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Colloquium on Trees in Algebra and Programming

CAAP 1981: CAAP '81 pp 135–146Cite as

Easy solutions are hard to find

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 112))

Abstract

There are two main results in this paper.

A new NP-complete problem is found: given a system (S) of recursion equations, determine whether (S) has a solution in a non-trivial "contraction algebra" in which one of the components is a projection. This problem, which arose in [3] where all solutions of a system of recursion equations in a contraction algebra A were found, is related to the equivalence problem for deterministic pushdown automata.

Secondly, for signatures Σ with a finite number of function symbols of positive rank, the free complete contraction Σ-algebras are shown to be isomorphic to algebras of "Σ-trees". When Σ has an infinite number of function symbols of positive rank, it is shown that there are no free complete contraction Σ-algebras.

on leave from Department of Pure and Applied Mathematics Stevens Institute of Technology Hoboken, N.J. 07030

Partially supported by NSF Grant MCS 78-00882

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References

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Author information

Authors and Affiliations

  1. Mathematical Sciences Department, IBM T.J. Watson Research Center, 10598, Yorktown Heights, N.Y.

    Stephen L. Bloom

  2. Division of Mathematics and Science, St. John's University, 10301, Staten Island, N.Y.

    David B. Patterson

Authors
  1. Stephen L. Bloom
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  2. David B. Patterson
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Editor information

Egidio Astesiano Corrado Böhm

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© 1981 Springer-Verlag Berlin Heidelberg

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Bloom, S.L., Patterson, D.B. (1981). Easy solutions are hard to find. In: Astesiano, E., Böhm, C. (eds) CAAP '81. CAAP 1981. Lecture Notes in Computer Science, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10828-9_59

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  • DOI: https://doi.org/10.1007/3-540-10828-9_59

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10828-3

  • Online ISBN: 978-3-540-38716-9

  • eBook Packages: Springer Book Archive

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