Laszlo Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254-- 276, 1988. Home/Search Document Not in Database Summary Related Articles Check |
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Polynomial-Time Normalizers for Permutation Groups With.. - Luks, Miyazaki (2002) (Correct)
....of them. So it is not surprising that, despite continued improvements in practical implementations, none of these problems is known to be solvable in polynomial time. Nevertheless, as with ISO [27] there is compelling evidence that the decision versions of these problems are not NP complete [5]. This has motivated extensive investigation into polynomial time computability for permutation group problems in general (see [13] 19] for surveys) but especially for Problems A D. Now, aside from the overall reducibility between the above problems, solutions geared to special group classes ....
L. BABAI and S. MORAN, Arthur--Merlin games: a randomized proof system and a hierarchy of complexity classes, J. Comput. System Sci. 36 (1988), 254--276.
Algebraic Geometry Over Four Rings and the Frontier to Tractability - Rojas (Correct)
....BPP. 14 Recall also that when a BPP algorithm is augmented by an NP oracle, and the number of oracle destined bits is always polynomial in the input size, one obtains the class BPP NP . Finally, when just one oracle call is allowed in a BPP NP algorithm, one obtains the ArthurMerlin class AM [Zac86, BM88]. Theorem 3. Koi96] Assuming the truth of GRH, HN2AM. While probabilistic algorithms for HN (and more general problems) have certainly existed at least since the early 1980 s, the above theorem is the rst and only example of a randomized algorithm for HN requiring a number of bit operations ....
....or the algorithm from section 2, is that it could happen that P 6=NP but the higher complexity classes we have been alluding to all collapse to the same level. For example, while it is known that NP[BPP AM P NP NP NP NP NP PSPACE, the properness of each inclusion is still unknown [Zac86, BM88, BF91, Pap95]. The algorithm for theorem 13 is almost as simple as the algorithm for theorem 4 given earlier, and can be outlined as follows: Step 0 Let NF (x) denote the weighted version of F (x) where we instead sum the total 28 number of roots in Z=pZ of the mod p reductions of F over all primes p x. ....
Babai, Laszlo and Moran, Shlomo, \Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes," Journal of Computer and System Sciences, 36:254{ 276, 1988.
On the Knowledge Complexity of ... - Petrank, Tardos (Correct)
....with logarithmic knowledgecomplexity are in AM co AM. The class AM is the class of languages that have two round Arthur Merlin proofs, or equivalently, have a constant round interactive proof. There is no restriction on the knowledge complexity of this constant round interactive proof. See [BM 88, GS 89] for de nitions of Arthur Merlin proofs, for some basic properties, and for the equivalence of the de nitions. It was shown in [BHZ 87] that if NP co AM then the polynomial time hierarchy collapses. It is believed that the polynomial time hierarchy does not collapse, and under this ....
....the interaction between P and V and thus ProbM [A] 2 k Prob (P;V) A] 2 (k 2) and we are done with the proof of part 2 of Lemma 5.1. 6 The main theorem We now use the above machinery to introduce a constant round interactive proof for the language L and its complement. Using [GS 89, BM 88] we get that L is in AM co AM. Formally, we prove the following theorem. Theorem 3 SKC(O(logn) AM coAM 18 We will only show that PKC(O(logn) AM co AM since it was shown in [GOP 94] see Theorem 1) that SKC(O(logn) PKC(O(logn) We remark that the theorem in [GOP 94] only ....
L. Babai and S. Moran. Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes. JCSS, Vol. 36, pages 254-276, 1988.
On Helping and Interactive Proof Systems - Arvind, Köbler, Schuler (1995) (2 citations) (Correct)
....a two round protocol starting with a message from Merlin is an apparently smaller class than AM. It turned out that the Arthur Merlin games model of computation is as powerful as the general interactive proof systems. In fact any interactive proof system can be simulated by an Arthur Merlin game [GS86, BM88] without increasing the number of rounds. In general the notation AM is used to denote single prover interactive proof systems with a constant number of interaction, whereas IP is used if there is no restriction. Following the advances made in [LFKN92] it was finally shown in [Sh90] that PSPACE = ....
L. Babai and S. Moran. Arthur-Merlin games: a randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences 36:254-276, 1988.
