Results 1 - 10
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35
Better quality in synthesis through quantitative objectives
- In CoRR, abs/0904.2638
, 2009
"... Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation tha ..."
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Cited by 57 (18 self)
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Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the “goodness ” of an implementation. Using games with corresponding quantitative objectives, we can synthesize “optimal ” implementations, which are preferred among the set of possible implementations that satisfy a given specification. In particular, we show how automata with lexicographic mean-payoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic mean-payoff games (for safety requirements), and the solution of games with both lexicographic mean-payoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games. 1
Strategy Logic
, 2007
"... We introduce strategy logic, a logic that treats strategies in two-player games as explicit first-order objects. The explicit treatment of strategies allows us to handle nonzero-sum games in a convenient and simple way. We show that the one-alternation fragment of strategy logic, is strong enough ..."
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Cited by 49 (2 self)
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We introduce strategy logic, a logic that treats strategies in two-player games as explicit first-order objects. The explicit treatment of strategies allows us to handle nonzero-sum games in a convenient and simple way. We show that the one-alternation fragment of strategy logic, is strong enough to express Nash-equilibrium, secure-equilibria, as well as other logics that were introduced to reason about games, such as ATL, ATL*, and game-logic. We show that strategy logic is decidable, by constructing tree automata that recognize sets of strategies. While for the general logic, our decision procedure is non-elementary, for the simple fragment that is used above we show that complexity is polynomial in the size of the game graph and optimal in the formula (ranging between 2EXPTIME and polynomial depending on the exact formulas).
Environment Assumptions for Synthesis
, 2008
"... The synthesis problem asks to construct a reactive finite-state system from an ω-regular specification. Initial specifications are often unrealizable, which means that there is no system that implements the specification. A common reason for unrealizability is that assumptions on the environment of ..."
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Cited by 25 (4 self)
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The synthesis problem asks to construct a reactive finite-state system from an ω-regular specification. Initial specifications are often unrealizable, which means that there is no system that implements the specification. A common reason for unrealizability is that assumptions on the environment of the system are incomplete. We study the problem of correcting an unrealizable specification ϕ by computing an environment assumption ψ such that the new specification ψ → ϕ is realizable. Our aim is to construct an assumption ψ that constrains only the environment and is as weak as possible. We present a two-step algorithm for computing assumptions. The algorithm operates on the game graph that is used to answer the realizability question. First, we compute a safety assumption that removes a minimal set of environment edges from the graph. Second, we compute a liveness assumption that puts fairness conditions on some of the remaining environment edges. We show that the problem of finding a minimal set of fair edges is computationally hard, and we use probabilistic games to compute a locally minimal fairness assumption.
Rational Synthesis
"... Abstract. Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. Modern systems often interact with other systems, or agents. Many times these agents have objectives of their own, other than to fail the sy ..."
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Cited by 21 (5 self)
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Abstract. Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. Modern systems often interact with other systems, or agents. Many times these agents have objectives of their own, other than to fail the system. Thus, it makes sense to model system environments not as hostile, but as composed of rational agents; i.e., agents that act to achieve their own objectives. We introduce the problem of synthesis in the context of rational agents (rational synthesis, for short). The input consists of a temporal-logic formula specifying the system, temporal-logic formulas specifying the objectives of the agents, and a solution concept definition. The output is an implementation T of the system and a profile of strategies, suggesting a behavior for each of the agents. The output should satisfy two conditions. First, the composition of T with the strategy profile should satisfy the specification. Second, the strategy profile should be an equilibrium in the sense that, in view of their objectives, agents have no incentive to deviate from the strategies assigned to them, where “no incentive to deviate” is interpreted as dictated by the given solution concept. We provide a method for solving the rational-synthesis problem, and show that for the classical definitions of equilibria studied in game theory, rational synthesis is not harder than traditional synthesis. We also consider the multi-valued case in which the objectives of the system and the agents are still temporal logic formulas, but involve payoffs from a finite lattice. 1
The complexity of Nash equilibria in infinite multiplayer games
- In Proceedings of the 11th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2008
, 2008
"... Abstract. We study the complexity of Nash equilibria in infinite (turnbased, qualitative) multiplayer games. Chatterjee & al. showed the existence of a Nash equilibrium in any such game with ω-regular winning conditions, and they devised an algorithm for computing one. We argue that in applicati ..."
