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Complexity of infinite trees

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Automata, Languages and Programming (ICALP 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 154))

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Abstract

Rational schemes interpreted over derived algebras permit a simple algebraic analysis of higher type recursion. Their equivalence is characterized by infinite trees. Measuring their complexity by the size of finite subtrees we obtain a direct proof of the recursion hierarchy.

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References

  1. Bekić, H: Definable operations in general algebras, and the theory of automata and flowcharts, Research Report, IBM Lb., Vienna, 1969

    Google Scholar 

  2. Damm, W.: The IO-and OI-hierarchies Theoret. Comput. Sci. 20 (1982) 2, 95–208

    Google Scholar 

  3. Goguen, J.A. et. al.: Initial algebra semantics and continuous algebras Journal ACM 24 (1977) 1, 68–95

    Google Scholar 

  4. Indermark, K.: On rational definitions in complete algebras without rank Theoret. Comput. Sci. 21 (1982), 281–313

    Google Scholar 

  5. Maibaum, T.S.E.: A generalized approach to formal languages Journal Comp. Syst. Sci. 8 (1974), 409–439

    Google Scholar 

  6. Nivat, M.: Langages algébriques sur le magma libre et sémantique des schémas de programme in: Automata, Languages, and Programming (M. Nivat, ed.) North-Holland P.C. (1972), 293–308

    Google Scholar 

  7. Nivat, M.: On the interpretation of recursion polyadic program schemes-Symposia Matematica 15, Rome 1975, 255–281

    Google Scholar 

  8. Wagner, E.G.: An algebraic theory of recursive definitions and recursive languages — Proc. 3rd ACM Symp. Theory of Computing (1971), 12–23

    Google Scholar 

  9. Wagner, E.G.: Languages for defining sets in arbitrary algebras-Proc. IEEE Conf. SWAT 12 (1971), 192–201

    Google Scholar 

  10. Wand, M.: A concrete approach to abstract recursive definitions-in: Automata, Languages, and Programming (M. Nivat, ed.) North-Holland P.C. (1972), 331–344

    Google Scholar 

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Josep Diaz

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© 1983 Springer-Verlag Berlin Heidelberg

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Indermark, K. (1983). Complexity of infinite trees. In: Diaz, J. (eds) Automata, Languages and Programming. ICALP 1983. Lecture Notes in Computer Science, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036920

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  • DOI: https://doi.org/10.1007/BFb0036920

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12317-0

  • Online ISBN: 978-3-540-40038-7

  • eBook Packages: Springer Book Archive

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