Relationships among PL, #L, and the determinant

Eric Allender, Mitsunori Ogihara

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the determinant is characterized by the complexity of counting the number of accepting computations of a nondeterministic logspace-bounded machine. (This class of functions is known as #L.) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of a theorem of Jung, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalTheoretical Informatics and Applications
Issue number1
StatePublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Science Applications


Dive into the research topics of 'Relationships among PL, #L, and the determinant'. Together they form a unique fingerprint.

Cite this