On the power of bounded concurrency I

Abstract

We investigate the descriptive succinctness of three fundamental notions for modeling concurrency: nondeterminism and pure parallelism, the two facets of alternation, and bounded cooperative concurrency , whereby a system configuration consists of a bounded number of cooperating states. Our results are couched in the general framework of finite-state automata, but hold for appropriate versions of most concurrent models of computation, such as Petri nets, statecharts or finite-state versions of concurrent programming languages. We exhibit exhaustive sets of upper and lower bounds on the relative succinctness of these features over Σ * and Σ ω , establishing that: For example, we prove exponential upper and lower bounds on the simulation of deterministic concurrent automata by AFAs, and triple-exponential bounds on the simulation of alternating concurrent automata by DFAs.