On Repetitive Finite Automata with Translucent Words

TL;DR

This paper introduces repetitive variants of finite automata with translucent words, demonstrating that these variants significantly increase the automata's expressive power beyond semi-linear languages.

Contribution

It defines and analyzes repetitive DFAwtw and NFAwtw, showing their enhanced expressive capabilities compared to standard automata.

Findings

Repetitive DFAwtw can accept non semi-linear languages.

Repetitive NFAwtw can continue computation after seeing the sentinel.

Repetitive automata expand the class of recognizable languages.

Abstract

We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting or rejecting, but it may change into another state and continue with its computation. We establish that a repetitive DFAwtw already accepts a language that is not even semi-linear, which shows that the property of being repetitive increases the expressive capacity of the DFAwtw and the NFAwtw considerably.