Tally NP sets and easy census functions

Judy Goldsmith, Mitsunori Ogihara, Jörg Rothe

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the question of whether every P set has an easy (i.e., polynomial-time computable) census function. We characterize this question in terms of unlikely collapses of language and function classes such as #P 1 ⊆ FP, where #P1 is the class of functions that count the witnesses for tally NP sets. We prove that every #P1 PH function can be computed in FP#p 1 #p1. Consequently, every P set has an easy census function if and only if every set in the polynomial hierarchy does. We show that the assumption #P1 ⊆ FP implies P = BPP and PH ⊆ MODkP for each k ≥ 2, which provides further evidence that not all sets in P have an easy census function. We also relate a set's property of having an easy census function to other well-studied properties of sets, such as rankability and scalability (the closure of the rankable sets under P-isomorphisms). Finally, we prove that it is no more likely that the census function of any set in P can be approximated (more precisely, can be nα -enumerated in time nβ for fixed α and β) than that it can be precisely computed in polynomial time.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages483-492
Number of pages10
Volume1450 LNCS
StatePublished - 1998
Externally publishedYes
Event23rd International Symposium on the Mathematical Foundations of Computer Science, MFCS 1998 - Brno, Czech Republic
Duration: Aug 24 1998Aug 28 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1450 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other23rd International Symposium on the Mathematical Foundations of Computer Science, MFCS 1998
CountryCzech Republic
CityBrno
Period8/24/988/28/98

Fingerprint

Tally
Census
Property of set
Polynomials
Polynomial time
Polynomial Hierarchy
Scalability
Isomorphism
Count
Closure
Likely
If and only if
Imply

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Goldsmith, J., Ogihara, M., & Rothe, J. (1998). Tally NP sets and easy census functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1450 LNCS, pp. 483-492). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1450 LNCS).

Tally NP sets and easy census functions. / Goldsmith, Judy; Ogihara, Mitsunori; Rothe, Jörg.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1450 LNCS 1998. p. 483-492 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1450 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Goldsmith, J, Ogihara, M & Rothe, J 1998, Tally NP sets and easy census functions. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1450 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1450 LNCS, pp. 483-492, 23rd International Symposium on the Mathematical Foundations of Computer Science, MFCS 1998, Brno, Czech Republic, 8/24/98.
Goldsmith J, Ogihara M, Rothe J. Tally NP sets and easy census functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1450 LNCS. 1998. p. 483-492. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Goldsmith, Judy ; Ogihara, Mitsunori ; Rothe, Jörg. / Tally NP sets and easy census functions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1450 LNCS 1998. pp. 483-492 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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