Language recognition by generalized quantum finite automata with unbounded error (abstract & poster)

TL;DR

This paper explores the computational power of generalized one-way quantum finite automata with unbounded error, showing their equivalence to classical probabilistic automata unless the tape head can stay put, which enlarges their language recognition capabilities.

Contribution

It extends previous results by demonstrating that allowing the tape head to stay put increases the class of recognizable languages in quantum finite automata.

Findings

Quantum automata are equivalent to probabilistic automata unless the head can stay put.

Allowing the head to stay put enlarges the class of recognized languages.

The proof of the main theorem was previously presented in an earlier version.

Abstract

In this note, we generalize the results of arXiv:0901.2703v1 We show that all one-way quantum finite automaton (QFA) models that are at least as general as Kondacs-Watrous QFA's are equivalent in power to classical probabilistic finite automata in this setting. Unlike their probabilistic counterparts, allowing the tape head to stay put for some steps during its traversal of the input does enlarge the class of languages recognized by such QFA's with unbounded error. (Note that, the proof of Theorem 1 in the abstract was presented in the previous version (arXiv:0901.2703v1).)