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43

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Introduction

**Skills and Expertise**

## Publications

Publications (43)

We study a game for recognising formal languages, in which two players with imperfect information should coordinate on a common decision, given private input words correlated by a finite graph. The players have a common objective to avoid an inadmissible decision, in spite of the uncertainty induced by the input.
We show that the acceptor model bas...

Grim-trigger strategies are a fundamental mechanism for sustaining equilibria in iterated games: the players cooperate along an agreed path, and as soon as one player deviates, the others form a coalition to play him down to his minmax level. A precondition to triggering such a strategy is that the identity of the deviating player becomes common kn...

Infinite games with imperfect information are known to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access to all the information that the following ones receive. In this paper we consider variations of this hierarchy...

We present a general theorem for distributed synthesis problems in coordination games with $\omega$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy, that is obtained by a retraction of the given one. In general, this does not lead to finite-state winning strateg...

Infinite games with imperfect information are deemed to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access to all the information that the following ones receive. In this paper we consider variations of this hierarchy...

We study a game for recognising formal languages, in which two players with imperfect information need to coordinate on a common decision, given private input strings correlated by a finite graph. The players have a joint objective to avoid an inadmissible decision, in spite of the uncertainty induced by the input.
We show that the acceptor model b...

Infinite games with imperfect information tend to be undecidable unless the
information flow is severely restricted. One fundamental decidable case occurs
when there is a total ordering among players, such that each player has access
to all the information that the following ones receive.
In this paper we consider variations of this hierarchy princ...

We investigate infinite games on finite graphs where the information flow is
perturbed by nondeterministic signalling delays. It is known that such
perturbations make synthesis problems virtually unsolvable, in the general
case. On the classical model where signals are attached to states, tractable
cases are rare and difficult to identify.
Here, we...

We propose a game for recognising formal languages, in which two players with
imperfect information need to coordinate on a common decision, given private
input information. The players have a joint objective to avoid an inadmissible
decision, in spite of the uncertainty induced by the input.
We show that this model of consensus acceptor games char...

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 con...

Infinite games where several players seek to coordinate under imperfect
information are known to be intractable, unless the information flow is
severely restricted. Examples of undecidable cases typically feature a
situation where players become uncertain about the current state of the game,
and this uncertainty lasts forever. Here we consider game...

We examine the complexity of solving parity games in the special case when the underlying game graph is undirected. For strictly alternating games, that is, when the game graph is bipartite between the players, we observe that the solution can be computed in linear time. In contrast, when the assumption of strict alternation is dropped, we show tha...

Entanglement is a parameter for the complexity of finite directed graphs that measures to what extent the cycles of the graph are intertwined. It is defined by way of a game similar in spirit to the cops and robber games used to describe treewidth, directed treewidth, and hypertree width. Nevertheless, on many classes of graphs, there are significa...

Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Tree-width can be characterised by a graph searching game where a number of cops attempt to capture a robber. We consider the natural adaptation of this game to directed...

Entanglement is a parameter for the complexity of finite directed graphs that measures to which extent the cycles of the graph are intertwined. It is defined by way of a game similar in spirit to the cops and robber games used to describe tree width, directed tree width, and hypertree width. Nevertheless, on many classes of graphs, there are signif...

We study a class of parity games equipped with counters that evolve according to arbitrary non-negative affine functions. These games capture several cost models for dynamic systems from the literature. We present an elementary algorithm for computing the exact value of a counter parity game, which both generalizes previous results and improves the...

We present a general construction for eliminating imperfect information from games with several players who coordinate against nature, and to transform them into two-player 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 m...

When seeking to coordinate in a game with imperfect infor- mation, it is often relevant for a player to know what other players know. Keeping track of the information acquired in a play of innite duration may, however, lead to innite hierarchies of higher-order knowledge. We present a construction that makes explicit which higher-order knowledge is...

We consider imperfect-information parity games in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e. to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-information game. Recen...

We consider two-player parity games with imperfect information in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e., to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-inform...

Alpaga is a solver for two-player parity games with imperfect information. Given the description of a game, it determines whether the first player can ensure to win and, if so, it constructs a winning strategy. The tool provides a symbolic implementation of a recent algorithm based on antichains.

We analyse two basic approaches of extending classical logics with quantifiers interpreted via games: Propositional Game Logic
of Parikh and Alternating-Time Temporal Logic of Alur, Henzinger, and Kupferman. Although the two approaches are historically
remote and they incorporate operationally orthogonal paradigms, we trace the formalisms back to c...

We investigate the prescriptive power of sequential iterated
admissibility in coordination games of the Gale-Stewart style, i.e.,
perfect-information games of infinite duration with only two payoffs. We
show that, on this kind of games, the procedure of eliminating weakly
dominated strategies is independent of the elimination order and that,
under...

