Turing machines, transition systems, and interaction

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

Research output: Contribution to journalArticle

66 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)101-128
Number of pages28
JournalInformation and Computation
Volume194
Issue number2 SPEC. ISS.
DOIs
Publication statusPublished - Nov 1 2004
Externally publishedYes

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Keywords

  • Interactive transition system
  • Models of interactive computation
  • Persistent stream language
  • Persistent Turing machine
  • Sequential interactive computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

Goldin, D. Q., Smolka, S. A., Attie, P. C., & Sonderegger, E. L. (2004). Turing machines, transition systems, and interaction. Information and Computation, 194(2 SPEC. ISS.), 101-128. https://doi.org/10.1016/j.ic.2004.07.002