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An overview of completion algorithms

  • Rewrite Rules And The Completion Procedure II
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EUROCAL '85 (EUROCAL 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 204))

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Bibliography

  • Ayoub, C. W., 1981: On constructing bases for ideals in polynomial rings over the integers. Techn. Rep. no. 8184, Pennsylvania State Univ., Univ.

    Google Scholar 

  • Bergman, G. M., 1978: The diamond lemma for ring theory. Advances in Math., vol. 29, pp. 178–218.

    Google Scholar 

  • Buchberger, B., 1965: An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal (German). Ph.D. Thesis, Univ. of Innsbruck (Austria), Math. Inst..

    Google Scholar 

  • Buchberger, B., 1979: A criterion for detecting unnecessary reductions in the construction of Gröbner bases. Proc. EUROSAM 79, Marseille, June 1979, (W. Ng, ed.), Lecture Notes in Computer Science. vol. 72, pp. 3–21.

    Google Scholar 

  • Buchberger, B., and Loos, R., 1982: Algebraic simplification. In: Computer Algebra — Symbolic and Algebraic Computation (B. Buchberger, G. Collins, R. Loos eds.), Springer, Wien — New York, pp. 11–43.

    Google Scholar 

  • Butler, G., Lankford, D., 1984: Dickson's Lemma, Hilbert's Basis Theorem, and applications to completion in commutative noetherian rings. Dept. Math. and Stat. Louisiana Tech. University.

    Google Scholar 

  • Caviness, B. F., 1970: On canonical forms and simplification. Ph.D. Diss., Pittsburgh, Carnegie-Mellon University, 1967, and J. ACM 17/2, 1970.

    Google Scholar 

  • Davis, M., Putnam, H., Robinson, J., 1961: The decision problem for exponential diophantine equations. Ann. Math. 74, 425.436.

    Google Scholar 

  • Dershowitz, N., 1979 A: Orderings for term-rewriting systems. Proc. 20th Symp. on Foundations of Comp. Sci., 123–131.

    Google Scholar 

  • Dershowitz, N., 1979 B: A note on simplification orderings. Inf. Process. Lett. 9/5, 212–215.

    Article  Google Scholar 

  • Dershowitz, N., 1982: Orderings for term-rewriting systems. Theoretical Computer Science Vol. 17.

    Google Scholar 

  • Evans, T., 1951: On multiplicative systems defined by generators and relations. I. Normal forms theorems, Proc. Cambridge Philosophy Soc. 47.

    Google Scholar 

  • Fages, F., 1983 A: Formes canoniques dans les algebres booleennes et applications a la demonstration automatique en logique de premier ordre. These 3eme cycle, Universite Paris 7 LITP.

    Google Scholar 

  • Fages, F., Huet, G., 1983 B: Complete seta of unifiers and matchers in equational theories. CAAP'83, LNCS 159, Springer-Verlag.

    Google Scholar 

  • Fay, M., 1979: First order unification in equational theory. 4th Workshop on Automated Deduction, Austin, Texas.

    Google Scholar 

  • Hsiang, J., 1982: Topics in automated theorem proving and program generation. Ph. D. Thesis, Univ. of Illinois at Urbana-Champaign, Dept. of Comp. Scie..

    Google Scholar 

  • Huet, G., Lankford, D. S., 1978: On the uniform halting problem for term rewriting systems. IRIA rapport Laboria 283.

    Google Scholar 

  • Huet, G., Oppen, D. C., 1980: Equations and rewriting rules: A survey. Tech. Rep. CSL-111, SRI International, Stanford.

    Google Scholar 

  • Huet, G., 1981: A complete proof of the Knuth-Bendix completion algorithm. J. Comp. and System Sci. 23.

    Google Scholar 

  • Hullot, J. M., 1980: Compilation de formes canoniques dans les theories equationnelles. Tese 3eme cycle, U. Paris Sud.

    Google Scholar 

  • Jouannaud, J. P., Lescanne, P., Reining, F., 1982: Recursive decomposition ordering. Conf. on Formal Description of Programming Concepts, Ed. D. Bjorner, North Holland.

    Google Scholar 

  • Kamin, S., Levy, J., 1980: Attempts for generalizing the recursive path ordering. Unpublished.

    Google Scholar 

  • Knuth, D. E., Bendix, P. B., 1967: Simple word problems in universal algebras. Proc. of the Conf. on Computational Problems in Abstract Algebra, Oxford, 1967, (Leech, J. ed.), Pergamon Press, Oxford, 1970.

    Google Scholar 

  • Lankford, D. S., 1975: Canonocal inference. Univ. of Texas, Austin: Dept. Math. Comput. Sci., Rep. ATP-32.

    Google Scholar 

  • Lankford, D. S., Ballantyne, A. M., 1977 A: Decision procedures for simple equational theories with commutative axioms: Complete sets of commutative reductions. Univ. of Texas, Austin: Dept. Math. Comput. Sci., Rep. ATP-35.

    Google Scholar 

  • Lankford, D. S., Ballantyne, A. M., 1977 B: Decision procedures for simple equational theories with permutative axioms: Complete sets of permutative reductions. Univ. of Texas, Austin: Dept. Math. Comput. Sci., Rep. ATP-37.

