Measuring Communication in Parallel Communicating Finite Automata

TL;DR

This paper investigates the computational power and decidability of deterministic finite automata systems with restricted communication, revealing an infinite hierarchy of language families based on communication bounds and showing some properties are undecidable.

Contribution

It introduces a hierarchy of language families based on communication bounds in parallel communicating finite automata and analyzes their decidability properties.

Findings

Existence of an infinite hierarchy of language families

Certain properties are undecidable for these automata systems

Communication bounds influence computational power

Abstract

Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of returning centralized systems, when the number of necessary communications during the computations of the system is bounded by a function depending on the length of the input. It is proved that an infinite hierarchy of language families exists, depending on the number of messages sent during their most economical recognitions. Moreover, several properties are shown to be not semi-decidable for the systems under consideration.