论文信息 - Self-Reducibility of Hard Counting Problems with Decision Version in P

Self-Reducibility of Hard Counting Problems with Decision Version in P

Many NP-complete problems have counting versions which are #P-complete. On the other hand, #Perfect Matchings is also Cook-complete for #P, which is surprising as Perfect Matching is actually in P (which implies that #Perfect Matchings cannot be Karp-complete for #P). Here, we study the complexity class #PE (functions of #P with easy decision version). The inclusion #PE ⊆ #P is proper unless P = NP. Several natural #PE problems (e.g., #Perfect Matchings, #DNF-Sat, #NonCliques) are shown to possess a specific self-reducibility property. This implies membership in class TotP [KPSZ98,PZ05]. We conjecture that all non-trivial problems of #PE share this self-reducibility property.

S. Zachos | Aris Pagourtzis

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