Latvian Quantum Finite State Automata for Unary Languages

TL;DR

This paper introduces Latvian quantum finite automata (LQFAs) capable of recognizing unary regular languages with isolated cut points, combining two modules for finite and periodic parts, with state complexity exponential in the minimal DFA size.

Contribution

The paper presents a novel architecture for LQFAs that efficiently recognizes unary regular languages by combining modules for different language parts.

Findings

LQFAs recognize unary regular languages with isolated cut points.

State complexity depends exponentially on minimal DFA size.

The modular approach effectively discriminates string lengths.

Abstract

We design Latvian quantum finite state automata (LQFAs for short) recognizing unary regular languages with isolated cut point 1/2. From an architectural point of view, we combine two LQFAs recognizing with isolated cut point, respectively, the finite part and the ultimately periodic part of any given unary regular language L. In both modules, we use a component addressed in the literature and here suitably adapted to the unary case, to discriminate strings on the basis of their length. The number of basis states and the isolation around the cut point of the resulting LQFA for L exponentially depends on the size of the minimal deterministic finite state automaton for L.