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Computers and universal algebra: some directions

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References

  1. Albert, M. A. andLawrence, J.,Unification in varieties of groups: Nilpotent varieties. Can. J. Math.46 (1994), 1135–1149.

    Google Scholar 

  2. Benninger, D. andSchmid, J.,Effective subdirect decomposition: a case study. Theoretical Computer Science100 (1992), 137–156.

    Google Scholar 

  3. Berman, J.,Algebraic properties of k-valued logics. Proc. 10th International Symposium on Multiple-Valued Logic, IEEE (1980), 192–204.

  4. Berman, J.,Free spectra of 3-element algebras. Fourth International Conference on Universal Algebra and Lattice Theory, Proceedings, Puebla 1982; Springer Lecture Notes1004 (1983), 10–53.

  5. Berman, J.,Finite algebras with large free spectra. Algebra Universalis26 (1989), 149–165.

    Google Scholar 

  6. Berman, J. andBlok, W. J.,Equational dependencies. J. Inform. Process. Cybernet. EIK28 (1992), 215–225.

    Google Scholar 

  7. Berman, J. andWolk, B.,Free lattices in some small varieties. Algebra Universalis10 (1980), 269–289.

    Google Scholar 

  8. Berman, J., Kiss, E., Pröhle, P. andSzendrei, A.,The set of types of a finitely generated variety. Discrete Math.112 (1993), 1–20.

    Google Scholar 

  9. Berman, J. andMcKenzie, R.,Clones satisfying the term condition. Discrete Math.52 (1984), 7–29.

    Google Scholar 

  10. Bloniarz, P. A., Hunt, IIIH. B. andRosenkrantz, D. J.,Algebraic structures with hard equivalence and minimization problems. J. Assoc. for Computing Machinery31 (1984), 879–904.

    Google Scholar 

  11. Bloniarz, P. A., Hunt, III H. B. andRosenkrantz, D. J.,On the computational complexity of algebra on lattices. Siam J. Computing16 (1987), 129–148.

    Google Scholar 

  12. Burris, S.,Discriminator varieties and symbolic computation. J. Symbolic Computation13 (1992), 175–207.

    Google Scholar 

  13. Burrts, S. andLawrence, J.,Unification in commutative rings is not finitary. Infor. Proc. Letters36 (1990), 37–38.

    Google Scholar 

  14. Burris, S. andLawrence, J.,Term rewrite rules for finite fields. International J. Algebra and ComputationI (1991), 353–369.

    Google Scholar 

  15. Burris, S. andLawrence, J.,Results on the equivalence problem for finite groups. Preprint, 1992.

  16. Burris, S. andLawrence, J.,The equivalence problem for finite rings. J. of Symbolic Computation15 (1993), 67–71.

    Google Scholar 

  17. Burris, S. andLee, S.,Tarski's High School Identities. Amer. Math. Monthly100 (1993), 231–236.

    Google Scholar 

  18. Burris, S. andLee, S.,Small models of the High School Identities. Internat. J. Algebra and Computation2 (1992), 139–178.

    Google Scholar 

  19. Cook, S.,The complexity of theorem proving procedures. Proc. Third Annual ACM Symposium on the Theory of Computing, 1971, 151–158.

  20. Day, A.,The lattice theory of functional dependencies and normal decompositions. International J. Algebra and Computation (to appear).

  21. Day, A.,A lattice interpretation of database dependencies, in: M. Droste and Yu. Gurevich (eds.),Semantics of Programming Languages and Model Theory, Series: Algebra and Logic Appl., 5, 1993, pp. 305–325. Gordon and Breach, London.

    Google Scholar 

  22. Demel, J.,Fast algorithms for finding a subdirect decomposition and interesting congruences of finite algebras. Kybernetika (Prague)18 (1982), 121–130.

    Google Scholar 

  23. Demlová, M., Demel, J. andKoubek, V.,Several algorithms for finite algebras. Proc. of FCT 79, Akademie-Verlag Berlin, 1979, 99–104.

    Google Scholar 

  24. Dershowitz, N. andJouannaud, J.-P.,Rewrite systems. Chap. 6 of the Handbook of Theoretical Computer Science, ed. J. van Leeuven, Elsevier Science Publishers, 1990, 245–320.

  25. Evans, T.,On multiplicative systems defined by generators and relations. J. Proc. Cambridge Philos. Soc.47 (1951), 637–649.

    Google Scholar 

  26. Freese, R. S.,Free lattice algorithms. Order3 (1987), 331–334.

    Google Scholar 

  27. Freese, R. S.,Finitely presented lattices: canonical forms and the covering relation. Trans. Amer. Math. Soc.312 (1989), 841–860.

