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Information tracking in games on graphs
 Journal of Logic, Language and Information
"... Abstract When seeking to coordinate in a game with imperfect information, it is often relevant for a player to know what other players know. Keeping track of the information acquired in a play of infinite duration may, however, lead to infinite hierarchies of higherorder knowledge. We present a co ..."
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Abstract When seeking to coordinate in a game with imperfect information, it is often relevant for a player to know what other players know. Keeping track of the information acquired in a play of infinite duration may, however, lead to infinite hierarchies of higherorder knowledge. We present a construction that makes explicit which higherorder knowledge is relevant in a game and allows us to describe a class of games that admit coordinated winning strategies with finite memory.
A PerfectInformation Construction for Coordination in Games
"... We present a general construction for eliminating imperfect information from games with several players who coordinate against nature, and to transform them into twoplayer games with perfect information while preserving winning strategy profiles. The construction yields an infinite game tree with e ..."
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We present a general construction for eliminating imperfect information from games with several players who coordinate against nature, and to transform them into twoplayer games with perfect information while preserving winning strategy profiles. The construction yields an infinite game tree with epistemic models associated to nodes. To obtain a more succinct representation, we define an abstraction based on homomorphic equivalence, which we prove to be sound for games with observable winning conditions. The abstraction generates finite game graphs in several relevant cases, and leads to a new semidecision procedure for multiplayer games with imperfect information.
A Decidable Timed µcalculus for EventRecording Automata
, 2009
"... The Logic WTµ is considered. We show decidability of the satisfiability checking problem for a fragment of WTµ called CWTµ. WTµ is an extension of the modal µcalculus with eventrecording clocks. CWTµ is more expressive than EventRecording logic, another EXPTIME complete decidable extension of t ..."
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The Logic WTµ is considered. We show decidability of the satisfiability checking problem for a fragment of WTµ called CWTµ. WTµ is an extension of the modal µcalculus with eventrecording clocks. CWTµ is more expressive than EventRecording logic, another EXPTIME complete decidable extension of the modal µcalculus with eventrecording clocks. Based on the techniques for deciding untimed µcalculus, we present a set of rules for constructing tableaux for formulas of CWTµ. The decidability problem is shown to be EXPTIME complete. We construct a witness eventrecording automaton that satisfies a given CWTµ formula. 1
Maximally Permissive Controlled System Synthesis for Modal Logic?
"... Abstract. We propose a new method for controlled system synthesis on nondeterministic automata, which includes the synthesis for deadlockfreeness, as well as invariant and reachability expressions. Our technique restricts the behavior of a Kripkestructure with labeled transitions, representing t ..."
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Abstract. We propose a new method for controlled system synthesis on nondeterministic automata, which includes the synthesis for deadlockfreeness, as well as invariant and reachability expressions. Our technique restricts the behavior of a Kripkestructure with labeled transitions, representing the uncontrolled system, such that it adheres to a given requirement specification in an expressive modal logic. while all noninvalidating behavior is retained. This induces maximal permissiveness in the context of supervisory control. Research presented in this paper allows a system model to be constrained according to a broad set of liveness, safety and fairness specifications of desired behavior, and embraces most concepts from RamadgeWonham supervisory control, including controllability and markerstate reachability. Synthesis is defined in this paper as a formal construction, which allowed a careful validation of its correctness using the Coq proof assistant. 1
Infinite games with finite knowledge gaps
"... Infinite games where several players seek to coordinate under imperfect information are believed to be intractable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting ..."
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Infinite games where several players seek to coordinate under imperfect information are believed to be intractable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow. Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play. We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under parity winning conditions.
The mucalculus and modelchecking
"... This chapter presents a part of the theory of the mucalculus that is relevant to the, broadly understood, modelchecking problem. The mucalculus is one of the most important logics in modelchecking. It is a logic with an exceptional balance between expressiveness and algorithmic properties. The ..."
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This chapter presents a part of the theory of the mucalculus that is relevant to the, broadly understood, modelchecking problem. The mucalculus is one of the most important logics in modelchecking. It is a logic with an exceptional balance between expressiveness and algorithmic properties. The chapter describes in length the game characterization of the semantics of the mucalculus. It discusses the theory of the mucalculus starting with the tree model property, and bisimulation invariance. Then it develops the notion of modal automaton: an automatonbased model behind the mucalculus. It gives a quite detailed explanation of the satisfiability algorithm, followed by the results on alternation hierarchy, proof systems, and interpolation. Finally, the chapter discusses the relations of the mucalculus to monadic secondorder logic as well as to some program and temporal logics. It also presents two extensions of the mucalculus that allow us to address issues such as inverse modalities.
Disjunctive Normal Form for EventRecording Logic
"... Abstract. We consider the semantics equivalence between formulas and formulas in disjunctive normal form. In the settings of the standard µcalculus, formulas and disjunctive formulas are equivalent. This question is open for timed extensions of the µcalculus. Sorea has introduced a timed µcalculu ..."
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Abstract. We consider the semantics equivalence between formulas and formulas in disjunctive normal form. In the settings of the standard µcalculus, formulas and disjunctive formulas are equivalent. This question is open for timed extensions of the µcalculus. Sorea has introduced a timed µcalculus called EventRecording Logic (ERL) and has provided an EXPTIME Complete decision procedure for its satisfiability problem. We provide another tableaubased decision procedure for the satisfiability problem of ERL. This procedure corrects a bug in the procedure of Sorea. We define disjunctive formulas for ERL and we show that formulas and disjunctive formulas are semantically equivalent. 1
1A look at the control of asynchronous automata
"... In the simplest case, the controller synthesis problem asks to find a model for a given specification. So it is just the satisfiability problem. In a more refined version one is given a system, referred to as a plant, and is asked to find a controller such that the controlled system ..."
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In the simplest case, the controller synthesis problem asks to find a model for a given specification. So it is just the satisfiability problem. In a more refined version one is given a system, referred to as a plant, and is asked to find a controller such that the controlled system
Synthesis of Winning Strategies for Interaction under Partial Information
, 2013
"... Interaction is a fundamental concept in computer science. Besides the interaction between human users and computing systems, many computing systems are inherently interactive themselves. The individual computers in a network, for example, interact with each other via a given communication structure ..."
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Interaction is a fundamental concept in computer science. Besides the interaction between human users and computing systems, many computing systems are inherently interactive themselves. The individual computers in a network, for example, interact with each other via a given communication structure according to certain protocols. In a reactive system, one or more computing devices, called controllers, interact with some kind of environment, trying to guarantee a correct behavior of the system. Logic as one of the foundations of computer science is intimately linked to interaction, demonstrated by various kinds of model checking games. Moreover, semantics of alternating computing devices as well as several graph complexity measures are characterized in terms of games. Many of these interactive scenarios take place under certain forms of uncertainty. An individual computer in a network, for example, does not necessarily know all the parameters of the other members of the network or the past message transmissions in the joint computation. The same holds for the controllers in reactive systems which often do not have full information about all the internal states of the other components or the history of past events in the whole system. Furthermore, model checking games for certain logics as well as several graph searching