On the power of bounded concurrency II: The pushdown automata level

Abstract

This is the second in a series of papers on the inherent power of bounded cooperative concurrency, whereby an automaton can be in some bounded number of states that cooperate in accepting the input. In this paper we deal with the level of pushdown automata. We are interested in differencies in power of expression and in discrepencies in succinctness between variants of pda's that incorporate nondeterminism, pure parallelism and bounded cooperative concurrency. In particular, our results provide further evidence for the general observation that the latter feature provides inherent exponential power, in both upper and lower bound senses, regardless of whether or not the two former features are also present. While we use the language of statecharts to capture these features, our results are extremely robust, and hold also for bounded versions of virtually all other concurrent languages.