On Complementation of Nondeterministic Finite Automata without Full Determinization (Technical Report)

TL;DR

This paper explores alternative methods for complementing nondeterministic finite automata that avoid full determinization, often resulting in smaller automata and more efficient computations.

Contribution

It introduces new constructions based on reverse powerset and NFA structures, providing practical alternatives to classical determinization-based complementation.

Findings

Alternative methods often produce smaller automata

New constructions outperform classical approach in many cases

Experimental results confirm efficiency improvements

Abstract

Complementation of finite automata is a basic operation used in numerous applications. The standard way to complement a nondeterministic finite automaton (NFA) is to transform it into an equivalent deterministic finite automaton (DFA) and complement the DFA. The DFA can, however, be exponentially larger than the corresponding NFA. In this paper, we study several alternative approaches to complementation, which are based either on reverse powerset construction or on two novel constructions that exploit a commonly occurring structure of NFAs. Our experiment on a large data set shows that using a different than the classical approach can in many cases yield significantly smaller complements.