G.L. Peterson and J.H. Reif. Multiple-person alternation. In Proc. 20th IEEE Symp. on FOCS, pages 348-363, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem can also be e ectively solved in this important setting, where the speci cations at the sites can state properties of the internal channels as well. The undecidability result of [PR90] follows from the study of multi player games of incomplete information by Peterson and Reif [PR79]. In this context, our results show that there are certain games where two players, playing against an adversary, have incomplete information about each other, and yet determining whether they have a winning strategy is decidable. In the next section we introduce the formal setting for our work, ....

G.L. Peterson and J.H. Reif. Multiple-person alternation. In Proc. 20th IEEE Symp. on FOCS, pages 348-363, 1979.

....which is not guaranteed to work. The second approach is to refer to the architecture of the distributed system from the outset and construct the underlying processes directly [PR90] Results on multi player games imply that the realizability problem for general distributed systems is undecidable [PR79, PR90] (the results in [PR79] refer to multiple person alternating Turing machines and are extended in [PR90] to the synthesis setting) Essentially, there is an architecture (in fact, a very simple architecture, consisting of two independent processes P 1 and P 2 that interact with the same ....

.... The second approach is to refer to the architecture of the distributed system from the outset and construct the underlying processes directly [PR90] Results on multi player games imply that the realizability problem for general distributed systems is undecidable [PR79, PR90] the results in [PR79] refer to multiple person alternating Turing machines and are extended in [PR90] to the synthesis setting) Essentially, there is an architecture (in fact, a very simple architecture, consisting of two independent processes P 1 and P 2 that interact with the same environment; that is I 1 (O 2 [ ....

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G.L. Peterson and J.H. Reif. Multiple-person alternation. In Proc. 20st IEEE Symp. on Foundation of Computer Science, pp. 348-363, 1979.

....problems, the problems we studied provably do not admit polynomial time algorithms, since P 6= NEXP. Second, we have drawn a connection between work on Markov decision processes and the body of work in complexity theory that deals with the exponential jump in complexity due to decentralization (Peterson Reif, 1979; Babai, Fortnow Lund, 1991) There are also more direct implications for researchers trying to solve problems of this nature. Consider the growing body of work on algorithms for obtaining exact or approximate solutions for POMDPs (e.g. Jaakkola, Singh Jordan, 1995; Cassandra, Littman ....

Peterson, G. L. & Reif, J. R. (1979). Multiple-person alternation. In 20th Annual Symposium on Foundations of Computer Science (pp. 348-363).

....problems, the problems we studied provably do not admit polynomial time algorithms, since P 6= NEXP. Second, we have drawn a connection between work on Markov decision processes and the body of work in complexity theory that deals with the exponential jump in complexity due to decentralization (Peterson Reif, 1979; Babai et al. 1991) Finally, the two agent DEC MDP case yields an interesting open problem. The solution of the problem may imply that the difference between planning for two agents and planning for more than two agents is a significant one in the case where the state is collectively observed ....

Peterson, G. L. & Reif, J. R. (1979). Multiple-person alternation. In 20th Annual Symposium on Foundations of Computer Science (pp. 348--363).

....identical to the model checking problem for the ATL formula hhAii3p on a turn based synchronous ATS with incomplete information. ut We note that for Fair ATL, proving undecidability is easier, and follows from undecidability results on asynchronous multi player games with incomplete information [PR79, PR90] 7.3 Single agent ATL with Incomplete Information Single agent ATL is the fragment of ATL in which every path quantifier is parameterized by a singleton set of agents. In this case, where agents cannot cooperate, the model checking problem is decidable also for incomplete information. ....

G.L. Peterson and J.H. Reif. Multiple-person alternation. In Proc. 20st IEEE Symposium on Foundation of Computer Science, pages 348--363, 1979.

....of the history and (2) decide only on the observable part of the next state. From undecidability results on multiplayer games with incomplete information, it follows that the model checking problem for ATL with incomplete information is undecidable in both the synchronous [Yan97] and asynchronous [PR79] cases. In the special case that all path quantifiers are parameterized by single agents, and no cooperation between agents with different information is possible, decidability follows from the results on module checking with incomplete information [KV97] In this case, the model checking ....

G.L. Peterson, J.H. Reif. Multiple-person alternation. Proc. IEEE FOCS, pp. 348--363, 1979.

....answers to these questions. One interesting aspect of items 2 and 3 is that they use both results and proof techniques from recent papers on the complexity of solving games [KMvS94, Ne91] Imperfect information games have been considered in several previous works in complexity theory, including [C89, CL86, KLRSS94, PR79, Re84]. A crucial difference between these works and ours is that the opposing players in [C89, CL86, KLRSS94, PR79, Re84] use deterministic (pure) strategies, whereas ours use randomized (mixed) strategies. 1 (These and other game theoretic terms are formally defined in the next section. We claim ....

