Advertisement

Matching under commutativity

  • Jörg Siekmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)

Abstract

A complete unification algorithm for terms involving a commutative function is presented. The main results are: the unification problem is decidable and the set of unifiers is always finite. The algorithm, as presented, is not minimal, but improves over the naive solution. This paper is a short version of [21.], which contains the proofs omitted here and some additional technical material.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8. References

  1. [1]
    Bennett, Easton, Guard, Settle. CRT-aided simiautomated mathematics. Techn. Report AFCRL 67-O167, 1967, Applied Logic Corp., Princeton.Google Scholar
  2. [2]
    B. Epp: ‘INTERLISP Programmierhandbuch', Institut für Deutsche Sprache, MannheimGoogle Scholar
  3. [3]
    J. Fischer, S. Patterson: 'string Matching and other Products', MIT, Project MAC, Report 41, 1974.Google Scholar
  4. [4]
    P.J. Faber, R.E. Griswald, I.P. Polonsky: "SNOBOL as String Manipulation Language'. JACM, vol 11, no. 2, 1966.Google Scholar
  5. [5]
    W.E. Gould. A matching procedure for ω-order logic. Scientific report no. 4, AFCRL-666-781, 1966.Google Scholar
  6. [6]
    J. Hmelevskij. The solution of certain systems of word equations. Dokt. Akad. Nauk. SSR (1964), (1966), (1967), (Soviet Math. Dokl.).Google Scholar
  7. [7]
    G. Huet. Unification in typed lambda calculus, "Springer Lecture Notes", No. 37, (ed) Goos, Hartmanis, 1975.Google Scholar
  8. [8]
    G. Huet. A unification algorithm for typed λ-calculus, Theoretical Comp. Sci. 1.1., 1975.Google Scholar
  9. [9]
    D.E. Knuth, P.B. Bendix. Simple Word Problems in Universal Algebras, in "Computational Problems in Abstract Algebra", J. Leech (ed), Pergamon Press, Oxford 1970.Google Scholar
  10. [10]
    Knuth, Morris, Pratt: ‘Fast Pattern Matching in Strings', Stan-CS-74-440, Stanford University, Computer Science Dept., 1974.Google Scholar
  11. [11]
    M. Livesey, J. Siekmann. Termination and Decidability Results for String Unification. Essex University, Computing Centre, Memo CSM-12, 1875.Google Scholar
  12. [12]
    M. Livesey, J. Siekmann. Unification of Sets and Multisets. SEKI-Report 3/76, Institut für Informatik I, Universität Karlsruhe, 1976.Google Scholar
  13. [13]
    G.S. Makanin: The Problem of Solvability of Equations in a Free Semigroup, Soviet Akad. Nauk SSSR, Tom 233, no. 2, 1977.Google Scholar
  14. [14]
    A.A. Markov. Trudy Mat. Inst. Steklov, No. 42, Izdat. Akad. Nauk SSR, 1954.Google Scholar
  15. [15]
    G. Plotkin. Building in equational theories. Machine Intelligence, vol 7, 1972.Google Scholar
  16. [16]
    J.A. Robinson. A machine oriented logic based on the resolution principle, JACM: 12, 1965.Google Scholar
  17. [17]
    P. Raulefs, J. Siekmann, P. Szabó, E. Unvericht. ‘A short survey on the state of the art in Matching and Unification Problems', Universität Karlsruhe, Institut für Informatik I, SEKI 3–78, 1978.Google Scholar
  18. [18]
    P. Raulefs, J. Siekmann, Unification of Idempotent Functions. Universität Karlsruhe, Institut für Informatik I, SEKI-Report.Google Scholar
  19. [19]
    J. Siekmann. String unification. Essex University, Memo CSM-7.Google Scholar
  20. [20]
    J. Siekmann. Unification of Commutative Terms, Universität Karlsruhe, Institut für Informatik I, SEKI-Report.Google Scholar
  21. [21]
    J. Siekmann. Unification and Matching Problems. Universität Karlsruhe, Institut für Informatik I, SEKI-Report.Google Scholar
  22. [22]
    J.R. Slagle. ATP for theories with simplifiers, commutativity and associativity. JACM, vol. 21, No. 4, 1974.Google Scholar
  23. [23]
    P. Szabó: ‘The undecidability of the D+A-unification problem’ Universität Karlsruhe, Institut für Informatik I, 1978.Google Scholar
  24. [24]
    P. Szabó, E. Unvericht, Unification und Distributivity, Universität Karlsruhe, Institut für Informatik I, SEKI-Report.Google Scholar
  25. [25]
    M. Stickel. A complete unification algorithm for associative-commutative functions. Proc. 4th IJCAI, Tblisi, USSR, 1975.Google Scholar
  26. [26]
    E. Vogel: Unifikationsalgorithmen für Morphismen. Diplomarbeit (forthcoming), Universität Karlsruhe, Institut für Informatik I, 1978.Google Scholar
  27. [27]
    G. Winterstein. Monadic Second Order Unification. Universität Kaiserslautern, 1976.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Jörg Siekmann
    • 1
  1. 1.Institut für Informatik IKarlsruheWest Germany

Personalised recommendations