Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 1-21 |
| Number of pages | 21 |
| Journal | Theoretical Informatics and Applications |
| Volume | 30 |
| Issue number | 1 |
| State | Published - 1996 |
| Externally published | Yes |
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Relationships among PL, #L, and the determinant. / Allender, Eric; Ogihara, Mitsunori.
In: Theoretical Informatics and Applications, Vol. 30, No. 1, 1996, p. 1-21.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Relationships among PL, #L, and the determinant
AU - Allender, Eric
AU - Ogihara, Mitsunori
PY - 1996
Y1 - 1996
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.
UR - http://www.scopus.com/inward/record.url?scp=0030554482&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0030554482&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0030554482
VL - 30
SP - 1
EP - 21
JO - RAIRO - Theoretical Informatics and Applications
JF - RAIRO - Theoretical Informatics and Applications
SN - 0988-3754
IS - 1
ER -