Bahareh Badban

Verification of a sliding window protocol in μ CRL and PVS

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, and has been checked in the theorem prover PVS.

Verifying a sliding window protocol in µCRL

We prove the correctness of a sliding window protocol with an arbitrary finite window size n and sequence numbers modulo 2n. We show 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, and was checked with the help of PVS.

Zero, successor and equality in BDDs

Abstract We extend BDDs (binary decision diagrams) for plain propositional logic to the fragment of first order logic, consisting of quantifier free logic with zero, successor and equality. We allow equations with zero and successor in the nodes of a BDD, and call such objects ( 0 , S , = ) -BDDs. We extend the notion of Ordered BDDs in the presence of zero, successor and equality. ( 0 , S , = ) -BDDs can be transformed to equivalent Ordered ( 0 , S , = ) -BDDs by applying a number of rewrite rules until a normal form is reached. All paths in these ordered ( 0 , S , = ) -BDDs represent satisfiable conjunctions. 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

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).