    Google Scholar 

  28. Freese, R. S., Ježek, J. andNation, J. B.,Term rewrite systems for lattice theory, J. Symbolic Computation16 (1993), 279–288.

    Google Scholar 

  29. Freese, R. S.,Ježek, J. andNation, J. B.,Free Lattices, AMS Math. Surveys and Monographs, Vol. 142, 1995.

  30. Garey, M. R. andJohnson, D. S.,Computers and Intractability: a Guide to the Theory of NP-Completeness. W. H. Freeman & Co., 1979.

  31. Goralčík, P.,Goralčíková, A. andKoubek, V.,Testing of properties of finite algebras. Proc. of ICALP 80, Lecture Notes in Comp. Sci.85, Springer Verlag, 1980, 273–281.

  32. Goralčík, P.,Goralčíková, A.,Koubek, V. andRödl, V.,Fast recognition of rings and lattices. Proc. of FCT 81, Lecture Notes in Comp. Sci.117, Springer Verlag, 1981, 137–145.

  33. Grätzer, G. andKisielewicz, A.,A survey of some open problems on pn-sequences and free spectra of algebras and varieties, in: A. Romanowska and J. D. H. Smith (eds.),Universal Algebra and Quasigroup Theory, Vol. 19 in Series: Research and Exposition in Mathematics. Heldermann Verlag, Berlin, 1992.

    Google Scholar 

  34. Gurevič R.,Equational theory of positive numbers with exponentiation. Proc. Amer. Math. Soc.94 (1985), 135–141.

    Google Scholar 

  35. Hobby, D.,Finding type sets is NP-hard. Internat. J. Algebra and Computation1 (1991), 437–444.

    Google Scholar 

  36. Hunt, IIIH. B. andStearns, R. E.,The complexity of equivalence for commutative rings. J. Symbolic Computation10 (1990), 411–436.

    Google Scholar 

  37. Knuth, D. E. andBendix, P. B.,Some simple word problems in universal algebras, in: J. Leech (ed.).Computational Problems in Abstract Algebra. Pergamon Press, Oxford, 1970, 263–297.

    Google Scholar 

  38. Kozen, D.,Complexity of finitely presented algebras. Proc. 9th Symposium STOC (1977), 164–177.

  39. Kučera, L. andTrnková, V.,The computational complexity of some problems of universal algebra. Universal Algebra and its Links with Logic, Algebra, Combinatorics, and Computer Science. Proc. “25. Arbeitstagung über Allgemeine Algebra”, Darmstadt 1983, P. Burmeister et al. (eds.), Heldermann Verlag, 1984, 216–229.

    Google Scholar 

  40. Kučera, L. andTrnkova, V.,Isomorphism testing of unary algebras. Siam. J. of Computing17 (1988), 673–686.

    Google Scholar 

  41. Lankford, D.,A unification algorithm for Abelian group theory. Internal Report MTP-1, Louisiana Tech. Univ., Ruston, 1979.

    Google Scholar 

  42. McKenzie, R. andValeriote, M.,Decidable Varieties. Birkkäuser, 1987.

  43. Nipkow, T.,Unification in primal algebras, their powers, and their varieties. J. Assoc. Comp. Mach.37 (1990), 742–776.

    Google Scholar 

  44. Plotkin, G.,Building in equational theories. Mach. Intelligence7, Halsted-Press, New York, 1972, 227–261.

    Google Scholar 

  45. Quackenbush, R. W.,Dedekind's problem. Order2 (1986), 415–417.

    Google Scholar 

  46. Słupecki, J.,Completeness criteria for systems of many-valued propositional calculus. Comptes rendus des Séances de la Société des Sciences et des Lettres de Varsovie Cl. II.32 (1939), 102–109. English transl. Studia Logica30 (1972), 153–157.

    Google Scholar 

  47. Stickel, M. E.,A case study of theorem proving by the Knuth-Bendix method: discovering that x3 ≈ x implies ring commutativity. 7th Internat. Conf. on Automated Deduction, Napa, California, Lecture Notes in Comp. Sci.170 (1984), 248–258.

  48. Tarjan, R. E.,Determining whether a groupoid is a group. Information Processing Letters1 (1972), 120–124.

    Google Scholar 

  49. Vuillement, J.,Comment verifier si une boucle est un groupe. Technical Report, Université de Paris-Sud, 1976, 1–12.

  50. Wiedemann, D.,A computation of the eighth Dedekind number. Order8 (1991), 5–6.

    Google Scholar 

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  1. Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    S. Burris

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Dedicated to the memory of Alan Day

Research supported by a grant from NSERC.

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Burris, S. Computers and universal algebra: some directions. Algebra Universalis 34, 61–71 (1995). https://doi.org/10.1007/BF01200490

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