are developing SiLCC an imperative and concurrent constraint programming language based on a single paradigm: the one of Vijay Saraswat's concurrent constraint programming extended with constraint systems based on Jean-Yves Girard's Linear Logic. From a constraint programming point of view, the unique combination of constraint programming with imperative features opens many new possibilities, among which:

The Constraint Handling Rules (CHR) language of Thom Frühwirth shares many similarities with SiLCC. CHR (and its modular version CHRat ) and SiLCC are based on the same model of concurrent computation, where agents communicate through a shared constraint store, with a synchronization mechanism based on constraint entailment. In particular, the Constraint Simplification Rules (CSR) subset of CHR and the flat subset of LCC, where agent nesting is restricted, are very close syntactically and semantically.

In , we analyze these similarities by providing translations between CSR and flat-LCC, on the one hand, and a transformation from the full LCC language to flat-LCC, on the other hand. This transformation is similar to -lifting in functional languages. In conjunction with the equivalence between CHR and CSR with respect to naive operational semantics, these results lead to semantics-preserving translations from full LCC to CHR and conversely. Immediate consequences of this work include new proofs for CHR linear logic and phase semantics, relying on corresponding results for LCC, plus an encoding of the -calculus in CHR.

Rules2CPis a rule-based modeling language which allows easy modelling of constraint satisfaction problems, together with specifications for search strategies and heuristic choice criterias. In , we describe the language and its compilation to constraint programs with a term rewriting system.

The expressiveness and effectiveness of Rules2CP have been illustrated through the development of the Packing Knowledge Modeling Language PKML as a library on top of Rules2CP, dedicated to bin packing problems. PKML language is used in the FP6 Strep Net-WMSto study and solve higher-dimensional bin packing problems and placement constraints, including common sense, physical and industrial requirements expressed by rules , , , .

Furthermore, in , we look at the application of Rules2CP to solve Open-Shop Problem, which is at the core of many scheduling problems. In this approach we are able to solve many of the Open Shop instances which have only been closed very recently with minimal effort.

One originality of Rules2CPas a modeling language is that it allows us to express search tree and labeling ordering heuristics declaratively by pattern matching on rule left-hand sides' derivation . The search trees are expressed by logical formulae, and heuristic choice criteria are defined by preference orderings on variables and formulae. This approach to specifying ordering heuristics by pattern matching should be applicable to other modeling languages that use definitions, such as Zinc for instance.

In order to deal with dynamic ordering criteria, a new compilation scheme for Rules2CP is introduced in for generating procedural constraint programming code, The comparison with the static expansion of Rules2CP models shows that the overhead at runtime is limited, with a gain in the size of the generated program which could be exponentially larger by static expansion.

In , a novel symmetry detection procedure is introduced for detecting symmetries not only in instanciated constraint satisfaction problems but in parametric constraint satisfaction programs or models. The method proceeds by normalization of expressions with a term rewriting system. The evaluation of the method on classical benchmark problems, expressed in the OPL modeling language, shows that the interesting symmetries that are easy to break with constraints are detected in a few seconds, or minutes for the generalized perfect square problem.

We worked on a general theory of trace design based on the observation of the way trace files are accumulated as knowledge bases and elaborated in differents fields of activity like software engeneering, rule based systems and resolution, learning in context, or personal experience storing systems. The state of this work is regularly updated on .

One of the important aspect of this research is to give a proper semantics to a trace, called “observational semantics” (OS). We followed two ways: the use of the simple fluent calculus as formalism for the OS, and the software component modeling approach to combine traces of components . This approach is presently used to specify and implement a versatile trace r of CHR ^vwith several extensions, in the framework called CHROME-REF . It includes three main component s: CHROME (input process), a Trace Driver (intermediator and trace query processor) and a Trace Analyzer (front-end). It is a useful experimental environment to contribute to elaborate a generic framework to generate explanatory traces for constraint solving and rule-based reasoning systems, as presented in .

