Combining Rewriting with Noetherian Induction to Reason on Non-orientable Equalities
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Integrating implicit induction proofs into certified proof environments
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Automated certification of implicit induction proofs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Applying a theorem prover to the verification of optimistic replication algorithms
Rewriting Computation and Proof
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The Available Bit Rate protocol (ABR) for ATM networks is well adapted to data traffic by providing minimum rate guarantees and low cell loss to the ABR source end system. An ABR conformance algorithm for controlling the source rates through an interface has been defined by ATM Forum, and a more efficient version of it has been designed by Rabadan and Klay. We present in this work the first complete mechanical verification of the equivalence between these two algorithms. The proof is involved and has been supported by the PVS theorem prover. It has required many lemmas, case analysis, and induction reasoning for the manipulation of unbounded scheduling lists. Some ABR conformance protocols have been verified in previous works. However, these protocols are approximations of the one we consider here. In particular, the algorithms assume a bound on the number of rates to be scheduled.