Forward Invariant Cuts to Simplify Proofs of Safety

The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid sys- tems; however, state-of-the-art theorem provers require ex- tensive manual intervention. Furthermore, there is often a gap between the type of assistance that a theorem prover requires to make progress on a proof task and the assis- tance that a system designer is able to provide. This paper presents an extension to KeYmaera, a deductive verification tool for differential dynamic logic; the new technique allows local reasoning using system designer intuition about per- formance within particular modes as part of a proof task. Our approach allows the theorem prover to leverage for- ward invariants, discovered using numerical techniques, as part of a proof of safety. We introduce a new inference rule into the proof calculus of KeYmaera, the forward invariant cut rule, and we present a methodology to discover useful forward invariants, which are then used with the new cut rule to complete verification tasks. We demonstrate how our new approach can be used to complete verification tasks that lie out of the reach of existing deductive approaches us- ing several examples, including one involving an automotive powertrain control system.Comment: Extended version of EMSOFT pape

Foliations for solving equations in groups: free, virtually free, and hyperbolic groups

We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm for solving equations and inequations in hyperbolic groups (maybe with torsion). Additionnally, we can deal with quasi-isometrically embeddable rational constraints.Comment: 70 pages, 7 figures, revised version. To appear in Journal of Topolog

Symbolic and analytic techniques for resource analysis of Java bytecode

Recent work in resource analysis has translated the idea of amortised resource analysis to imperative languages using a program logic that allows mixing of assertions about heap shapes, in the tradition of separation logic, and assertions about consumable resources. Separately, polyhedral methods have been used to calculate bounds on numbers of iterations in loop-based programs. We are attempting to combine these ideas to deal with Java programs involving both data structures and loops, focusing on the bytecode level rather than on source code

A framework for proof certificates in finite state exploration

Model checkers use automated state exploration in order to prove various properties such as reachability, non-reachability, and bisimulation over state transition systems. While model checkers have proved valuable for locating errors in computer models and specifications, they can also be used to prove properties that might be consumed by other computational logic systems, such as theorem provers. In such a situation, a prover must be able to trust that the model checker is correct. Instead of attempting to prove the correctness of a model checker, we ask that it outputs its "proof evidence" as a formally defined document--a proof certificate--and that this document is checked by a trusted proof checker. We describe a framework for defining and checking proof certificates for a range of model checking problems. The core of this framework is a (focused) proof system that is augmented with premises that involve "clerk and expert" predicates. This framework is designed so that soundness can be guaranteed independently of any concerns for the correctness of the clerk and expert specifications. To illustrate the flexibility of this framework, we define and formally check proof certificates for reachability and non-reachability in graphs, as well as bisimulation and non-bisimulation for labeled transition systems. Finally, we describe briefly a reference checker that we have implemented for this framework.Comment: In Proceedings PxTP 2015, arXiv:1507.0837