On the Complexity of Symbolic Finite-State Automata

TL;DR

This paper analyzes the computational complexity of operations on symbolic finite-state automata (SFAs), focusing on state count, transition complexity, and predicate size, with special attention to normalized, neat SFAs, and SFAs over monotonic Boolean algebras.

Contribution

It provides a detailed complexity analysis of key procedures on SFAs, considering various special forms and algebraic structures, which was not thoroughly explored before.

Findings

Complexity bounds for intersection and emptiness procedures on SFAs.

Analysis of how normalization and neat forms affect automata complexity.

Insights into the impact of Boolean algebra properties on SFA procedures.

Abstract

We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a state, and the size of the most complex transition predicate. We pay attention to the special forms of SFAs: {normalized SFAs} and {neat SFAs}, as well as to SFAs over a {monotonic} effective Boolean algebra.