Selected publications at LSV

Abstract:
We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader). Processes have unique identifiers (pids) from an infinite, totally ordered domain. An algorithm proceeds in synchronous rounds, each round allowing a process to perform a bounded sequence of actions such as send or receive a pid, store it in some register, and compare register contents wrt. the associated total order. An algorithm is supposed to be correct independently of the number of processes. To specify correctness properties, we introduce a logic that can reason about processes and pids. Referring to leader election, it may say that, at the end of an execution, each process stores the maximum pid in some dedicated register. We show that the verification problem of distributed algorithms can be reduced to satisfiability of a formula from propositional dynamic logic with loop and converse (LCPDL), interpreted over grids over a finite alphabet. This translation is independent of any restriction imposed on the algorithm. However, since the verification problem (and satisfiability for LCPDL) is undecidable, we propose an underapproximation technique, which bounds the number of rounds. This is an appealing approach, as the number of rounds needed by a distributed algorithm to conclude is often exponentially smaller than the number of processes. Using our reduction to LCPDL, we provide an automata-theoretic solution, reducing model checking to emptiness for alternating two-way automata on words. Overall, we show that round-bounded verification of distributed algorithms over rings is PSPACE-complete, provided the number of rounds is given in unary.

@article{ABG-ic17,
   author = {Aiswarya, C. and Bollig, Benedikt and Gastin, Paul},
   journal = {Information and Computation},
   note = {To appear},
   publisher = {Elsevier Science Publishers},
   title = {An Automata-Theoretic Approach to the Verification of Distributed Algorithms},
   year = {2017},
}

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