A higher-order characterization of probabilistic polynomial time
We present RSLR, an implicit higher-order characterization of the class PP of those problems which can be decided in probabilistic polynomial time with error probability smaller than 12. Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extension of Hofmann...
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| Published in: | Information and computation Vol. 241; pp. 114 - 141 |
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| Language: | English |
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01.04.2015
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| Abstract | We present RSLR, an implicit higher-order characterization of the class PP of those problems which can be decided in probabilistic polynomial time with error probability smaller than 12. Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extension of Hofmann's SLR with a probabilistic primitive, which enjoys basic properties such as subject reduction and confluence. Polynomial time soundness of RSLR is obtained by syntactical means, as opposed to the standard literature on SLR-derived systems, which use semantics in an essential way. |
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| AbstractList | We present RSLR, an implicit higher-order characterization of the class PP of those problems which can be decided in probabilistic polynomial time with error probability smaller than 12. Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extension of Hofmann's SLR with a probabilistic primitive, which enjoys basic properties such as subject reduction and confluence. Polynomial time soundness of RSLR is obtained by syntactical means, as opposed to the standard literature on SLR-derived systems, which use semantics in an essential way. We present RSLR, an implicit higher-order characterization of the class PP of those problems which can be decided in probabilistic polynomial time with error probability smaller than 1 /2. Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extension of Hofmann's SLR with a probabilistic primitive, which enjoys basic properties such as subject reduction and confluence. Polynomial time soundness of RSLR is obtained by syntactical means, as opposed to the standard literature on SLR-derived systems, which use semantics in an essential way. |
| Author | Parisen Toldin, Paolo Dal Lago, Ugo |
| Author_xml | – sequence: 1 givenname: Ugo surname: Dal Lago fullname: Dal Lago, Ugo email: dallago@cs.unibo.it – sequence: 2 givenname: Paolo surname: Parisen Toldin fullname: Parisen Toldin, Paolo email: parisent@cs.unibo.it |
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| Keywords | Probabilistic classes Implicit computational complexity Linear types Lambda calculus |
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| References | Dal Lago, Masini, Zorzi (br0060) 2010; 411 Hofmann (br0080) 1997; vol. 1414 Leivant (br0020) 1993 Leivant, Marion (br0030) 1995; vol. 933 Mitchell, Mitchell, Scedrov (br0110) 1998 Bellantoni, Cook (br0010) 1992; 2 Bonfante, Kahle, Marion, Oitavem (br0050) 2008; vol. 5213 Zhang (br0120) 2010; 20 Fortnow, Santhanam (br0150) 2004 Arora, Barak (br0160) 2009 Schwichtenberg, Bellantoni (br0140) 2001 Bellantoni (br0090) 1995 Bellantoni, Niggl, Schwichtenberg (br0130) 2000; 104 Jones (br0040) 1999; 228 Dal Lago, Martini, Sangiorgi (br0070) 2010; vol. 41 Gill (br0100) 1977; 6 Bonfante (10.1016/j.ic.2014.10.009_br0050) 2008; vol. 5213 Hofmann (10.1016/j.ic.2014.10.009_br0080) 1997; vol. 1414 Zhang (10.1016/j.ic.2014.10.009_br0120) 2010; 20 Bellantoni (10.1016/j.ic.2014.10.009_br0010) 1992; 2 Bellantoni (10.1016/j.ic.2014.10.009_br0130) 2000; 104 Arora (10.1016/j.ic.2014.10.009_br0160) 2009 Leivant (10.1016/j.ic.2014.10.009_br0020) 1993 Jones (10.1016/j.ic.2014.10.009_br0040) 1999; 228 Leivant (10.1016/j.ic.2014.10.009_br0030) 1995; vol. 933 Dal Lago (10.1016/j.ic.2014.10.009_br0060) 2010; 411 Fortnow (10.1016/j.ic.2014.10.009_br0150) 2004 Schwichtenberg (10.1016/j.ic.2014.10.009_br0140) 2001 Dal Lago (10.1016/j.ic.2014.10.009_br0070) 2010; vol. 41 Mitchell (10.1016/j.ic.2014.10.009_br0110) 1998 Bellantoni (10.1016/j.ic.2014.10.009_br0090) 1995 Gill (10.1016/j.ic.2014.10.009_br0100) 1977; 6 |
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| Title | A higher-order characterization of probabilistic polynomial time |
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