If NP has Polynomial-Size Circuits, then MA = AM - Arvind, Köbler, Schöning.. (1995) (1 citation) (Correct)
....Q Qk 6 6 6 6 6 6 6 Q Q Q Q Qk j j j j j3 H H H H H HY Phi Phi Phi Phi Phi Phi j j j j j j j j j j j j3 Q Q Q Q Q Q Q Q Q Q Q Qk . co NP BPP NP BPP 6 6 Figure 1: Classes of the polynomial time and the Arthur Merlin hierarchy. The classes MA and AM have been introduced in [BM88] as classes of the ArthurMerlin hierarchy. Their definition can be stated as follows. A set A is in MA if there is a predicate B 2 P such that for all strings x the following holds: x 2 A ) 9y P r[ hx; y; zi 2 B ] 3=4; x 62 A ) 8y P r[ hx; y; zi 2 B ] 1=4: A set A is in AM if there is a ....
....9y hx; y; zi 2 B ] 1=4: In both definitions all strings y; z are of some polynomial length in jxj, say p(jxj) where z is chosen uniformly at random from all the strings of that length. The following inclusion relations are known: NP BPP MA AM Pi P 2 , and MA Sigma P 2 Pi P 2 [BM88]. Figure 1 contains all known inclusions. As preparation to the forthcoming proof, we observe (as in [Ho81] that any (nonuniform) family of circuits for the NP complete set SAT can be converted into a new (non uniform) circuit family in which the circuits are still polynomial in their input 2 P ....
L. Babai and S. Moran. Arthur-Merlin games: a randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences 36 (1988) 254--276.
A Complete Problem for Statistical Zero Knowledge - Sahai, Vadhan (2000) (Correct)
....cast as deciding whether a pair of eciently samplable distributions are statistically close or far apart. The starting point for our proof of the Completeness Theorem is a powerful theorem of Okamoto [Oka00] which states that all languages in SZK have public coin (also known as Arthur Merlin [BM88] statistical zero knowledge proofs. Using the approach pioneered by Fortnow [For89] we analyze the simulator of such a proof system and show that statistical properties of the simulator s output distribution can be used to distinguish between yes and no instances of the problem in ....
Laszlo Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254-276, 1988.
Playing Savitch. - Boas (Correct)
....initial results may have been so nice that people believed the problem to be solved: games characterize PSPACE . Also subsequent investigations involved more complex situations, including probabilistic moves, and even incomplete information as exemplified by the theory of interactive proof systems [1, 10], Zero Knowledge systems [7] and their multi party generalizations. Evidently the idea of considering games to be a computational model accepting languages or solving problems (the Games as acceptors paradigm) has not captured the minds of the theoreticians or our colleagues developing agent ....
Babai, L. & Moran, S., Arthur-Merlin Games: a Randomized Proof System and a Hierarchy of Complexity Classes, J. Comput. Syst. Sci., 36, 1988, 254-276.
On the Interactive Complexity of Graph Reliability - Jean-Marc Couveignes Juan (Correct)
....Shamir [8] extended their technique to prove that IP coincides with the complexity class PSPACE: One of the important parameters of an interactive proof system is the number of rounds, that is the number of messages exchanged between the prover and the verifier. Babai and Moran have proven [3] that the number of rounds in an unbounded interactive proof system can be reduced by a constant factor. Babai [1] has shown that bounded round interactive proof systems can be simulated by a protocol in just two round, where the first ENS, LIENS, 45, rue d Ulm, 75005 Paris, France. y CNRS, URA ....
L. Babai and S. Moran (1988), Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes, Journal of Computer and System Sciences 36, 254-276.
New Collapse Consequences Of NP Having Small Circuits - Köbler, Watanabe (1998) (Correct)
....hand, Harry Buhrman [12] and independently Thomas Thierauf [36] pointed out to us that Theorem 4.8 (which is proved by a nonrelativizable proof technique) can be used to show that MA exp #co MA exp contains non P poly sets. Here, MA exp denotes the exponential time version of Babai s class MA [5]. That is, MA exp = MA[2 n O(1) where a language L is in MA[f(n) if there exists a set B # DTIME[O(n) such that for all x of length n, x # L # #y, y = f(n) Pr[#x, y, z# # B] 2 3, x ## L # #y, y = f(n) Pr[#x, y, z# # B] 1 3, where z is chosen uniformly at random ....
