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34
Tile Bisimilarity Congruences for Open Terms and Term Graphs
 in: Proc. CONCUR 2000, LNCS 1877 (2000
, 2000
"... The definition of sos formats ensuring that bisimilarity on closed terms is a congruence has received much attention in the last two decades. For dealing with open system specifications, the congruence is usually lifted from closed terms to open terms by instantiating the free variables in all possi ..."
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Cited by 12 (7 self)
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The definition of sos formats ensuring that bisimilarity on closed terms is a congruence has received much attention in the last two decades. For dealing with open system specifications, the congruence is usually lifted from closed terms to open terms by instantiating the free variables in all possible ways; the only alternatives considered in the literature relying on Larsen and Xinxin's context systems and Rensink's conditional transition systems. We propose a different approach based on tile logic, where both closed and open terms are managed analogously. In particular, we analyze the `bisimilarity as congruence' property for several tile formats that accomplish di erent concepts of subterm sharing.
A Gap Property of Deterministic Tree Languages
"... We show that a tree language recognized by a deterministic parity automaton is either hard for the coBüchi level and therefore cannot be recognized by a weak alternating automaton, or is on a very low level in the hierarchy of weak alternating automata. We also give a new simple proof of the strict ..."
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Cited by 12 (4 self)
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We show that a tree language recognized by a deterministic parity automaton is either hard for the coBüchi level and therefore cannot be recognized by a weak alternating automaton, or is on a very low level in the hierarchy of weak alternating automata. We also give a new simple proof of the strictness of the hierarchy of weak alternating automata.
On the Search for Tractable Ways of Reasoning about Programs
, 2001
"... This paper traces the important steps in the history up to around 1990 of research on reasoning about programs. The main focus is on sequential imperative programs but some comments are made on concurrency. Initially, researchers focussed on ways of verifying that a program satifies its specific ..."
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Cited by 9 (1 self)
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This paper traces the important steps in the history up to around 1990 of research on reasoning about programs. The main focus is on sequential imperative programs but some comments are made on concurrency. Initially, researchers focussed on ways of verifying that a program satifies its specification (or that two programs were equivalent). Over time it has become clear that post facto verification is only practical for small programs and attention turned to verification methods which support the development of programs; for larger programs it is necesary to exploit a notion of composability.
Hereditary history preserving bisimilarity is undecidable
 STACS 2000, 17th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings, volume 1770 of Lecture Notes in Computer Science
, 2000
"... Abstract History preserving bisimilarity (hpbisimilarity) and hereditary history preserving bisimilarity (hhpbisimilarity) are behavioural equivalences taking into account causal relationships between events of concurrent systems. Their prominent feature is being preserved under action refinement, ..."
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Cited by 9 (1 self)
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Abstract History preserving bisimilarity (hpbisimilarity) and hereditary history preserving bisimilarity (hhpbisimilarity) are behavioural equivalences taking into account causal relationships between events of concurrent systems. Their prominent feature is being preserved under action refinement, an operation important for the topdown design of concurrent systems. We show thatunlike hpbisimilaritychecking hhpbisimilarity for finite labelled asynchronous transition systems is not decidable, by a reduction from the halting problem of 2counter machines. To make the proof more transparent we introduce an intermediate problem of checking domino bisimilarity for origin constrained tiling systems, whose undecidability is interesting in its own right. We also argue that the undecidability of hhpbisimilarity holds for finite labelled 1safe Petri nets. 1 Introduction The notion of behavioural equivalence that has attracted most attention in concurrency theory is bisimilarity, originally introduced by Park [20] and Milner [15]; concurrent programs are considered to have the same meaning if they are bisimilar. The prominent role of bisimilarity is due to many pleasant properties it enjoys; we mention a few of them here. A process of checking whether two transition systems are bisimilar can beseen as a two player game which is in fact an EhrenfeuchtFra"iss'e type of game
Efficient and Flexible Matching of Recursive Types
, 2000
"... Equality and subtyping of recursive types have been studied in the 1990s by Amadio and Cardelli; Kozen, Palsberg, and Schwartzbach; Brandt and Henglein; and others. Potential applications include automatic generation of bridge code for multilanguage systems and typebased retrieval of software m ..."
