Two solutions to incorporate zero, successor and equality in binary decision diagrams

In this article we extend BDDs (binary decision diagrams) for plain propositional logic to the fragment of first order logic, consisting of quantifier free logic with equality, zero and successor. We insert equations with zero and successor in BDDs, and call these objects (0,S,=)-BDDs. We extend the notion of {em Ordered} BDDs in the presence of equality, zero and successor. (0,S,=)-BDDs can be transformed to equivalent Ordered (0,S,=)-BDD s by applying a number of rewrite rules. All paths in these extended OBDDs are satisfiable. The major advantage of transforming a formula to an equivalent Ordered (0,S,=)-BDD is that on the latter it can be observed in constant time whether the formula is a tautology, a contradiction, or just satisfiable

Mechanical Verification of a Two-Way Sliding Window Protocol (Full version including proofs)

We prove the correctness of a two-way sliding window protocol with piggybacking, where the acknowledgments of the latest received data are attached to the next data transmitted back into the channel. The window size of both parties are considered to be finite, though they can be of different sizes. We show that this protocol is equivalent (branching bisimilar) to a pair of FIFO queues of finite capacities. The protocol is first modeled and manually proved for its correctness in the process algebraic language of muCRL. We use the theorem prover PVS to formalize and to mechanically prove the correctness. This implies both safety and liveness (under the assumption of fairness)

Verifying a sliding window protocol in mCRL

We prove the correctness of a sliding window protocol with an arbitrary finite window size n and sequence numbers modulo 2n. The correctness consists of showing that the sliding window protocol is branching bisimilar to a queue of capacity 2n. The proof is given entirely on the basis of an axiomatic theory

Model-Based Testing of Safety Critical Real-Time Control Logic Software

The paper presents the experience of the authors in model based testing of safety critical real-time control logic software. It describes specifics of the corresponding industrial settings and discusses technical details of usage of UniTESK model based testing technology in these settings. Finally, we discuss possible future directions of safety critical software development processes and a place of model based testing techniques in it.Comment: In Proceedings MBT 2012, arXiv:1202.582

Distributed Branching Bisimulation Minimization by Inductive Signatures

We present a new distributed algorithm for state space minimization modulo branching bisimulation. Like its predecessor it uses signatures for refinement, but the refinement process and the signatures have been optimized to exploit the fact that the input graph contains no tau-loops. The optimization in the refinement process is meant to reduce both the number of iterations needed and the memory requirements. In the former case we cannot prove that there is an improvement, but our experiments show that in many cases the number of iterations is smaller. In the latter case, we can prove that the worst case memory use of the new algorithm is linear in the size of the state space, whereas the old algorithm has a quadratic upper bound. The paper includes a proof of correctness of the new algorithm and the results of a number of experiments that compare the performance of the old and the new algorithms

Culling predicates for the Verification of Real-Time Models

Abstract. We present an algorithm that generates invariants for real-time models. The algorithm, further, prunes the model by first detecting, and then removing idle discrete transitions (transitions which can never be traversed). We next demonstrate how the generated invariants can be used to create a finite-state abstraction for the original model. To this end, we enhance the idea of predicate abstraction through fully incorporating locations of the concrete timed automata model in the abstraction phase.

Prove with GDPLL-WD : A Complete Proof Procedure for Recursive Data Structures

In this paper we present a terminating, sound and complete algorithm for the verification of recursively defined data structures. To mention some, nat, list and tree data types and also record are commonly used examples of such structures. Recursively defined data structures are of value for use in software verification.Many programming languages support recursive data structures. The best known example on this kind is the LISP programming language, which uses list. Our algorithm, GDPLL-WD, which is an extension of the Davis, Putnam, Logemann and Loveland (DPLL) procedure solves satisfiability problem of recursive data types through providing witness assignments

A term rewriting technique for decision graphs

We provide an automatic verification for a fragment of FOL quantifier-free logic with zero, successor and equality. We use BDD representation of such formulas and to verify them, we first introduce a (complete) term rewrite system to generate an equivalent Ordered (0, S,=)-BDD from any given (0, S,=)-BDD. Having the ordered representation of the BDDs, one can verify the original formula in constant time. Then, to have this transformation automatically, we provide an algorithm which will do the whole process