On restarting automata with window size one

  • Authors:

  • Friedrich Otto

  • Affiliations:

  • Fachbereich Elektrotechnik, Informatik, Universität Kassel, Kassel, Germany

  • Venue:
  • DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
  • Year:
  • 2011

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Abstract

The restarting automaton is a machine model that is motivated by the technique of analysis by reduction from linguistics. It consists of a finite-state control, a flexible tape with end markers and a read/write window of fixed size. This paper begins with a short description of the general model of the restarting automaton and its major variants. In particular, the question for the influence of the size of the read/write window on the expressive power of the various types of restarting automata is addressed. The main part then focuses on the weakest model of the restarting automaton and its variants: the so-called R-automaton with a read/write window of size one (R(1)-automaton for short). It is well-known that R(1)-automata only accept regular languages, but it will be shown that several seemingly rather powerful extensions have just the same expressive power. Accordingly it is of interest to study the descriptional complexity of these types of restarting automata in relation to the R(1)-automata on the one hand and the (deterministic and nondeterministic) finite-state acceptors on the other hand. Then various types of cooperating distributed systems (CD-systems) of deterministic R(1)-automata are presented. If all components of such a system are stateless, then the language accepted by the system has a semi-linear Parikh image, and actually the rational trace languages and the context-free trace languages have been characterized in terms of certain CD-systems of stateless deterministic R(1)-automata. Also for these devices the question for their descriptional complexity will be addressed in short.