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A hierarchy theorem for the μ-calculus

  • Session 2: Fairness, Domination, and the μ-Calculus
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Automata, Languages and Programming (ICALP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1099))

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Abstract

We consider the positive mu-calculus with successors PμS, namely a variant of Kozen's modal mu-calculus L μ [9] where negation is suppressed and where the basic modalities are a sequence of successor operators l 1,..., l n,4. In particular we are interested in the sublanguages of PμS determined by the value of the Emerson-Lei alternation depth

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References

  1. Bradfield, J. C.: The modal mu-calculus alternation hierarchy is strict. Manuscript, 1995.

    Google Scholar 

  2. Clarke, E. M., Emerson, E. A.: Design and synthesis of synchronization skeletons using Branching Time Temporal Logic. Proc. Workshop on Logics of Programs, Lecture Notes in Computer Science 131, 1981, pp. 52–71.

    Google Scholar 

  3. Emerson, E. A.: Temporal and Modal Logic. In Handbook of Theoretical Computer Science vol. B (J. van Leeuwen, ed.), North-Holland, 1990, pp. 995–1072.

    Google Scholar 

  4. Emerson, E. A., Halpern, J.: “Sometimes” and “Not never” revisited: on Branching versus Linear Time Temporal Logic. Journal of the ACM 33, 1986, pp. 151–178.

    Article  Google Scholar 

  5. Emerson, E. A., Jutla, C.: The complexity of tree automata and logics of programs. Extended version from FOCS '88, 1988.

    Google Scholar 

  6. Emerson, E. A., Lei, C. L.: Efficient model checking in fragments of the propositional mu-calculus. Proc. First IEEE Symp. on Logic in Computer Science, 1986, pp. 267–278.

    Google Scholar 

  7. Emerson, E. A., Streett, R.: An automata-theoretic decision procedure for the propositional mu-calculus. Information and Computation 81, 3, 1989, pp. 249–264.

    Article  Google Scholar 

  8. Fischer, M., Ladner, R.: Propositional Dynamic Logic of regular programs. JCSS 18, 1979, pp. 194–211.

    Google Scholar 

  9. Kozen, D.: Results on the propositional mu-calculus. Theoretical Computer Science 27, 1983, pp. 333–354.

    Article  Google Scholar 

  10. Kaivola, R.: On modal mu-calculus and Büchi tree automata. Inf. Proc. Letters 54, 1995, pp. 17–22.

    Article  Google Scholar 

  11. Niwiński, D.: On fixed point clones. Proc. 13th ICALP, Lecture Notes in Computer Science 226, 1986, pp. 464–473.

    Google Scholar 

  12. Pnueli, A.: The temporal logic of programs. 18th IEEE Symp. on Foundations of Computer Science, 1977, pp. 46–57.

    Google Scholar 

  13. Pratt, V.: A decidable mu-calculus. 22nd IEEE Symp. on Foundations of Computer Science, 1981, pp. 421–427.

    Google Scholar 

  14. Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 55, 1955, pp. 285–309.

    Google Scholar 

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Friedhelm Meyer Burkhard Monien

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© 1996 Springer-Verlag Berlin Heidelberg

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Lenzi, G. (1996). A hierarchy theorem for the μ-calculus. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_119

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  • DOI: https://doi.org/10.1007/3-540-61440-0_119

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61440-1

  • Online ISBN: 978-3-540-68580-7

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