On the power of bounded concurrency I: finite automata

  • Authors:
  • Doron Drusinsky;David Harel

  • Affiliations:
  • Weizmann Institute of Science, Rehovot, Israel;Weizmann Institute of Science, Rehovot, Israel

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1994

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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 &Sgr;* and &Sgr;&ohgr;, establishing that:(1) Each of the three features represents an exponential saving in succinctness of the representation, in a manner that is independent of the other two and additive with respect to them.(2) Of the three, bounded concurrency is the strongest, representing a similar exponential saving even when substituted for each of the others.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.