The Power of Centralized PC Systems of Pushdown Automata

TL;DR

This paper investigates the computational power of centralized parallel communicating pushdown automata (PCPA), demonstrating their universality and clarifying their relation to other automata models, thus advancing understanding of their capabilities.

Contribution

It proves the universality of centralized PCPA in returning mode and improves the known bounds for generating recursively enumerable languages.

Findings

Centralized PCPA in returning mode are universal.

The paper refutes previous claims about simulation limitations.

It reduces the degree bound for generating all recursively enumerable languages.

Abstract

Parallel communicating systems of pushdown automata (PCPA) were introduced in (Csuhaj-Varj{\'u} et. al. 2000) and in their centralized variants shown to be able to simulate nondeterministic one-way multi-head pushdown automata. A claimed converse simulation for returning mode (Balan 2009) turned out to be incomplete (Otto 2012) and a language was suggested for separating these PCPA of degree two (number of pushdown automata) from nondeterministic one-way two-head pushdown automata. We show that the suggested language can be accepted by the latter computational model. We present a different example over a single letter alphabet indeed ruling out the possibility of a simulation between the models. The open question about the power of centralized PCPA working in returning mode is then settled by showing them to be universal. Since the construction is possible using systems of degree two, this also improves the previous bound three for generating all recursively enumerable languages. Finally PCPAs are restricted in such a way that a simulation by multi-head automata is possible.