TY - GEN

T1 - Relationships among PL, #L, and the determinant

AU - Allender, Eric

AU - Ogihara, Mitsunori

PY - 1994/12/1

Y1 - 1994/12/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:0028599687

SN - 0818656727

T3 - Proceedings of the IEEE Annual Structure in Complexity Theory Conference

SP - 267

EP - 278

BT - Proceedings of the IEEE Annual Structure in Complexity Theory Conference

A2 - Anon, null

PB - Publ by IEEE

T2 - Proceedings of the 9th Annual Structure in Complexity Theory Conference

Y2 - 28 June 1994 through 1 July 1994

ER -