We present a polynomial-time reduction from parity games with imperfect information to safety games with imperfect information. Similar reductions for games with perfect information typically increase the game size exponentially. Our construction avoids such a blow-up by using imperfect information to realise succinct counters which cover a range e...

Most of the logics commonly used in verification, such as LTL, CTL, CTL*, and PDL can be embedded into the two-variable fragment of the μ-calculus. It is also known that properties occurring at
arbitrarily high levels of the alternation hierarchy can be formalised using only two variables. This raises the question
of whether the number of fixed-poi...

We analyse the notion of iterated admissibility, i.e., avoidance of weakly dominated strategies, as a solution concept for extensive games of infinite horizon. This concept is known to provide a valuable criterion for selecting among multiple equilibria and to yield sharp predictions in finite games. However, generalisations to the infinite are inh...

We investigate two models of finite-state automata that op- erate on rooted directed graphs by marking either vertices (V-automata) or edges (E-automata). Runs correspond to locally consistent markings and acceptance is defined by means of regular conditions on the paths emanating from the root. Comparing the expressive power of these two notions o...

Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Tree-width is characterised by a game known as the cops-and-robber game where a number of cops chase a robber on the graph. We consider the natural adaptation of this ga...

The modal μ-calculus Lμ
attains high expressive power by extending basic modal logic with monadic variables and binding them to extremal fixed points of definable operators. The number of variables occurring in a formula provides a relevant measure of its conceptual complexity. In a previous paper with Erich Grädel we have shown, for the existentia...

The model-checking games associated with fixed-point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time. We study Solitaire-LFP, a fragment of least fixed- point logic, whose evaluation games are nested soltaire games. This means that on each strongly connected compo...

We propose a new parameter for the complexity of finite directed graphs which measures to what extent the cycles of the graph are intertwined. This measure, called entanglement, is defined by way of a game that is somewhat similar in spirit to the robber and cops games used to describe tree width, directed tree width, and hypertree width. Neverthel...

We study determinacy, definability and complexity issues of path games on finite and infinite graphs.
Compared to the usual format of infinite games on graphs (such as Gale-Stewart games) we consider here a different variant where the players select in each move a path of arbitrary finite length, rather than just an edge. The outcome of a play is a...

We investigate the expressive power of Parikh's Game Logic interpreted in Kripke structures, and show that the syntactical alternation hierarchy of this logic is strict. This is done by encoding the winning condition for parity games of rank n. It follows that Game Logic is not captured by any finite level of the modal -calculus alternation hierarc...

We study determinacy, de nability and complexity issues of path games on nite and in nite graphs.

We study determinacy, definability and complexity issues of path games on finite and infinite graphs. Compared to the usual format of infinite games on graphs (such as Gale-Stewart games) we consider here a different variant where the players select in each move a path of arbitrary finite length, rather than just an edge. The outcome of a play is a...

We investigate the structure of the modal μ-calculus L
μ
with respect to the question of how many different fixed point variables are necessary to define a given property. Most of the logics commonly used in verification, such as CTL, LTL, CTL*, PDL, etc. can in fact be embedded into the two-variable fragment of the μ-calculus. It is also known tha...

The model checking games associated with fixed point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time. We study Solitaire-LFP, a fragment of least fixed point logic, whose model checking games are nested soltaire games. This means that on each strongly connected co...

We investigate the model checking problems for guarded first-order and fixed point logics byreducing them to paritygames.
This approach is known to provide good results for the modal μ-calculus and is verycloselyrelated to automata-based methods.
To obtain good results also for guarded logics, optimized constructions of games have to be provided....

Initiated by the work of Büchi, Läuchli, Rabin, and Shelah in the late 60s, the investigation of monadic second-order logic
(MSO) has received continuous attention. The attractiveness of MSO is due to the fact that, on the one hand, it is quite expressive
subsuming - besides first-order logic - most modal logics, in particular the μ-calculus. On th...

The guarded fixed point logics μGF and μCGF introduced in the previous chapter extend the guarded fragments of first-order
logic GF and CGF on the one hand and the modal μ-calculus on the other hand. Thereby, the expressive power of the underlying
formalisms is increased considerably. On transition systems, for instance, μGF already subsumes the μ-...

Zur Analyse interaktiver Systeme bietet die Spieltheorie ein reiches Gefüge an Modellen und eine intuitive, unbefangene Sprache. Ihrerseits, beruht die Wirksamkeit spieltheoretischer Methoden auf logischen Grundlagen der formalen Spezifikation und Folgerung. Im Hinblick auf ihre Ziele sind Logik und Spieltheorie demnach eng verzahnt; nichtsdestotro...