Approximate Automata for Omega-Regular Languages

TL;DR

This paper introduces methods for approximating omega-automata, which recognize infinite words, within specific classes to balance complexity and precision, aiding verification and synthesis of reactive systems.

Contribution

It develops techniques for approximating omega-automata with simpler acceptance conditions while controlling language precision, and analyzes the state complexity of these approximations.

Findings

Provides constructions for automata approximation within various classes.

Analyzes the state complexity of different approximation methods.

Enables more efficient automata-based verification and synthesis.

Abstract

Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic omega-automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism. In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition.