Abstract
A subproblem of a problem A is the restriction of A to some polynomial time computable set. A set A is subproblem complete (s.c.) if every polynomial time (p-) degree below the p-degree of A contains a subproblem of A. A is decomposition complete (d.c.) if every splitting of the p-degree of A is witnessed by a decomposition of A into two subproblems. We show that all p-cylinders and thus most of the "natural" problems are s.c. and d.c. with respect to p-many-one (Karp) reducibility. We also show, however, that not every problem has these properties. Furthermore, we discuss these completeness properties with respect to p-Turing (Cook) reducibility.
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Ambos-Spies, K. (1984). On the relative complexity of subproblems of intractable problems. In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023989
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DOI: https://doi.org/10.1007/BFb0023989
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