(k,l)-Unambiguity and Quasi-Deterministic Structures

TL;DR

This paper introduces $(k,l)$-unambiguous automata, a class with favorable properties enabling the construction of smaller quasi-deterministic structures that improve membership testing efficiency over traditional automata.

Contribution

It defines and explores $(k,l)$-unambiguous automata, showing how to compute smaller quasi-deterministic structures with enhanced computational advantages.

Findings

Quasi-deterministic structures are smaller than equivalent DFAs.

These structures enable faster membership testing than NFAs.

The family of $(k,l)$-unambiguous automata generalizes deterministic $k$-lookahead automata.

Abstract

We focus on the family of $(k,l)$-unambiguous automata that encompasses the one of deterministic $k$-lookahead automata introduced by Han and Wood. We show that this family presents nice theoretical properties that allow us to compute quasi-deterministic structures. These structures are smaller than DFAs and can be used to solve the membership problem faster than NFAs.