L. Babai and S. Moran, Arthur-merlin games: A randomized proof system and a hierarchy of complexity classes, J. Comput. System Sci., 36 (1988), pp. 254--276.
Locally Random Reductions in Interactive Complexity Theory - Feigenbaum (1993) (14 citations) (Correct)
....Fortnow have made some progress on this question. 23 Theorem 7.3 [FF] If any NP complete set is nonadaptively rsr, then the polynomialtime hierarchy collapses at the third level. Sketch of proof: We use the notation AM(r) to denote the class of sets accepted by r move Arthur Merlin games [BM]. The prover Merlin is denoted by P and the verifier Arthur by V ; a cheating prover is denoted by P . The class AM(r) poly consists of all sets accepted by r move Arthur Merlin games in which the verifier is given nonuniform, polynomial size advice as well as probabilistic polynomial time. Let ....
L. Babai and S. Moran. Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes, J. Comput. System Sci. 36 (1988), 254--276.
Zero Knowledge and Soundness are Symmetric - Shien Jin Ong (Correct)
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Laszlo Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254-- 276, 1988.
Derandomization in Cryptography - Barak, Ong, Vadhan (2005) (Correct)
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Laszlo Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254-- 276, 1988.
A Relationship between One-Wayness and Correlation Intractability - Hada, Tanaka (1999) (2 citations) (Correct)
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L. Babai and S. Moran, "Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes," J. Comput. System Sci., 36, pp.254-276, 1988.
Comparing Entropies in Statistical Zero-Knowledge with.. - Goldreich, Vadhan (1998) (6 citations) (Correct)
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L'aszl'o Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254--276, 1988.
Lower Bounds for Non-Black-Box Zero Knowledge - Barak, Lindell, Vadhan (2004) (1 citation) (Correct)
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L. Babai and S. Moran. Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes. J. Comput. Syst. Sci., 36:254--276, 1988.
Probabilistically Checkable Debate Systems and - Approximation Algorithms For (1993) (Correct)
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L. Babai and S. Moran, Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes, J. Comput. System Sci., 36 (1988), pp. 254--276.
Interactive Verification of co-NP Statements - March In This (Correct)
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L. Babai, S. Moran. "Arthur-Merlin games: a randomized proof system and a hierarchy of complexity classes". JCSS, Vol. 36, No. 2, pp. 254276, 1988.
Making Games Short (Extended Abstract) - Feige, Kilian (Correct)
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L. Babai, S. Moran. "Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity classes." J. Computer and Sys. Sci. 36 (1988), 254--276.
Uniform hardness vs. randomness tradeoffs for Arthur-Merlin .. - Gutfreund, Shaltiel, al. (Correct)
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L. Babai and S. Moran. Arthur-merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254--276, 1988.
A Complete Problem for Statistical Zero Knowledge - Sahai, Vadhan (2002) (Correct)
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Laszlo Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254-276, 1988. 44
Unknown - (Correct)
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Babai, Laszlo and Moran, Shlomo, \Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes," Journal of Computer and System Sciences, 36:254-276, 1988.
On the Power of Finite Automata with both Nondeterministic - And Probabilistic States (Correct)
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L. Babai and S. Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes, J. Comput. System Sci., 36 (1988), 254--276.
Statistical Zero-Knowledge Languages Can Be Recognized in Two.. - Aiello, Hastad (1991) (24 citations) (Correct)
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Babai L. and S. Moran, "Arthur Merlin Games: a Randomized Proof System and a Hierarchy of Complexity Classes," JCSS, Vol. 36 (1988), No. 2, pp 254--276.
Probabilistic Proof Systems - Part I - Vadhan (2000) (Correct)
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Laszlo Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254-276, 1988.
Statistical Zero-Knowledge Languages Can Be Recognized in Two.. - Aiello, Hastad (1991) (24 citations) (Correct)
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Babai L. and S. Moran, "Arthur Merlin Games: a Randomized Proof System and a Hierarchy of Complexity Classes," JCSS, Vol. 36 (1988), No. 2, pp 254--276.
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