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Home > Art, Film & Photography > Probabilistic Complexity Classes: BPP, Bqp, Rp, Zpp, IP, Postbqp, Pp, Qma, Rl, Bpl, Awpp, Zpl, Qcma, Am, Ma
Probabilistic Complexity Classes: BPP, Bqp, Rp, Zpp, IP, Postbqp, Pp, Qma, Rl, Bpl, Awpp, Zpl, Qcma, Am, Ma

Probabilistic Complexity Classes: BPP, Bqp, Rp, Zpp, IP, Postbqp, Pp, Qma, Rl, Bpl, Awpp, Zpl, Qcma, Am, Ma


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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Bpp, Bqp, Rp, Zpp, Ip, Postbqp, Pp, Qma, Rl, Bpl, Awpp, Zpl, Qcma, Am, Ma, Co-Rp. Excerpt: In computational complexity theory, an Arthur Merlin protocol is an interactive proof system in which the verifier's coin tosses are constrained to be public (i.e. known to the prover too). This notion was introduced by Babai (1985). Goldwasser and Sipser (1986) proved that all languages with interactive proofs of arbitrary length with private coins also have interactive proofs with public coins. The basic assumption is that Arthur is a standard computer (or verifier) equipped with a random number generating device, while Merlin is effectively an oracle with infinite computational power (also known as a prover); but Merlin is not necessarily honest, so Arthur must analyze the information provided by Merlin in response to Arthur's queries and decide the problem itself. A problem is considered to be solvable by this protocol if whenever the answer is "yes," Merlin has some series of responses which will cause Arthur to accept at least 2/3 of the time, and if whenever the answer is "no," Arthur will never accept more than 1/3 of the time. Thus, Arthur acts as a BPP verifier, assuming it is allotted polynomial time to make its decisions and queries. MA The simplest such protocol is the 1-message protocol where Merlin sends Arthur a message, and then Arthur decides whether to accept or not by running a probabilistic polynomial time computation. (This is similar to the verifier-based definition of NP, the only difference being that Arthur is allowed to use randomness here.) Merlin does not have access to Arthur's coin tosses in this protocol, since it is a single message protocol and Arthur tosses his coins only after receiving Merlin's message. This protocol is called MA . Informally, a lang...


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Product Details
  • ISBN-13: 9781155256306
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: BPP, Bqp, Rp, Zpp, IP, Postbqp, Pp, Qma, Rl, Bpl, Awpp, Zpl, Qcma, Am, Ma
  • Width: 229 mm
  • ISBN-10: 1155256301
  • Publisher Date: 02 May 2010
  • Binding: Paperback
  • Spine Width: 5 mm
  • Weight: 127 gr


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