In , we present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as a Constraint Satisfaction Problem (CSP). The use of Petri-nets to manipulate reaction models,and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, especially in the context of module decomposition. In our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws and consistency checking, thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri-nets correspond to well-known techniques in CSPs, like symmetry-breaking. A simple prototype based on GNU-Prolog's FD solver, and including symmetry detection and breaking, was incorporated into the BIOCHAMmodelling environment.

Other uses of Petri Nets structural properties computation were investigated in , and most notably an incomplete symbolic search for steady states based on T-invariants computation and other structural properties.

These developments are focused on the applications of the CALAMARANR project, where large models of the E2F/RB pathway and of other cancer-related processes are studied. This project also dwelves, on the formal side, on relationships between different formalisms, whether BIOCHAM-like reaction-centered, or regulation-centered like logical models , the Petri Net level being common to both frameworks.

Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also more and more employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and positive/negative influence graphs. The analysis of circuits in the influence graphs has been introduced by René Thomas in the late 70's with necessary conditions for oscillations (homeostasie) and multistability (cell differentiation).

In , model reduction techniques preserving the circuits in the influence graph are investigated and evaluated on a gene regulatory network responsible for segment polarity in Drosophilia. In , general structural model reduction techniques based on graph edition operations are investigated and evaluated on models of cell signalling. The perspective of these preliminary studies is to relate models at different levels of details by formal graph transformation operations, and design systematic model reduction/expansion strategies.

In , an extension of the syntax of reaction rules with antagonists is proposed for SBML and BIOCHAM in order to make visible in the rules the inhibitors of a reaction that are often hidden in the kinetic expression. This extension allows us to efficiently compute the influence graph of a reaction model and to compare models at different levels of details.

The two element mutual activation and inhibitory positive feedback loops are a common motifs that occur in many biological systems in both isolated and interlocked form, as for example,in the cell division cycle and thymus differentiation in eukaryotes.

In , the properties of three element interlocked positive feedback loops that embeds both mutual activation and inhibition are studied indepth for their bistable properties by performing bifurcation and stochastic analysis. Codimension one and two bifurcations reveal important properties like robustness to parameter variations and adaptability under various conditions by its ability to fine tune the threshold to a wide range of values and to maintain a wide bistable regime. Furthermore, we show that in the interlocked circuit, mutual inhibition controls the decision to switch from OFF to ON state, while mutual activation enforces the decision. This view is supported through a concrete biological example Candida albicans, a human fungal pathogen that can exist in two distinctive cell types: one in the default white state and the other in an opaque form. Stochastic switching between these two forms takes place due to the epigenetic alternation induced by the transcriptional regulators in the circuit, albeit without any rearrangement of the nuclear chromosomes. The transcriptional regulators constitute interlocked mutualactivation and inhibition feedback circuits that provide adaptable threshold and wide bistable regime. These positive feedback loops are shown to be responsible for robust noise induced transitions without chattering, persistence of particular phenotypes for many generations and selective exhibition of onep articular form of phenotype when mutated. Finally, we propose for synthetic biology constructs touse interlocked positive feedback loops instead of two element positive feedback loops because they are better controlled than isolated mutual activation and mutual inhibition feedback circuits.

Temporal logics and model-checking are at the core of BIOCHAMto express biological properties of complex biochemical systems and automatically verify their satisfaction in both qualitative and quantitative models. In particular, linear time logic constraints (QFLTL( )) are used to formalize the global behavior of the system known from biological experiments, and infer the unknown parameter values of the model.

In we have studied the abstract properties of this approach and have given a general constraint solving algorithm for branching time logics (CTL) over arbitrary computation domains D. We have shown that the QFCTL constraint satisfiability problem is decidable in finite Kripke structures over an arbitrary computation domain with a decidable language of constraints, i.e. that any constraint solver can be lifted to a temporal logic constraint solver over finite Kripke structures. We have presented a generic QFCTL constraint solver which computes validity domains for the free variables of a formula, in quadratic time in the number of states. We show that when Dis a metric space, this allows us to define a continuous degree of satisfaction for a temporal logic formula in a given Kripke structure, opening up the field of model-checking to optimization, in a very general setting.