    Google Scholar 

  • Lankford, D. S., Ballantyne, A. M., 1977 C: Decision procedures for simple equational theories with commutative-associative axioms: Complete sets of commutative-associative reductions. Univ. of Texas, Austin: Dept. Math. Comput. Sci., Rep. ATP-39.

    Google Scholar 

  • Lankford, D. S., 1979 A: A unification algorithm for Abelian Group theory. Rep. MTP-1, Math. Dept. Lousiana Tech. U.

    Google Scholar 

  • Lankford, D. S., 1979 B: Some new approaches to the theory and applications of conditional rewriting systems. Math. Dept. Louisiana Tech. U.

    Google Scholar 

  • Le Chenadec, P., 1983: Canonical forms in finitely presented algebras (French). Ph. D. Thesis, Univ. of Paris-Sud, Centre d' Orsay.

    Google Scholar 

  • Lescanne, P., 1982: Computer experiments with REVE term rewriting system generator. Proc. 10th POPL conference.

    Google Scholar 

  • Livesey, M., Siekmann, J., 1976: Unification of bags and sets. Internal report 3/76, Inst. f. Informatik I, U. Karlsruhe.

    Google Scholar 

  • Llopis de Trias, R., 1983: Canonical forms for residue classes of polynomial ideals and term rewriting systems. Dept. U.S.B. rep. 84-03.

    Google Scholar 

  • Makanin, G.S., 1977: The Problem of Solvability of Equations in a Free Semigroup. Akad. Nauk. SSSR, TOM 233,2.

    Google Scholar 

  • Manna, Z., Ness, S., 1970: On the Termination of Markov Algorithms. Third Hawai International Conference on System Sciences., 789–792.

    Google Scholar 

  • Martelli, A., Montanari, U., 1982: An Efficient Unification Algorithm. ACM TOPLAS, Vol. 4, No. 2.

    Google Scholar 

  • Matiyasevic, J., 1970: Diophantine representation of recursively enumerable predicates. Proc. Second Scandinavian Logic Symposium, Amsterdam, North Holland.

    Google Scholar 

  • Moses, J., 1971: Algebraic Simplification: A Guide for the Perplexed. Comm. of the ACM, Vol. 14/8, pp.527–537.

    Google Scholar 

  • Newman, M.H.A., 1942: On Theories With a Combinatorial Definition of "Equivalence". Annals of Math., Vol.43/2, pp.223–243.

    Google Scholar 

  • Peterson, G.E., Stickel, M.E., 1981: Complete Set of Reductions for Equational Theories. J. ACM 28/2.

    Google Scholar 

  • Plaisted, D., 1978: A Recursively Defined Ordering for Proving Termination of Term Rewriting Systems. Univ. of Illinois at Urbana-Champaign, Dept. of Comp. Science, Report 78-943.

    Google Scholar 

  • Plotkin, G., 1972: Building-In Equational Theories. Machine-Intelligence, Vol. 7, 73–90.

    Google Scholar 

  • Richardson, D., 1968: Some Unsolvable Problems Involving Elementary Functions of a Real Variable. J. of Symbolic Logic Vol.33, pp.511–520.

    Google Scholar 

  • Robinson, J.A., 1965: Machine-Oriented Logic Based on the Resolution Principle. J. of the ACM, Vol.12(1), 23–41.

    Article  Google Scholar 

  • Rody, A.K., Kapur, D., 1984: Algorithms for computing Gröbner Bases of polynomial ideals over various euclidean rings. EUROSAM 84, Cambridge.

    Google Scholar 

  • Siekmann, J., 1978: Unification and Matching Problems. Ph.D. Thesis, Univ. of Essex, Memo CSM-4-78.

    Google Scholar 

  • Slagle, J.R., 1974: Automated Theorem Proving for Theories with Simplifiers, Commutativity and Associativity. Journal ACM Vol.21, pp.622–642.

    Google Scholar 

  • Stickel, M. E., 1981: A unification algorithm for associative commutative functions. J. ACM. 28/3.

    Google Scholar 

  • Winkler, F., 1983: A unification algorithm for constructing detaching bases in the ring of polynomials over a field. Computer Algebra LNCS 162, Springer-Verlag.

    Google Scholar 

  • Winkler, F., 1984: The Church-Rosser property in computer algebra and special theorem proving: An investigation of critical pair completion algorithms. Dissertation, Joh. Kepler University, Linz.

    Google Scholar 

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Authors and Affiliations

  1. Universidad Simòn Bolìvar, Caracas, Venezuela

    Regina Llopis de Trias

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  1. Regina Llopis de Trias
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Bob F. Caviness

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© 1985 Springer-Verlag Berlin Heidelberg

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Llopis de Trias, R. (1985). An overview of completion algorithms. In: Caviness, B.F. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15984-3_303

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  • DOI: https://doi.org/10.1007/3-540-15984-3_303

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  • Print ISBN: 978-3-540-15984-1

  • Online ISBN: 978-3-540-39685-7

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