Simulation Algorithms for Symbolic Automata (Technical Report)

TL;DR

This paper explores efficient algorithms for computing simulation relations over symbolic finite automata, proposing advanced methods to mitigate exponential transition growth and evaluating their practical performance.

Contribution

It introduces two novel algorithms for symbolic automata simulation, improving efficiency by local mintermisation and a new symbolic transition handling approach.

Findings

Local mintermisation reduces exponential blowup.

New symbolic method outperforms counting-based techniques.

All algorithms show practical merits depending on context.

Abstract

We investigate means of efficient computation of the simulation relation over symbolic finite automata (SFAs), i.e., finite automata with transitions labeled by predicates over alphabet symbols. In one approach, we build on the algorithm by Ilie, Navaro, and Yu proposed originally for classical finite automata, modifying it using the so-called mintermisation of the transition predicates. This solution, however, generates all Boolean combinations of the predicates, which easily causes an exponential blowup in the number of transitions. Therefore, we propose two more advanced solutions. The first one still applies mintermisation but in a local way, mitigating the size of the exponential blowup. The other one focuses on a novel symbolic way of dealing with transitions, for which we need to sacrifice the counting technique of the original algorithm (counting is used to decrease the dependency of the running time on the number of transitions from quadratic to linear). We perform a thorough experimental evaluation of all the algorithms, together with several further alternatives, showing that all of them have their merits in practice, but with the clear indication that in most of the cases, efficient treatment of symbolic transitions is more beneficial than counting.