The Complexity of Satisfiability Checking for Symbolic Finite Automata

TL;DR

This paper analyzes the computational complexity of satisfiability checking for symbolic finite automata, providing tight bounds and extending to linear arithmetic constraints, thereby advancing understanding of automata decision problems.

Contribution

It introduces a decomposition approach for satisfiability problems in symbolic finite automata and derives tight complexity bounds, including for extended classes with arithmetic constraints.

Findings

Complexity bounds for satisfiability checking are established.

Decomposition reduces automata problems to simpler theories.

Extensions with linear arithmetic are also analyzed.

Abstract

We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our decomposition to obtain tight computational complexity bounds on the decision problem for this automata class and an extension that considers linear arithmetic constraints on the underlying effective Boolean algebra.