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A hierarchy of sets of infinite trees

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Theoretical Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 145))

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Abstract

A hierarchy of sets of infinite (valued) trees is introduced which has no counterpart in the theory of sets of infinite strings ("ω-languages"). As a consequence we obtain that for sets of infinite trees an analogue of McNaughton's fundamental theorem on ω-languages does not hold.

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References

  1. J.R. Büchi, On a decision method in restricted second-order arithmetic, Proc. Int. Congr. Logic, Method., Philos. Sci. 1960, Stanford Univ. Press 1962, pp. 1–11.

    Google Scholar 

  2. J. Doner, Tree acceptors and some of their applications, JCSS 4 (1970), 406–451.

    Google Scholar 

  3. R. McNaughton, Testing and generating infinite sequences by a finite automation, Inf. Contr. 9 (1966), 521–530.

    Google Scholar 

  4. M. Nivat, D. Perrin, Ensembles reconnaissables de mots biinfinis, Proc. Ann. ACM Symp. on the Theory of Comp. 1982, 47–59.

    Google Scholar 

  5. M.O. Rabin, Automata on infinite objects and Church's problem, Regional Conf. Ser. in Math. No. 13, Amer. Math. Soc. 1972.

    Google Scholar 

  6. M.O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc. 141 (1969), 1–35.

    Google Scholar 

  7. M.O. Rabin, Weakly definable relations and special automata, Math. Logic and Found. of Set Theory (Ed. Bar-Hillel), North-Holland, Amsterdam 1970, pp. 1–23.

    Google Scholar 

  8. H. Rogers, Theory of recursive functions and effective computability, Mc Graw Hill, New York 1967.

    Google Scholar 

  9. J.W. Thatcher, J.B. Wright, Generalized finite automata theory with an application to a decision problem of second-order logic, Math. Systems Theory 2 (1968), 57–81.

    Google Scholar 

  10. W. Thomas, A combinatorial approach to the theory of ω-automata, Inf. Contr. 48 (1981), 261–283.

    Google Scholar 

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Authors and Affiliations

  1. Lehrstuhl für Informatik II, Büchel 29/31, D-5100, Aachen

    Wolfgang Thomas

Authors
  1. Wolfgang Thomas
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Editor information

Armin B. Cremers Hans-Peter Kriegel

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© 1982 Springer-Verlag Berlin Heidelberg

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Thomas, W. (1982). A hierarchy of sets of infinite trees. In: Cremers, A.B., Kriegel, HP. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036493

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  • DOI: https://doi.org/10.1007/BFb0036493

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11973-9

  • Online ISBN: 978-3-540-39421-1

  • eBook Packages: Springer Book Archive

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