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International Workshop on Computer Science Logic

CSL 1991: Computer Science Logic pp 367–381Cite as

Control of ω-automata, Church's problem, and the emptiness problem for tree ω-automata

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 626))

Abstract

Church's problem and the emptiness problem for Rabin automata on infinite trees, which represent basic paradigms for program synthesis and logical decision procedures, are formulated as a control problem for automata on infinite strings. The alphabet of an automaton is interpreted not as a set of input symbols giving rise to state transitions but rather as a set of output symbols generated during spontaneous state transitions; in addition, it is assumed that automata can be “controlled” through the imposition of certain allowable restrictions on the set of symbols that may be generated at a given instant. The problems in question are then recast as that of deciding membership in a deterministic Rabin automaton's controllability subset — the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition. The new formulation leads to a direct, efficient and natural solution based on a fixpoint representation of the controllability subset. This approach combines advantages of earlier solutions and admits useful extensions incorporating liveness assumptions.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant number OGP0007399, a Postgraduate Scholarship and a Postdoctoral Fellowship, and through S.T.A.R. Awards and Open Fellowships from the University of Toronto and College Fellowships from Trinity College in the University of Toronto. The report was prepared while the first author was visiting the Department of Engineering of the University of Cambridge.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, 94720, Berkeley, CA, USA

    J. G. Thistle (Visitor)

  2. Systems Control Group Department of Electrical Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    W. M. Wonham

Authors
  1. J. G. Thistle
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  2. W. M. Wonham
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Editor information

Egon Börger Gerhard Jäger Hans Kleine Büning Michael M. Richter

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© 1992 Springer-Verlag Berlin Heidelberg

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Thistle, J.G., Wonham, W.M. (1992). Control of ω-automata, Church's problem, and the emptiness problem for tree ω-automata. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023782

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  • DOI: https://doi.org/10.1007/BFb0023782

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55789-0

  • Online ISBN: 978-3-540-47285-8

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