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One pebble does not suffice to search plane labyrinths

  • Frank Hoffmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 117)

Abstract

In 1975 L. Budach proved in a groundbreaking paper ([7]) that there is no finite automaton which is able to search (to master) all finite (cofinite) plane labyrinths. On the other side we have a result of M. Blum, D. Kozen (1978, [4]) saying that the search can be implemented with just two pebbles. The aim of our paper is to show that one pebble does not suffice, answering a question of Blum,Kozen. Furthermore we present a new construction for universal traps (see H.Antelmann, L.Budach, H.-A.Rollik 1979, [2]).

Keywords

Finite Automaton Maximal Curvature Finite Deterministic Automaton Search Plane Infinite Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    H. Antelmann, Über den Platzbedarf von Fallen für endliche Automaten, Diss., Berlin 1980Google Scholar
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    H. Antelmann, L. Budach, H.-A. Rollik, On universal traps, EIK 15/3, 123–131, 1979Google Scholar
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    G. Asser, Bemerkungen zum Labyrinth-Problem, EIK 13/4–5, 203–216, 1977Google Scholar
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    M. Blum, D. Kozen, On the Power of the Compass, 19th IEEE FOCS Conf. 1978, 132–142Google Scholar
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    M. Blum, W. Sakoda, On the capability of finite automata in 2 and 3-dimensional space, 18th IEEE FOCS Conf. 1977Google Scholar
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    L. Budach, Environments, Labyrinths and Automata, in Lect.Notes in Computer Science 56, 54–64, Springer 1977Google Scholar
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    L. Budach, Automata and Labyrinths, Math. Nachrichten 86, 195–282, 1978Google Scholar
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    L. Budach, Ch. Meinel, Umwelten und Automaten in Umwelten, Seminarberichte Sekt. Mathematik d. Humboldt-Universität zu Berlin, Nr.23, 1980Google Scholar
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    F. Hoffmann, 1-Pebble automata and labyrinths, to appear 1981Google Scholar
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    F. Hoffmann, K. Kriegel, Quasiplane labyrinths, to appear 1981Google Scholar
  11. [11]
    H. Müller, Automata catching labyrinths with at most three components, EIK 15/1–2, 3–9, 1979Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Frank Hoffmann
    • 1
  1. 1.Institut f. Mathematik der Akademie der Wissenschaften der DDRBerlinG.D.R.

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