Repetitive Finite Automata With Translucent Letters

TL;DR

This paper introduces repetitive finite automata with translucent letters, extending existing models to allow state changes at tape end, thereby increasing expressiveness in the deterministic case while maintaining equivalence in the nondeterministic case.

Contribution

It proposes a new automaton model that enhances the capabilities of existing translucent letter automata by enabling state changes at tape end, bridging gaps between known automata classes.

Findings

Deterministic version is more expressive than DFAwtl.

Nondeterministic version is equivalent to NFAwtl.

New model fills expressive gaps between existing automata classes.

Abstract

Here we propose an extension of the (deterministic and the nondeterministic) finite automaton with translucent letters (DFAwtl and NFAwtl), which lies between these automata and their non-returning variants (that is, the nr-DFAwtl and the nr-NFAwtl). This new model works like a DFAwtl or an NFAwtl, but on seeing the end-of-tape marker, it may change its internal state and continue with its computation instead of just ending it, accepting or rejecting. This new type of automaton is called a repetitive deterministic or nondeterministic finite automaton with translucent letters (RDFAwtl or RNFAwtl). In the deterministic case, the new model is strictly more expressive than the DFAwtl, but less expressive than the nr-DFAwtl, while in the nondeterministic case, the new model is equivalent to the NFAwtl.