.... from recent papers on the complexity of solving games [KMvS94, Ne91] Imperfect information games have been considered in several previous works in complexity theory, including [C89, CL86, KLRSS94, PR79, Re84] A crucial difference between these works and ours is that the opposing players in [C89, CL86, KLRSS94, PR79, Re84] use deterministic (pure) strategies, whereas ours use randomized (mixed) strategies. 1 (These and other game theoretic terms are formally defined in the next section. We claim that allowing the players to use mixed strategies is a fundamental part of the game theoretic paradigm. Language ....

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G. Peterson and J. Reif, "Multiple Person Alternation," Proceedings of the 20th Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, 1979, pp. 348--363.

....We have been able to treat the case of single agent knowledge based specifications in this paper. Is it possible to generalize our results to the multi agent case In general, it is not. Using ideas from Peterson and Reif s study of the complexity of multi agent games of incomplete information [28], Pnueli and Rosner [31] show that realizability of linear temporal logic specifications in the context of two agents with incomplete information is undecidable. This result immediately applies to our more expressive specification language. However, there are limited classes of situations in which ....

G.L. Peterson and J.H. Reif. Multiple-person alternation. In Proc. 20st IEEE Symposium on Foundation of Computer Science, pages 348--363, 1979.

....and the provers responses are constant size. We show that two competing prover proof systems have similar power. Stockmeyer [St77] used games between competing players to characterize languages in the polynomialtime hierarchy. Other uses of competing players to study complexity classes include [Reif84, PR79]. Feige, Shamir and Tennenholtz [FST88] proposed an interactive proof system in which the notion of competition is present. Recently, Condon, Feigenbaum, Lund and Shor [CFLS93a, CFLS93b] characterized PSPACE by systems in which a verifier with O(log n) random bits can read only a constant number ....

G. Peterson, and J. Reif. "Multiple-person alternation". In Proc. of the 20th IEEE FOCS, pages 348-363, 1979.

....1.1 and the result that IP = PSPACE have the same flavor of replacing universal quantification by probabilistic quantification. PSPACE is exactly the class of languages accepted by a game between two players, one who makes existential moves and the other makes universal moves. Peterson and Reif [32] show that NEXP can be described by a game with three players, two existential players unable to communicate and one universal player who communicates with the other two. Simon [36] and Orponen [30] describe a game between an existential oracle and a universal player and show the equivalence to ....

....and x an input of length n for the membership problem in L. We construct in polynomial time an instance (B; r; s) of oracle 3 satisfiability which is accepted if and only if x 2 L. The first part of this construction is essentially due to J. Simon [36] similar proofs appear in Peterson Reif [32] and Orponen [30] describing NEXP analogues of the Cook Levin theorem (NP completeness of 3 SAT) Let M be the NEXP Turing machine accepting L. Look at the tableau describing the computation of M on input x. Convert this to a 3 CNF Phi x like in the proof of the Cook Levin theorem. There ....

G. Peterson and J. Reif, Multiple-person alternation, Proc. 20th Ann. IEEE Symp. Foundations of Comp. Sci., 1979, 348-363. 38 Babai, Fortnow & Lund

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Gary L. Peterson and John H. Reif. Multiple-person alternation. In Proceedings of 20th IEEE Symposium on Foundations of Computer Science, pages 348--363, October 1979.

....Science Department, Duke University, Durham, NC 27706, U.S.A. Salman AZHAR Computer Science Department, Duke University, Duke University, Durham, NC 27706, U.S.A. Abstract Extending the complexity results of Reif [1, 2] for two player games of incomplete information, this paper (also see [3]) presents algorithms for deciding the outcome for various classes of multiplayer games of incomplete information, i.e. deciding whether or not a team has a winning strategy for a particular game. Our companion paper (Peterson, Reif, and Azhar [4] shows that these algorithms are indeed ....

....lower bounds. The classes of games to which our algorithms are applicable include games which were not previously known to be decidable. We apply our algorithms to provide alternative upper bounds, and new time space trade offs on the complexity of multi person alternating Turing machines [3]. We analyze the algorithms to characterize the space complexity of multiplayer games in terms of the complexity of deterministic computation on Turing machines. In hierarchical multiplayer games each additional clique (subset of players with the same information) increases the complexity of ....

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Gary L. Peterson and John H. Reif. Multiple-person alternation. In Proceedings of 20th IEEE Symposium on Foundations of Computer Science, pages 348--363, October 1979.

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Gary L. Peterson and John H. Reif, "Multiple-Person Alternation", in Proceedings of 20th IEEE Symposium on Foundations of Computer Science, pages 348-363, October 1979.

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Gary L. Peterson and John H. Reif, "Multiple-Person Alternation", in Proceedings of 20th IEEE Symposium on Foundations of Computer Science, pages 348-363, October 1979.

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