The Power of Centralized PC Systems of Pushdown Automata

Abstract

In (Csuhaj-Varjú et. al. 2000) parallel communicating systems of pushdown automata (PCPA) were introduced 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 decidable 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 accepting all recursively enumerable languages with non-centralized systems. A similar technique can be applied to centralized PCPA working in non-returning mode improving the previous bound on the number of components to two for accepting all recursively enumerable languages. Finally PCPAs are restricted in such a way that a simulation by multi-head automata is possible.