Real-time reversible iterative arrays

  • Authors:

  • Martin Kutrib;Andreas Malcher

  • Affiliations:

  • Institut für Informatik, Universität Giessen, Giessen, Germany;Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt am Main, Germany

  • Venue:
  • FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
  • Year:
  • 2007

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Abstract

Iterative arrays are one-dimensional arrays of interconnected interacting finite automata. The cell at the origin is equipped with a oneway read-only input tape. We investigate iterative arrays as acceptors for formal languages. In particular, we consider real-time devices which are reversible on the core of computation, i.e., from initial configuration to the configuration given by the time complexity. This property is called real-time reversibility. It is shown that real-time reversible iterative arrays can simulate restricted variants of stacks and queues. It turns out that real-time reversible iterative arrays are strictly weaker than realtime reversible cellular automata. On the other hand, a nonsemilinear language is accepted. We show that real-time reversibility itself is not even semidecidable, which extends the undecidability for cellular automata and contrasts the general case, where reversibility is decidable for one-dimensional devices. Moreover, we prove the non-semidecidability of several other properties. The closure under Boolean operations is also derived.