Rewriting, Induction and Decision Procedures: A Case Study of Presburger Arithmetic

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Symbolic Algebraic Methods and Verification Methods

Abstract

Theorem provers and automated reasoning tools are not as widely used in specification analysis, debugging and verification of hardware and software as one would hope. A major reason is perhaps that these tools are often found difficult to use. The learning curve for a typical theorem prover is quite high; it takes a great deal of effort by typical users to effectively use such a tool for their application domain. Even then, considerable resources must be expended by building a large knowledge base and library of useful properties in a representation suitable for the prover, to bring it to a level so that it can start playing a useful role.

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References

  • Gupta, A. (1994): Inductive Boolean Function Manipulation: A Hardware Verifieation Methodology tor Automatic Induction. Ph.D. Thesis, CMU, Pittsburgh.

    Google Scholar 

  • Boyer, R.S., and Moore, J.S. (1988): A Computational Logic Handbook. Academic Press.

    Google Scholar 

  • Boyer, R.S., and Moore, J.S. (1988): “Integrating decision procedures into heuristic theorem provers: A case study of linear arithmetic”, Machine Intelligence 11, P. Hayes, D. Mitchie and J. Richards (eds).

    Google Scholar 

  • Bryant, R.E. (1986): “Graph-based algorithms for boolean function manipulation,” IEEE Trans. on Computers, C-35(8).

    Google Scholar 

  • Dershowitz, N. (1986): “Termination of rewriting,” J. Symbolic Computation, 3, 69–116.

    Article  MathSciNet  Google Scholar 

  • Enderton, H. (1972): A MathematiCal Introduction to Logic. Academic Press.

    Google Scholar 

  • Kapur, D. (1994): “Automated tools for analyzing completeness of specifications,” Proc. 1994 Intl. Symp. on Software Testing and Analysis (ISSTA), Seattle, WA.28–43.

    Google Scholar 

  • Kapur, D. (1997a): “Shostak’s congruence closure as completion,” Proc. Intl. Conf. on Rewriting Techniques and Applications (RTA-91), Barcelona, Spain.

    Google Scholar 

  • Kapur, D. (1997b): “Rewriting, decision procedures and lemma speculation for automated hardware verification,” Proc. Theorem Provers in Higher-order Logics, (ed. Gunter and Felty), Springer LNCS 1275, Murray Hill, 171–182.

    Google Scholar 

  • Kapur, D., Narendran, P., Rosenkrantz, D., and Zhang, H. (1991): “Sufficient-completeness, quasi-reducibility and their complexity,” Acta Informatica, 28,311–350.

    Article  MathSciNet  MATH  Google Scholar 

  • Kapur, D., and Nie, X. (1994): “Reasoning about numbers in Tecton,” Proc. 8th Intl. Symp. Methodologies tor Intelligent Systems, Charlotte, North Carolina, 57–70.

    Google Scholar 

  • Kapur, D., and Subramaniam, M. (1996a): “New uses of linear arithmetic in automated theorem proving for induction,” J. Automated Reasoning, 16(1–2), 39–78.

    Article  MathSciNet  MATH  Google Scholar 

  • Kapur, D., and Subramaniam, M. (1996b): “Mechanically verifying a family of multiplier circuits,” Proc. CAV, (eds. Alur and Henzinger), LNCS 1102, 135–146.

    Google Scholar 

  • Kapur, D., and Subramaniam, M. (1997): “Mechanizing reasoning about arithmetic circuits: SRT division,” Proc. 17th FSTTCS, Springer LNCS 1346, Kharagpur, India.

    Google Scholar 

  • Kapur, D., and Subramaniam, M. (1998a): “Mechanical verification of adder circuits using powerlists,” J. Formal Methods in System Design, 13(2), 127–158.

    Article  Google Scholar 

  • Kapur, D., and Subramaniam, M. (1998b): “Mechanizing reasoning about large finite tables in a rewrite based theorem prover,”, Proc. ASIAN-98, LNCS 1538, Manila.

    Google Scholar 

  • Kapur, D., and Subramaniam, M. (2000a): “Extending decision procedures with induction schemes” Proc. CADE-17 (ed. McAllester) Springer LNAI 1831, Pittsburgh.

    Google Scholar 

  • Kapur, D., and Subramaniam, M. (2000b): D. Kapur and M. Subramaniam, “Using an induction prover for verifying arithmetic circuits,” J. Software Tools for Technology Transfer, Springer Verlag, Sep 2000.

    Google Scholar 

  • Kapur, D., and Zhang, H. (1995): “An overview of Rewrite Rule Laboratory (RRL),” J. of Computer and Mathematics with Applications, 29, 2, 91–114.

    Article  MathSciNet  Google Scholar 

  • Nelson, G., and Oppen, D.C. (1979): “Simplification by unnperating decision procedures,” ACM Trans. on Programming Languages and Systems 1 (2), 245–257.

    Article  MATH  Google Scholar 

  • Shostak, R.E. (1984): “Deciding combination of theories,” J. ACM 31 (1), 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  • Subramaniam, M. (1997): Failure Analyses in Inductive Theorem Provers. Ph.D. Thesis, Department of Computer Science, University of Albany, New York.

    Google Scholar 

  • Zhang, H. (1992): “Implementing contextual rewriting,” Proc. 3rd Intl. Workshop on Conditional Term Rewriting Systems, (eds. Remy and Rusinowitch), Springer LNCS 656, France, 363–377.

    Google Scholar 

  • Zhang, H., Kapur, D., and Krishnamoorthy, M.S. (1988): “A mechanizable induction principle for equational specifications,” Proc. 9th Intl. Conf. Automated Deduction (CADE), (eds. Lusk and Overbeek), Springer LNCS 310, Chicago, 250–265.

    Google Scholar 

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© 2001 Springer-Verlag Wien

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Kapur, D. (2001). Rewriting, Induction and Decision Procedures: A Case Study of Presburger Arithmetic. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_13

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  • DOI: https://doi.org/10.1007/978-3-7091-6280-4_13

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83593-7

  • Online ISBN: 978-3-7091-6280-4

  • eBook Packages: Springer Book Archive

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