Turing machines, transition systems, and interaction

  • Authors:

  • Dina Q. Goldin;Scott A. Smolka;Paul C. Attie;Elaine L. Sonderegger

  • Affiliations:

  • Computer Science and Engineering Department, University of Connecticut, Storrs, CT;Department of Computer Science, SUNY at Stony Brook, Stony Brook, NY;College of Computer Science, Northeastern University, Boston, MA;Computer Science and Engineering Department, University of Connecticut, Storrs, CT

  • Venue:
  • Information and Computation - Special issue: Commemorating the 50th birthday anniversary of Paris C. Kanellakis
  • Year:
  • 2004

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Abstract

This paper presents persistent Turing machines (PTMs), a new way of interpreting Turing-machine computation, based on dynamic stream semantics. A PTM is a Turing machine that performs an infinite sequence of "normal" Turing machine computations, where each such computation starts when the PTM reads an input from its input tape and ends when the PTM produces an output on its output tape. The PTM has an additional worktape, which retains its content from one computation to the next; this is what we mean by persistence. A number of results are presented for this model, including a proof that the class of PTMs is isomorphic to a general class of effective transition systems called interactive transition systems; and a proof that PTMs without persistence (amnesic PTMs) are less expressive than PTMs. As an analogue of the Church-Turing hypothesis which relates Turing machines to algorithmic computation, it is hypothesized that PTMs capture the intuitive notion of sequential interactive computation.