Algorithms for the computation of free lattices

  • Z. Lomecky
6. Algorithms III
Part of the Lecture Notes in Computer Science book series (LNCS, volume 144)


For a class of extensions of lattice theory by unary function symbols and equational axioms (including modularity) algorithms for the computation of the corresponding initial algebra (if this is finite) are presented. In the case of finitely presented lattices the method amounts to a decision procedure for term equality and can be used for the computation of finite sublattices. Several examples and performance comparisons are provided.


Word Problem Decision Procedure Lattice Theory Partial Algebra Term Equality 


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  1. — Cannon,A., Implementation and Analysis of the Todd-Coxeter Algorithm, Math. Comp., 27(1973)Google Scholar
  2. — Grätzer, G., General Lattice Theory, Birkhäuser, Basel, 1978Google Scholar
  3. — Gross,H., Quadratic Forms in Infinite Dimensional Vector Spaces, Progress in Mathematics, 1(1979)Google Scholar
  4. — Huet,G., Confluent Reductions: Abstract Properties and Applications, J. ACM, 27(1980)Google Scholar
  5. — Knuth,D.E. and P.A.Bendix, Simple Word Problems in Universal Algebras, "Computational Problems in Abstract Algebra", J.Leech, Ed., Oxford and New York,1969Google Scholar
  6. — Loos,R., Term Reduction Systems and Algebraic Algorithms, Springer Informatik-Fachberichte 47Google Scholar
  7. — Whitman, P.M., Free Algebras, Ann. Math., 42(1941)Google Scholar
  8. — Wille,R., Subdirekte Produkte vollständiger Verbände, J. Math.,283/284(1973)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Z. Lomecky
    • 1
  1. 1.ETH ZurichSwitzerland

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