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One pebble does not suffice to search plane labyrinths

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Fundamentals of Computation Theory (FCT 1981)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 117))

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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]).

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References

  1. H. Antelmann, Über den Platzbedarf von Fallen für endliche Automaten, Diss., Berlin 1980

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  2. H. Antelmann, L. Budach, H.-A. Rollik, On universal traps, EIK 15/3, 123–131, 1979

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  3. G. Asser, Bemerkungen zum Labyrinth-Problem, EIK 13/4–5, 203–216, 1977

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  4. M. Blum, D. Kozen, On the Power of the Compass, 19th IEEE FOCS Conf. 1978, 132–142

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  5. M. Blum, W. Sakoda, On the capability of finite automata in 2 and 3-dimensional space, 18th IEEE FOCS Conf. 1977

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  6. L. Budach, Environments, Labyrinths and Automata, in Lect.Notes in Computer Science 56, 54–64, Springer 1977

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  8. L. Budach, Ch. Meinel, Umwelten und Automaten in Umwelten, Seminarberichte Sekt. Mathematik d. Humboldt-Universität zu Berlin, Nr.23, 1980

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  9. F. Hoffmann, 1-Pebble automata and labyrinths, to appear 1981

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  10. F. Hoffmann, K. Kriegel, Quasiplane labyrinths, to appear 1981

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  11. H. Müller, Automata catching labyrinths with at most three components, EIK 15/1–2, 3–9, 1979

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Author information

Authors and Affiliations

  1. Institut f. Mathematik der Akademie der Wissenschaften der DDR, Mohrenstr. 39, 1080, Berlin, G.D.R.

    Frank Hoffmann

Authors
  1. Frank Hoffmann
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Ferenc Gécseg

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© 1981 Springer-Verlag Berlin Heidelberg

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Hoffmann, F. (1981). One pebble does not suffice to search plane labyrinths. In: Gécseg, F. (eds) Fundamentals of Computation Theory. FCT 1981. Lecture Notes in Computer Science, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10854-8_47

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  • DOI: https://doi.org/10.1007/3-540-10854-8_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10854-2

  • Online ISBN: 978-3-540-38765-7

  • eBook Packages: Springer Book Archive

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