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

We classify component-based models of computation into component models and interface models. A component model specifies for each component how the component behaves in an arbitrary environment; an interface model specifies for each component what the component expects from the environment.

We present a theory of timed interfaces, which is capable of specifying both the timing of the inputs a component expects from the environment, and the timing of the outputs it can produce. Two timed interfaces are compatible if there is a way to use them together such that their timing expectations are met. Our theory provides algorithms for checking the compatibility between two interfaces and for deriving the composite interface; the theory can thus be viewed as a type system for real-time interaction. Technically, a timed interface is encoded as a timed game between two players, representing the inputs and outputs of the component. The algorithms for compatibility checking and interface composition are thus derived from algorithms for solving timed games.

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A procedure for the analysis of state spaces is called symbolic if it manipulates not individual states, but sets of states that are represented by constraints. Such a procedure can be used for the analysis of infinite state spaces, provided termination is guaranteed. We present symbolic procedures, and corresponding termination criteria, for the solution of infinite-state games, which occur in the control and modular verification of infinite-state systems. To characterize the termination of symbolic procedures for solving infinite-state games, we classify these game structures into four increasingly restrictive categories: 1. Class 1 consists of infinite-state structures for which all safety and reachability games can be solved...

We draw parallels between coalition game logics developed in [Pauly, 2000b] and [Pauly, 2000c] on one hand, and alternating-time temporal logics of computations in-troduced in [Alur et al, 97] on the other. In particular, we show equivalence of their semantics, embedding of coalition game logics into alternating-time temporal logic, and propose axiomatic systems for these logics. 1

Abstract. An open system is a system whose behavior is jointly determined by its internal structure, and by the input it receives from the environment. To solve control and verification problems, open systems have often been modeled as games between the system and the environment; we argue that the game view of open systems should be extended also to the definitions of system refinement and composition. We give a symmetrical interpretation to games between system and environment: the moves of the system represent the outputs that the system can generate (the output guarantees), and symmetrically, the moves of the environment represent the inputs that the system can accept (the input assumptions). We argue in favor of defining refinement of open systems in terms of alternating simulation, which is the relation between games that plays the same role of simulation between transition systems. Alternating simulation captures the principle that a component refines another if it has weaker input assumptions, and stronger output guarantees. Furthermore, we argue in favor of a notion of composition that accounts for the compatibility between input assumptions and output guarantees, and that enables the synthesis of new input guarantees for the composed system. These game-theoretical notions of refinement and compatibility are related to the type-theoretical notions of subtyping and type compatibility, and give rise to an expressive modeling framework for component-based design and verification. 1

In order to study control problems for hybrid systems, we generalize hybrid automata to hybrid games -- say, controller vs. plant. If we specify the continuous dynamics by constant lower and upper bounds, we obtain rectangular games. We show that for rectangular games with objectives expressed in Ltl (linear temporal logic), the winning states for each player can be computed, and winning strategies can be synthesized. Our result is sharp, as already reachability is undecidable for generalizations of rectangular systems, and optimal -- singly exponential in the size of the game structure and doubly exponential in the size of the Ltl objective. Our proof systematically generalizes the theory of hybrid systems from automata (single-player structures) [9] to games (multi-player structures): we show that the successively more general infinite-state classes of timed, 2d rectangular, and rectangular games induce successively weaker, but still finite, quotient structures called game bisimilarity, game similarity, and game trace equivalence. These quotients can be used, in particular, to solve the Ltl control problem.

Abstract — We present an approach to automatic synthesis of specifications given in Linear Time Logic. The approach is based on a translation through universal co-Büchi tree automata and alternating weak tree automata [1]. By careful optimization of all intermediate automata, we achieve a major improvement in performance. We present several optimization techniques for alternating tree automata, including a game-based approximation to language emptiness and a simulation-based optimization. Furthermore, we use an incremental algorithm to compute the emptiness of nondeterministic Büchi tree automata. All our optimizations are computed in time polynomial in the size of the automaton on which they are computed. We have applied our implementation to several examples and show a significant improvement over the straightforward implementation. Although our examples are still small, this work constitutes the first implementation of a synthesis algorithm for full LTL. We believe that the optimizations discussed here form an important step towards making LTL synthesis practical. I.

We present a new procedure for the translation of propositional linear-time temporal logic (LTL) formulas to equivalent nondeterministic Büchi automata. Our procedure is based on simulation relations for alternating Büchi automata. Whereas most of the procedures that have been described in the past compute simulation relations in the last step of the translation (after a nondeterministic Büchi automaton has already been constructed), our procedure computes simulation relations for alternating Büchi automata in an early stage and uses them in an on-the-fly fashion. This decreases the time and space consumption without sacrificing the potential of simulation relations. We present experimental results...