In BIOCHAM, our method for solving QFLTL(R) constraints allows us to define a continuous degree of satisfaction of LTL(R) formulae in a given trace, and use it as a fitness function in continuous optimization methods namely the Covariance Matrix Adaptation Evolutionary Strategy CMAESof Nikolaus Hansen from the TAO project-team.in order to find unknown parameter values in a model satisfying a set of biological properties formalized in temporal logic . This approach is heavily used in BIOCHAM for inferring unknown kinetic parameter values, initial concentrations, and/or control parameters from a formalization of the global behavior of the system in temporal logic.

The study of similar metrics and methods for stochastic processes is under investigation.

In , we propose a general definition of robustness that applies to any biological function expressible in temporal logic LTL, and to broad model classes and perturbation types. This measure of the robustness of a given behavior with respect to a given set of perturbations can be estimated with a constraint solving method, implemented in BIOCHAMv2.8, for computing the continuous degree of satisfaction of QFLTL(R) formulae. The applicability and biological relevance of our approach is demonstrated by testing and improving the robustness of the timed behavior of a synthetic transcriptional cascade that could be used as a biological timer for synthetic biology applications. These novel methods are evaluated on models of the cell cycle and of the MAPK signalling cascade. In , they are used to analyze a gene activation cascade in synthetic biology.

Qualitative piecewise-affine differential equation (PADE) models offer an attractive formalism for representing genetic regulatory networks in absence of precise information on parameter values. Predictions on systems behaviors can be obtained in the form of a discrete state transition system simply by using parameter relative order. In this work, we encode in a symbolic way the transition relation of the graph and use symbolic model checkers to automatically select the set of models whose parameter order is consistent with a set of observations. Because in PADE systems the dynamics in a state may be defined with respect to the dynamics in neighbouring states, the main difficulty was to obtain a purely state-based encoding of the transition relation, similar to those used by model checkers. This approach is applied to a synthetic gene network built in E. colifor in vivobenchmarking of reverse-engineering and modeling approaches (IRMA). This work is done in collaboration with Hidde de Jong and Michel Page in the IBIS research group (INRIA Rhône-Alpes/UPMF).

Recent advances in cancer chronotherapy techniques support the evidence that there exist some links between the cell cycle and the circadian clock genes . One purpose for modeling the entrainment in period of the cell cycle by the circadian clock is to better understand how to efficiently target malignant cells depending on the phase of the day. This is at the heart of our participation in the EU STREP project TEMPOin collaboration with the BANG project-team.

In , we show how temporal logic constraints, and the new features of BIOCHAMfor parameter search, can be used to couple dynamical models. This approach is illustrated by a coupled model composed of:

This coupled model allows us to minimize the toxicity of irinotecan on healthy cells, using BIOCHAM's parameter search method applied on the drug administration control law.

In , , purely qualitative models of the cell cycle are shown to provide other useful information, and surprisingly informative results. In , a model of the G1/S transition of the cell cycle is used to find targets for drug resistance.

One important perspective that is common to all this modeling work around the cell cycle is the promise of patient-tailored therapeutics .

In collaboration with Eric Reiter (UMR CNRS-INRA 6175) and Frédérique Clément (SISYPHE) in the framework of the Initiative Action REGATE, we analyse the connectivity and dynamics of the FSH signalling network in its target cells, and embedding the network within a multi-scale representation, from the molecular up to the organic level.

We study the relative contributions of different pathways to the cell response to FSH signal, in order to determine how each pathway controls downstream cascades and which mechanisms are involved in the transition between different cellular states.

A systems biology approach is followed using BIOCHAM's features for rule-based modeling with temporal logic constraints used for searching unknown kinetic parameter values. In , this approach is applied more generally to G protein-coupled receptor signalling which is of great importance in pharmacology.