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45
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 74 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
Monadic Second Order Logic on TreeLike Structures
, 1996
"... An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of ..."
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Cited by 19 (6 self)
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An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of monadic second order logic (MSOL) over treelike structures. Using this characterisation it is proved that MSOL theory of treelike structures is effectively reducible to that of the original structures. As another application of the characterisation it is shown that MSOL on trees of arbitrary degree is equivalent to first order logic extended with unary least fixpoint operator.
Visibly pushdown games
 In FSTTCS 2004
, 2004
"... Abstract. The class of visibly pushdown languages has been recently defined as a subclass of contextfree languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is gi ..."
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Cited by 18 (6 self)
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Abstract. The class of visibly pushdown languages has been recently defined as a subclass of contextfree languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is given by a visibly pushdown language. We establish that, unlike pushdown games with pushdown winning conditions, visibly pushdown games are decidable and are 2Exptimecomplete. We also show that pushdown games against Ltl specifications and Caret specifications are 3Exptimecomplete. Finally, we establish the topological complexity of visibly pushdown languages by showing that they are a subclass of Boolean combinations of Σ3 sets. This leads to an alternative proof that visibly pushdown automata are not determinizable and also shows that visibly pushdown games are determined. 1
ORBIT INEQUIVALENT ACTIONS OF NONAMENABLE GROUPS
, 2008
"... Consider two free measure preserving group actions Γ � (X, µ), ∆ � (X, µ), and a measure preserving action ∆ � a (Z, ν) where (X, µ), (Z, ν) are standard probability spaces. We show how to construct free measure preserving actions Γ � c (Y, m), ∆ � d (Y, m) on a standard probability space such ..."
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Cited by 12 (2 self)
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Consider two free measure preserving group actions Γ � (X, µ), ∆ � (X, µ), and a measure preserving action ∆ � a (Z, ν) where (X, µ), (Z, ν) are standard probability spaces. We show how to construct free measure preserving actions Γ � c (Y, m), ∆ � d (Y, m) on a standard probability space such that E d ∆ ⊂ E c Γ and d has a as a factor. This generalizes the standard notion of coinduction of actions of groups from actions of subgroups. We then use this construction to show that if Γ is a countable nonamenable group, then Γ admits continuum many orbit inequivalent free, measure preserving, ergodic actions on a standard probability space.
Games with winning conditions of high borel complexity
 In Proceedings of ICALP’04, volume 3142 of LNCS
, 2004
"... Abstract. We first consider infinite twoplayer games on pushdown graphs. In previous work, Cachat, Duparc and Thomas [4] have presented a winning decidable condition that is Σ3complete in the Borel hierarchy. This was the first example of a decidable winning condition of such Borel complexity. We ..."
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Cited by 7 (2 self)
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Abstract. We first consider infinite twoplayer games on pushdown graphs. In previous work, Cachat, Duparc and Thomas [4] have presented a winning decidable condition that is Σ3complete in the Borel hierarchy. This was the first example of a decidable winning condition of such Borel complexity. We extend this result by giving a family of decidable winning conditions of arbitrary high finite Borel complexity. From this family, we deduce a family of decidable winning conditions of arbitrary finite Borel complexity for games played on finite graphs. The problem of deciding the winner for these winning conditions is shown to be nonelementary complete. Keywords: Pushdown Automata, Twoplayer Games, Borel Complexity. 1
Weak MSO with the unbounding Quantifier
"... A new class of languages of infinite words is introduced, called the maxregular languages, extending the class of ωregular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic secondorder logic ..."
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Cited by 7 (2 self)
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A new class of languages of infinite words is introduced, called the maxregular languages, extending the class of ωregular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic secondorder logic with a bounding quantifier). Effective translations between the logic and automata are given.
L 2 Betti numbers of discrete measured groupoids
 Internat. J. Algebra Comput
"... Abstract. There are notions of L2Betti numbers for discrete groups (Cheeger ..."
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Cited by 7 (1 self)
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Abstract. There are notions of L2Betti numbers for discrete groups (Cheeger
Duality for borel measurable cost function
"... measure theoretic setting. Our main result states that duality holds if c: X × Y → [0, ∞) is an arbitrary Borel measurable cost function on the product of Polish spaces X, Y. In the course of the proof we show how to relate a non optimal transport plan to the optimal transport costs via a “subsidy ..."
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Cited by 5 (2 self)
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measure theoretic setting. Our main result states that duality holds if c: X × Y → [0, ∞) is an arbitrary Borel measurable cost function on the product of Polish spaces X, Y. In the course of the proof we show how to relate a non optimal transport plan to the optimal transport costs via a “subsidy ” function and how to identify the dual optimizer. We also provide some examples showing the limitations of the duality relations. 1.