Acceptor-definable counting classes

Kiayias, A; Pagourtzis, A; Sharma, K; Zachos, S

dc.contributor.author	Kiayias, A	en
dc.contributor.author	Pagourtzis, A	en
dc.contributor.author	Sharma, K	en
dc.contributor.author	Zachos, S	en
dc.date.accessioned	2014-03-01T01:18:35Z
dc.date.available	2014-03-01T01:18:35Z
dc.date.issued	2003	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15099
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-35248812634&partnerID=40&md5=82cc8cbdb0ab8b9077a103c5ffedc38a	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	COMPLEXITY	en
dc.title	Acceptor-definable counting classes	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	Counting functions that can be defined on non-deterministic acceptors (Turing machines without output), as opposed to those defined by transducers (Turing machines with output), have attracted much interest since 1979, when Valiant introduced the important class #P [19]. Apart from #P, several such classes have been defined in the literature [2, 5, 3, 12, 6]. Here we study the path-order complexity classes RAP, LAP and MAP, introduced in [6], which consist of functions that output the order of the rightmost, leftmost and middle accepting computation path (respectively) of a polynomial-time non-deterministic Turing acceptor (PNTM). We also consider TotP [6], the class of functions that output the total number of paths of a PNTM. We show several properties of these classes. In particular we prove that RAP and LAP are are equivalent under the Cook[1] sense with #P and TotP. This implies that all these classes are equally powerful when used as oracles to a polynomial computation, even if only one query is allowed. We also show that problems #PERFECT MATCHINGS and #DNF-SAT are complete for RAP and LAP in the Cook[1] sense and for MAP in the Cook sense. Path-order classes give rise to corresponding path-order operators; these operators applied on the class NP provide alternative characterizations for known classes of optimization problems. Using these characterizations, we present natural complete problems for optimization classes. © Springer-Verlag Berlin Heidelberg 2003.	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.isi	ISI:000183490000029	en
dc.identifier.volume	2563	en
dc.identifier.spage	453	en
dc.identifier.epage	463	en