Simplifying Nondeterministic Finite Cover Automata

TL;DR

This paper explores the complexity of minimizing nondeterministic finite cover automata and proposes methods to simplify them, highlighting their potential for more compact representations of finite languages.

Contribution

It systematically studies the minimization complexity of NFCAs and adapts existing methods to simplify these automata, extending the understanding of their computational properties.

Findings

Minimization of NFCAs can be as hard as NFA minimization.

Methods for reducing NFA and DFA sizes can be adapted for NFCAs.

Simplification techniques improve automata compactness for finite language representation.

Abstract

The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA '98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language, Nondeterministic Finite Automata (NFA) may significantly reduce the number of states used. The combined power of the succinctness of the representation of finite languages using both cover languages and non-determinism has been suggested, but never systematically studied. In the present paper, for nondeterministic finite cover automata (NFCA) and l-nondeterministic finite cover automaton (l-NFCA), we show that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets. Moreover, we show how we can adapt the methods used to reduce, or minimize the size of NFAs/DFCAs/l-DFCAs, for simplifying NFCAs/l-NFCAs.