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Solving Equations Involving Sequence Variables and Sequence Functions

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Artificial Intelligence and Symbolic Computation (AISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3249))

Abstract

Term equations involving individual and sequence variables, and individual and sequence function symbols are studied. Function symbols can have either fixed or flexible arity. A new unification procedure for solving such equations is presented. Decidability of unification is proved. Completeness and almost minimality of the procedure is shown.

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References

  1. Abdulrab, H., Pécuchet, J.-P.: Solving word equations. J. Symbolic Computation 8(5), 499–522 (1990)

    Article  Google Scholar 

  2. Baader, F., Schulz, K.U.: Unification in the union of disjoint equational theories: Combining decision procedures. J. Symbolic Computation 21(2), 211–244 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baader, F., Snyder, W.: Unification theory. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, ch. 8, pp. 445–532. Elsevier Science, Amsterdam (2001)

    Chapter  Google Scholar 

  4. Bledsoe, W.W., Feng, G.: Set-Var. J. Automated Reasoning 11(3), 293–314 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Boley, H. (ed.): A Tight, Practical Integration of Relations and Functions. LNCS (LNAI), vol. 1712. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  6. Buchberger, B., Dupré, C., Jebelean, T., Kriftner, F., Nakagawa, K., Vasaru, D., Windsteiger, W.: The Theorema project: A progress report. In: Kerber, M., Kohlhase, M. (eds.) Proc. of Calculemus 2000 Conference, St. Andrews, UK, August 6-7, pp. 98–113 (2000)

    Google Scholar 

  7. Ginsberg, M.L.: User’s guide to the MVL system. Technical report, Stanford University, Stanford, California, US (1989)

    Google Scholar 

  8. Jaffar, J.: Minimal and complete word unification. J. ACM 37(1), 47–85 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kohlhase, M.: A mechanization of sorted higher-order logic based on the resolution principle. PhD Thesis. Universität des Saarlandes. Saarbrücken, Germany (1994)

    Google Scholar 

  10. Kutsia, T.: Solving and proving in equational theories with sequence variables and flexible arity symbols. Technical Report 02-31, RISC-Linz, Austria (2002)

    Google Scholar 

  11. Kutsia, T.: Equational prover of Theorema. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 367–379. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Kutsia, T.: Solving equations involving sequence variables and sequence functions. Technical Report 04-01, RISC, Johannes Kepler University, Linz, Austria (2004), http://www.risc.uni-linz.ac.at/people/tkutsia/papers/SeqUnif.ps

  13. Marin, M., Kutsia, T.: On the implementation of a rule-based programming system and some of its applications. In: Konev, B., Schmidt, R. (eds.) Proc. of the 4th Int. Workshop on the Implementation of Logics (WIL 2003), Almaty, Kazakhstan, pp. 55–68 (2003)

    Google Scholar 

  14. Paulson, L.: Isabelle: the next 700 theorem provers. In: Odifreddi, P. (ed.) Logic and Computer Science, pp. 361–386. Academic Press, London (1990)

    Google Scholar 

  15. Plotkin, G.: Building in equational theories. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 7, pp. 73–90. Edinburgh University Press (1972)

    Google Scholar 

  16. Richardson, J., Fuchs, N.E.: Development of correct transformation schemata for Prolog programs. In: Fuchs, N.E. (ed.) LOPSTR 1997. LNCS, vol. 1463, pp. 263–281. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  17. Schmidt, R.: E-Unification for subsystems of S4. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 106–120. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. Wolfram, S.: The Mathematica Book, 4th edn. Cambridge University Press and Wolfram Research, Inc. (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University Linz, A-4040, Linz, Austria

    Temur Kutsia

Authors
  1. Temur Kutsia
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Editor information

Editors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria

    Bruno Buchberger

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    John Campbell

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© 2004 Springer-Verlag Berlin Heidelberg

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Kutsia, T. (2004). Solving Equations Involving Sequence Variables and Sequence Functions. In: Buchberger, B., Campbell, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2004. Lecture Notes in Computer Science(), vol 3249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30210-0_14

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  • DOI: https://doi.org/10.1007/978-3-540-30210-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23212-4

  • Online ISBN: 978-3-540-30210-0

  • eBook Packages: Springer Book Archive

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