Conventional type systems specify interfaces in terms of values and domains.

Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computationally intractable. The approach is to generate the normal form of the game (the matrix containing the payoff for each strategy combination), and then solve a linear program (LP) or a linear complementarity problem (LCP). The size of the normal form, however, is typically exponential in the size of the game tree, thus making this method impractical in all but the simplest cases. This paper describes a new representation of strategies which results in a practical linear formulation of the problem of two-player games with perfect recall (i.e., games where players never forget anything, which is a standard assumption). Standard LP or LCP solvers can then be applied to find optimal randomized strategies. The resulting algorithms are, in general, exponentially better than the standard ones, both in terms of time and in terms of space.

Even if access to the internal structure of the tested system is possible, it is not always a good idea to use it when performing tests, as this may lead to a bias in the testing process. Furthermore, the

We consider the problem of synthesizing controllers for timed systems modeled using timed automata. The point of departure from earlier work is that we consider controllers that have only a partial observation of the system that it controls. In discrete event systems (where continuous time is not modeled), it is well known how to handle partial observability, and decidability issues do not differ from the complete information setting. We show however that timed control under partial observability is undecidable even for internal specifications (while the analogous problem under complete observability is decidable) and we identify a decidable subclass.

Abstract. When we verify the correctness of an open system with respect to a desired requirement, we should take into consideration the different environments with which the system may interact. Each environment induces a different behavior of the system, and we want all these behaviors to satisfy the requirement. Module checking is an algorithmic method that checks, given an open system (modeled as a finite structure) and a desired requirement (specified by a temporal-logic formula), whether the open system satisfies the requirement with respect to all environments. In this paper we extend the module-checking method with respect to two orthogonal issues. Both issues concern the fact that often we are not interested in satisfaction of the requirement with respect to all environments, but only with respect to these that meet some restriction. We consider the case where the environment has incomplete information about the system; i.e., when the system has internal variables, which are not readable by its environment, and the case where some assumptions are known about environment; i.e., when the system is guaranteed to satisfy the requirement only when its environment satisfies certain assumptions. We study the complexities of the extended module-checking problems. In particular, we show that for universal temporal logics (e.g., LTL, ¥ CTL, and ¥ CTL ¦), module checking with incomplete information coincides with module checking, which by itself coincides with model checking. On the other hand, for non-universal temporal logics (e.g., CTL and CTL ¦), module checking with incomplete information is harder than module checking, which is by itself harder than model checking. 1

Abstract. We propose and evaluate a new algorithm for checking the universality of nondeterministic finite automata. In contrast to the standard algorithm, which uses the subset construction to explicitly determinize the automaton, we keep the determinization step implicit. Our algorithm computes the least fixed point of a monotone function on the lattice of antichains of state sets. We evaluate the performance of our algorithm experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, the antichain algorithm outperforms the standard one by several orders of magnitude. We also show how variations of the antichain method can be used for solving the language-inclusion problem for nondeterministic finite automata, and the emptiness problem for alternating finite automata. 1

Game-theoretic characterizations of complexity classes have often proved useful in understanding the power and limitations of these classes. One well-known example tells us that PSPACE can be characterized by two-person, perfect-information games in which the length of a played game is polynomial in the length of the description of the initial position [Chandra et al., Journal of the ACM, 28 (1981), pp. 114--133]. In this paper, we investigate the connection between game theory and interactive computation. We formalize the notion of a polynomially definable game system for the language L, which, informally, consists of two arbitrarily powerful players P 1 and P 2 and a ...

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We study competing-prover one-round interactive proof systems. We show that one-round proof systems in which the first prover is trying to convince a verifier to accept and the second prover is trying to make the verifier reject recognize languages in NEXPTIME, and, with restrictions on communication and randomness, languages in NP. We extended the restricted model to an alternating sequence of k competing provers, which we show characterizes \Sigma P k\Gamma1 . Alternating oracle proof systems are also examined.

This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof system also has a quantum refereed game in which the verifier exchanges just one round of messages with each prover. A key part of our proof is the fact that there exists a single quantum measurement that reliably distinguishes between mixed states chosen arbitrarily from disjoint convex sets having large minimal trace distance from one another. We also show how to reduce the probability of error for some classes of quantum refereed games. 1