The complexity of counting functions with easy decision version

Pagourtzis, A; Zachos, S

dc.contributor.author	Pagourtzis, A	en
dc.contributor.author	Zachos, S	en
dc.date.accessioned	2014-03-01T02:44:12Z
dc.date.available	2014-03-01T02:44:12Z
dc.date.issued	2006	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/31755
dc.subject	Complexity Class	en
dc.subject	Counting Function	en
dc.subject	Perfect Match	en
dc.subject	Polynomial Time	en
dc.subject	Structural Properties	en
dc.subject	turing machine	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	Complexity class	en
dc.subject.other	Computation paths	en
dc.subject.other	Counting problems	en
dc.subject.other	Computation theory	en
dc.subject.other	Computational complexity	en
dc.subject.other	Polynomials	en
dc.subject.other	Problem solving	en
dc.subject.other	Turing machines	en
dc.subject.other	Functions	en
dc.title	The complexity of counting functions with easy decision version	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/11821069_64	en
heal.identifier.secondary	http://dx.doi.org/10.1007/11821069_64	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	We investigate the complexity of counting problems that belong to the complexity class #P and have an easy decision version. These problems constitute the class #PE which has some well-known representatives such as #PERFECT MATCHINGS, #DNF-SAT, and NONNEGATIVE PERMANENT. An important property of these problems is that they are all #P-complete, in the Cook sense, while they cannot be #P-complete in the Karp sense unless P = NP. We study these problems in respect to the complexity class TotP, which contains functions that count the number of all paths of a PNTM. We first compare TotP to #P and #PE and show that FP ⊆ TotP ⊆ #PE ⊆ #P and that the inclusions are proper unless P = NP. We then show that several natural #PE problems -including the ones mentioned above -belong to TotP. Moreover, we prove that TotP is exactly the Karp closure of self-reducible functions of #PE. Therefore, all these problems share a remarkable structural property: for each of them there exists a polynomial-time nondeterministic Turing machine which has as many computation paths as the output value. © Springer-Verlag Berlin Heidelberg 2006.	en
heal.publisher	SPRINGER-VERLAG BERLIN	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
heal.bookName	LECTURE NOTES IN COMPUTER SCIENCE	en
dc.identifier.doi	10.1007/11821069_64	en
dc.identifier.isi	ISI:000240271700064	en
dc.identifier.volume	4162 LNCS	en
dc.identifier.spage	741	en
dc.identifier.epage	752	en