Easy solutions are hard to find

  • Stephen L. Bloom
  • David B. Patterson
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 112)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Stephen L. Bloom
    • 1
  • David B. Patterson
    • 2
  1. 1.Mathematical Sciences DepartmentIBM T.J. Watson Research CenterYorktown Heights
  2. 2.Division of Mathematics and ScienceSt. John's UniversityStaten Island

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