Section: Overall Objectives

Overall Objectives

The VeriDis project team includes members of the MOSEL group at LORIA, the computer science laboratory in Nancy, and members of the research group Automation of Logic at Max-Planck-Institut für Informatik in Saarbrücken. It is headed by Stephan Merz and Christoph Weidenbach. VeriDis was created in 2010 as a local research group of Inria Nancy – Grand Est and has been an Inria project team since July 2012.

The objectives of VeriDis are to contribute to advances in verification techniques, including automated and interactive theorem proving, and to make them available for the development and analysis of concurrent and distributed algorithms and systems, based on mathematically precise and practically applicable development methods. The techniques that we develop are intended to assist designers of algorithms and systems in carrying out formally proved developments, where proofs of relevant properties, as well as bugs, can be found with a high degree of automation.

Within this context, we work on techniques for automated theorem proving for expressive languages based on first-order logic, with support for theories (fragments of arithmetic, set theory etc.) that are relevant for specifying algorithms and systems. Ideally, systems and their properties would be specified in high-level, expressive languages, errors in specifications would be discovered automatically, and finally, full verification could also be performed completely automatically. Due to the fundamental undecidability of the problem, this cannot be achieved in general. Nevertheless, we have observed important advances in automated deduction in recent years, to which we have contributed. These advances suggest that a substantially higher degree of automation can be achieved over what is available in today's tools supporting deductive verification. Our techniques are developed within SMT (satisfiability modulo theories) solving and superposition reasoning, the two main frameworks of contemporary automated reasoning that have complementary strengths and weaknesses, and we are interested in making them converge when appropriate. Techniques developed within the symbolic computation domain, such as algorithms for quantifier elimination for appropriate theories, are also relevant, and we are working on integrating them into our portfolio of techniques. In order to handle expressive input languages, we are working on techniques that encompass tractable fragments of higher-order logic, for example for specifying inductive or co-inductive data types, for automating proofs by induction, or for handling collections defined through a characteristic predicate.

Since full automatic verification remains elusive, another line of our research targets interactive proof platforms. We intend these platforms to benefit from our work on automated deduction by incorporating powerful automated backends and thus raise the degree of automation beyond what current proof assistants can offer. Since most conjectures stated by users are initially wrong (due to type errors, omitted hypotheses or overlooked border cases), it is also important that proof assistants be able to detect and explain such errors rather than letting users waste considerable time in futile proof attempts. Moreover, increased automation must not come at the expense of trustworthiness: skeptical proof assistants expect to be given an explanation of the proof found by the backend prover that they can certify.

Our methodological and foundational research is accompanied by the development of efficient software tools, several of which go beyond pure research prototypes: they have been used by others, have been integrated in proof platforms developed by other groups, and participate in international competitions. We also validate our work on proof techniques by applying them to the formal development of algorithms and systems. We mainly target high-level descriptions of concurrent and distributed algorithms and systems. This class of algorithms is by now ubiquitous, ranging from multi- and many-core algorithms to large networks and cloud computing, and their formal verification is notoriously difficult. Targeting high levels of abstraction allows the designs of such systems to be verified before an actual implementation has been developed, contributing to reducing the costs of formal verification. The potential of distributed systems for increased resilience to component failures makes them attractive in many contexts, but also makes formal verification even more important and challenging. Our work in this area aims at identifying classes of algorithms and systems for which we can provide guidelines and identify patterns of formal development that makes verification less an art and more an engineering discipline. We mainly target components of operating systems, distributed and cloud services, and networks of computers or mobile devices.

Beyond formal verification, we pursue applications of some of the symbolic techniques that we are developing in other domains. We have observed encouraging success in using techniques of symbolic computation for the qualitative analysis of biological and chemical regulation networks described by systems of ordinary differential equations that were previously only accessible to large-scale simulation. This work is being pursued within a large-scale interdisciplinary collaboration. It aims for our work grounded in verification having an impact on the sciences, beyond engineering, which will feed back into our core formal methods community.