On the representability of relations by deterministic and nondeterministic multi-tape automata

  • Peter H. Starke
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 32)


The paper investigates the behavior of multi-tape automata, i.e. accepting devices the input of which consists of a certain number n of tapes with a one-way read-only head on each of them. In each step depending on the current state some of these heads are activated and read one symbol from the corresponding tape. Depending on the symbols read and on the numbers of the tapes from which they are read the current state is changed in a deterministic respectively nondeterministic way. The behavior of the automaton is the set of all n-tuples of words which can be read completely by the automaton if it is started in an initial state, and which can transit it to a designated final state. Thereby we make no use of endmarkers. In the first two sections we characterize the behavior of infinite and finite, deterministic and nondeterministic multi-tape automata, in the last section we apply the results to a so far unsolved problem from the theory of nondeterministic generalized sequential machines.


Binary Relation Regular Expression Input Tape Deterministic Automaton Output Tape 
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Bibliographical remarks

Notation and terminology are used as in

  1. Starke, P. H.: Abstract Automata. North-Holland Publ. Co., Amsterdam 1972.Google Scholar

Papers on multi-tape automata

  1. Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. & Dev. 3 (1959) 114–125Google Scholar
  2. Rosenberg, A.L.: On n-tape finite state acceptors. IEEE Conf. Rec. Switch. Circ. Th. & Log. Design (5th Ann. Symp.) New York 1964.Google Scholar
  3. Fischer, P.C., Rosenberg, A.L.: Multi-tape one-way nonwriting automata. J. Computer & Systems Sci. 2 (1968).Google Scholar
  4. Makarevski, A., Stockaja, E: Predstavimost v determinirovannyh mnogolentočnyh avtomatah. Kibernetika (Kiev) 4 1969Google Scholar
  5. Stockaja, E.: O mnogolentočnyh avtomatov bes konečnyh markerov. Avtomatika i Telemehanika 9 (1971) 105–110.Google Scholar

Papers on nondeterministic generalized sequential machines

  1. Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM J.Res.& Dev. 9 (1965) 47–68.Google Scholar
  2. Griffiths, T.V.: The unsolvability of the equivalence problem for e-free nondeterministic generalized machines. J. ACM 15 (1968) 3, 409–413.CrossRefGoogle Scholar
  3. Grabowski, J.: Anwendung topologischer Methoden in der Theorie der ND-Automaten. Elektron. Inf.-verarb. u. Kybernetik 9 (1973) 10, 615–633.Google Scholar

The proofs of the theorems in the present paper are found in

  1. Starke, P.H.: Über die Darstellbarkeit von Relationen in Mehrbandautomaten. To appear in: Elektron. Inf.-verarb. u. Kybernetik.Google Scholar
  2. Starke, P.H.: Entscheidungsprobleme für autonome Mehrbandautomaten. To appear in: Z. f. Math. Logik u. Grundl. d. Math. Google Scholar
  3. Starke, P.H.: Über eine Anwendung der Theorie der Mehrbandautomaten in der Theorie der asynchronen ND-Automaten. In preparation.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Peter H. Starke
    • 1
  1. 1.Sektion Mathematik der HumboldtUniversität zu BerlinBerlin

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