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Implementing WS1S via finite automata: Performance issues

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Book cover Automata Implementation (WIA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1436))

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Abstract

A previous paper described the implementation of the decision procedure for the weak second-order theory of one successor (WSlS), especially those parts critical to its overall performance. This paper explores further some of the topics described in that paper, including minimization, representation of automata, subset construction, and other aspects of the decision procedure. New data will be presented to illustrate how various approaches to the above procedure affect the algorithm's performance.

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References

  1. J. R. Büchi. Weak second order arithmetic and finite automata. Zeitscrift für mathematische Logic and Grundlagen der Mathematik, 6:66–92, 1960.

    Google Scholar 

  2. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. The MIT Press, 1990.

    Google Scholar 

  3. J. Glenn and W. Gasarch. Implementing Ws1s via finite automata. In Proceedings of the First International Workshop on Implementing Automata, pages 87–98, August 1996.

    Google Scholar 

  4. J. E. Hopcroft. An n log n algorithm for minimizing the states in a finite automaton. In Z. Kohavi, editor, Theory of Machines and Computation, pages 189–196. Academic Press, 1976.

    Google Scholar 

  5. J. Johnson and D. Wood. Instruction computation in subset construction. In Proceedings of the First International Workshop on Implementing Automata, pages 1–9, August 1996.

    Google Scholar 

  6. A. R. Meyer. Weak monadic second order theory of succesor is not elementaryrecursive. In Logic Colloquim, number 453 in Lecture Notes in Mathematics, pages 132–154. Springer-Verlag, 1974.

    Google Scholar 

  7. M. O. Rabin. Decidablilty of second-order theories and automata on infinite trees. Trans. AMS, 141:1–35, July 1969.

    Google Scholar 

  8. D. R. Raymond and D. Wood. The Grail Papers. version 2.0. Dept. of Comp. Science, Univ. of Waterloo, Canada, January 1994.

    Google Scholar 

  9. B. W. Watson. Taxonomies and Toolkits of Regular Language Algorithms. PhD thesis, Eindhoven University of Technology, 1995.

    Google Scholar 

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Derick Wood Sheng Yu

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© 1998 Springer-Verlag Berlin Heidelberg

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Glenn, J., Gasarch, W. (1998). Implementing WS1S via finite automata: Performance issues. In: Wood, D., Yu, S. (eds) Automata Implementation. WIA 1997. Lecture Notes in Computer Science, vol 1436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031382

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  • DOI: https://doi.org/10.1007/BFb0031382

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64694-5

  • Online ISBN: 978-3-540-69104-4

  • eBook Packages: Springer Book Archive

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