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Cited by 9 (3 self)
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Equality and subtyping of recursive types have been studied in the 1990s by Amadio and Cardelli; Kozen, Palsberg, and Schwartzbach; Brandt and Henglein; and others. Potential applications include automatic generation of bridge code for multilanguage systems and typebased retrieval of software modules from libraries. Auerbach, Barton, and Raghavachari advocate a highly exible combination of matching rules for which there, until now, are no ecient algorithmic techniques. In this paper, we present an ecient decision procedure for a notion of type equality that includes unfolding of recursive types, and associativity and commutativity of product types, as advocated by Auerbach et al. For two types of size at most n, our algorithm decides equality in O(n 2 ) time. The algorithm iteratively prunes a set of type pairs, and eventually it produces a set of pairs of equal types. In each iteration, the algorithm exploits a socalled coherence property of the set of type pairs pr...
Local Variations on a Loose Theme: Modal Logic and Decidability
"... This chapter is about decidability and complexity issues in modal logic; more specifically, we confine ourselves to satisfiability (and the complementary validity) problems. The satisfiability problem is the following: for a fixed class of ..."
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Cited by 8 (1 self)
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This chapter is about decidability and complexity issues in modal logic; more specifically, we confine ourselves to satisfiability (and the complementary validity) problems. The satisfiability problem is the following: for a fixed class of
Open Ended Systems, Dynamic Bisimulation and Tile Logic
, 2000
"... The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence pro ..."
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Cited by 8 (4 self)
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The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence property with such axioms and with the specication of open ended systems, where states can be recongured at runtime, at the cost of an innitary operation at the metalevel. We show that the compositional framework oered by tile logic is suitable to deal with structural axioms and open ended systems specications, allowing for a nitary presentation of context closure. Keywords: Bisimulation, sos formats, dynamic bisimulation, tile logic. Introduction The semantics of dynamic systems can be conveniently expressed via labelled transition systems (lts) whose states are terms over a certain algebra and whose labels describe some abstract behavioral information. Provided such informatio...
Compositional abstractions of hybrid control systems
 In Proceedings of the 40th IEEE Conference on Decision and Control
, 2001
"... Abstract. Abstraction is a natural way to hierarchically decompose the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts an abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature ..."
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Cited by 7 (1 self)
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Abstract. Abstraction is a natural way to hierarchically decompose the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts an abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature area, whereas abstractions of continuous systems is a recent activity. In this paper we present a framework for abstraction that applies to discrete, continuous, and hybrid systems. We introduce a composition operator that allows to build complex hybrid systems from simpler ones and show compatibility between abstractions and this compositional operator. Besides unifying the existing methodologies we also propose constructions to obtain abstractions of hybrid control systems.
Bisimulation Invariance and Finite Models
 IN LOGIC COLLOQUIUM ’02
, 2006
"... We study bisimulation invariance over finite structures. This investigation leads to a new, quite elementary proof of the van BenthemRosen characterisation of basic modal logic as the bisimulation invariant fragment of firstorder logic. The ramification of this characterisation for the finer no ..."
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Cited by 7 (0 self)
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We study bisimulation invariance over finite structures. This investigation leads to a new, quite elementary proof of the van BenthemRosen characterisation of basic modal logic as the bisimulation invariant fragment of firstorder logic. The ramification of this characterisation for the finer notion of global twoway bisimulation equivalence is based on bisimulation respecting constructions of models that recover in finite models some of the desirable properties of the usually in finite bisimilar unravellings.
Metric semantics for reactive probabilistic processes
, 1997
"... In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these syst ..."
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Cited by 6 (1 self)
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In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these systems. Two processes are identified with respect to this equivalence if, for all experiments, the probabilities of the respective processes passing a given experiment are equal. We next consider a probabilistic process calculus including external choice, internal choice, actionguarded probabilistic choice, synchronous parallel and recursion. We give operational semantics for this calculus be means of our generalised labelled transition systems and show that our equivalence is a congruence for this language. Following the methodology introduced by de Bakker & Zucker, we then give denotational semantics to the calculus by means of a complete metric space of probabilistic processes. The derived metric, although not an ultrametric, satisfies the intuitive property that the distance between two processes tends to 0 if a measure of the dif