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Cited by 19 (8 self)
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Abstract. We study the complexity of Nash equilibria in infinite (turnbased, qualitative) multiplayer games. Chatterjee & al. showed the existence of a Nash equilibrium in any such game with ω-regular winning conditions, and they devised an algorithm for computing one. We argue that in applications it is often insufficient to compute just some Nash equilibrium. Instead, we enrich the problem by allowing to put (qualitative) constraints on the payoff of the desired equilibrium. Our main result is that the resulting decision problem is NP-complete for games with co-Büchi, parity or Streett winning conditions but fixed-parameter tractable for many natural restricted classes of games with parity winning conditions. For games with Büchi winning conditions we show that the problem is, in fact, decidable in polynomial time. We also analyse the complexity of strategies realising a Nash equilibrium. In particular, we show that pure finite-state strategies as opposed to arbitrary mixed strategies suffice to realise any Nash equilibrium of a game with ω-regular winning conditions with a qualitative constraint on the payoff. 1
Generalized parity games
- In FoSSaCS’07, LNCS 4423
, 2007
"... Abstract. We consider games where the winning conditions are disjunctions (or dually, conjunctions) of parity conditions; we call them generalized parity games. These winning conditions, while ω-regular, arise naturally when considering fair simulation between parity automata, secure equilibria for ..."
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Cited by 11 (2 self)
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Abstract. We consider games where the winning conditions are disjunctions (or dually, conjunctions) of parity conditions; we call them generalized parity games. These winning conditions, while ω-regular, arise naturally when considering fair simulation between parity automata, secure equilibria for parity conditions, and determinization of Rabin automata. We show that these games retain the computational complexity of Rabin and Streett conditions; i.e., they are NP-complete and co-NP-complete, respectively. The (co-)NP-hardness is proved for the special case of a conjunction/disjunction of two parity conditions, which is the case that arises in fair simulation and secure equilibria. However, considering these games as Rabin or Streett games is not optimal. We give an exposition of Zielonka’s algorithm when specialized to this kind of games. The complexity of solving these games for k parity objectives with d priorities, n states, and m edges is O(n 2kd ·m) · (k·d)! d! k, as compared to O(n 2kd ·m)·(k·d)! when these games are solved as Rabin/Streett games. We also extend the subexponential algorithm for solving parity games recently introduced by Jurdziński, Paterson, and Zwick to generalized parity games. The result-ing complexity of solving generalized parity games is n O( √ n) · (k·d)! d! k. As a corollary we obtain an improved algorithm for Rabin and Streett games with d pairs, with time complexity n O( √ n) · d!. 1
Solution concepts and algorithms for infinite multiplayer games
- IN NEW PERSPECTIVES ON GAMES AND INTERACTION
, 2008
"... We survey and discuss several solution concepts for infinite turn-based multiplayer games with qualitative (i.e. win-lose) objectives of the players. These games generalise in a natural way the common model of games in verification which are two-player, zero-sum games with ω-regular winning conditi ..."
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Cited by 11 (0 self)
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We survey and discuss several solution concepts for infinite turn-based multiplayer games with qualitative (i.e. win-lose) objectives of the players. These games generalise in a natural way the common model of games in verification which are two-player, zero-sum games with ω-regular winning conditions. The generalisation is in two directions: our games may have more than two players, and the objectives of the players need not be completely antagonistic. The notion of a Nash equilibrium is the classical solution concept in game theory. However, for games that extend over time, in particular for games of infinite duration, Nash equilibria are not always satisfactory as a notion of rational behaviour. We therefore discuss variants of Nash equilibria such as subgame perfect equilibria and secure equilibria. We present criteria for the existence of Nash equilibria and subgame perfect equilibria in the case of arbitrarily many players and for the existence of secure equilibria in the two-player case. In the second part of this paper, we turn to algorithmic questions: For each of the solution concepts that we discuss, we present algorithms that decide the existence of a solution with certain requirements in a game with parity winning conditions. Since arbitrary ω-regular winning conditions can be reduced to parity conditions, our algorithms are also applicable to games with arbitrary ω-regular winning conditions.
Nash equilibria for reachability objectives in multi-player timed games
- LAB. SPÉCIFICATION & VÉRIFICATION, ENS
, 2010
"... We propose a procedure for computing Nash equilibria in multi-player timed games with reachability objectives. Our procedure is based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibria in (possibly infinite) concurrent games. Along the way, we use ..."
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Cited by 10 (6 self)
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We propose a procedure for computing Nash equilibria in multi-player timed games with reachability objectives. Our procedure is based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibria in (possibly infinite) concurrent games. Along the way, we use our characterization to compute Nash equilibria in finite concurrent games.
