On-the-fly bisimulation equivalence checking for fresh-register automata

Abstract

Register automata are one of the simplest classes of automata that operate on infinite input alphabets. Each automaton comes equipped with a finite set of registers where it can store data values and compare them with others from the input. Fresh-register automata are additionally able to accept a given data value just if it is fresh in the computation history. One such use for this is representing processes in the π-calculus, where private names need to be fresh with respect to any process context. The bisimilarity problem for fresh-register automata is known to be in NP, when empty registers and duplicate register content are forbidden. In this paper, we investigate on-the-fly algorithms for solving bisimilarity, which attempt to build a bisimulation relation starting from a given input configuration pair. We propose an algorithm that uses concise representations of candidate bisimulation relations based on generating systems. While the algorithm runs in exponential time in the worst case, we demonstrate through a series of benchmarks its efficiency compared to existing algorithms and tools. We moreover define and implement a novel translation from π-calculus processes to fresh-register automata, and use the latter to obtain a (strong early) bisimilarity checking tool for finitary π-calculus processes. Using a series of benchmarks for this, we demonstrate an improvement in run-time compared to another equivalence checker.