Non-Returning Finite Automata With Translucent Letters

TL;DR

This paper introduces a new automaton model called non-returning finite automaton with translucent letters (nrNFAwtl), which extends previous models by not returning to the tape's start after reading a letter, and explores its expressive power and properties.

Contribution

It defines the non-returning finite automaton with translucent letters, analyzes its expressive capacity, and compares it to existing models, including deterministic variants.

Findings

nrNFAwtl is more expressive than NFAwtl.

The paper studies closure properties of language classes.

Decision problems for nrNFAwtl are examined.

Abstract

Here we propose a variant of the nondeterministic finite automaton with translucent letters (NFAwtl) which, after reading and deleting a letter, does not return to the left end of its tape, but rather continues from the position of the letter just deleted. When the end-of-tape marker is reached, our automaton can decide whether to accept, to reject, or to continue, which means that it again reads the remaining tape contents from the beginning. This type of automaton, called a non-returning finite automaton with translucent letters or an nrNFAwtl, is strictly more expressive than the NFAwtl. We study the expressive capacity of this type of automaton and that of its deterministic variant. Also we are interested in closure properties of the resulting classes of languages and in decision problems.