Reactive turing machines

  • Authors:
  • Jos C. M. Baeten;Bas Luttik;Paul van Tilburg

  • Affiliations:
  • Eindhoven University of Technology;Eindhoven University of Technology;Eindhoven University of Technology

  • Venue:
  • FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
  • Year:
  • 2011
  • Turing meets milner

    CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory

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Abstract

We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction. We show that every effective transition system is simulated modulo branching bisimilarity by an RTM, and that every computable transition system with a bounded branching degree is simulated modulo divergencepreserving branching bisimilarity. We conclude from these results that the parallel composition of (communicating) RTMs can be simulated by a single RTM. We prove that there exist universal RTMs modulo branching bisimilarity, but these essentially employ divergence to be able to simulate an RTM of arbitrary branching degree. We also prove that modulo divergence-preserving branching bisimilarity there are RTMs that are universal up to their own branching degree. Finally, we establish a correspondence between RTMs and the process theory TCPτ.