Message complexity for unary multiautomata systems

TL;DR

This paper investigates unary multiautomata systems with broadcasting states, demonstrating that bounded message complexity leads to recognition of only regular languages.

Contribution

It introduces a model of automata systems with broadcasting and proves bounded message complexity restricts their language recognition to regular languages.

Findings

Bounded message complexity implies regular language recognition

Broadcasting automata can simulate regular automata under certain conditions

Unbounded message complexity can lead to non-regular language recognition

Abstract

Finitely many two-way automata work independently and synchronously on a unary input. Some of their states are broadcasting, i.e., dispatched to all other automata. At each step of the computation, each automaton changes state and moves right, left or stay in place according to the current state and the possible messages dispatched. The input is recognized if the following occurs: starting from the initial configuration (the heads of all automata are positioned to the left end of the tape) one automaton reaches a final state when its head is positioned to the right end of the tape. We show that if the number of messages sent during the computation is bounded by some integer which is independent of the length of the input, then the language recognized is regular,