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108
A Framework for the Verification of InfiniteState Graph Transformation Systems
, 2008
"... We propose a technique for the analysis of infinitestate graph transformation systems, based on the construction of finite structures approximating their behaviour. Following a classical approach, one can construct a chain of finite underapproximations (ktruncations) of the Winskel style unfolding ..."
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Cited by 15 (3 self)
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We propose a technique for the analysis of infinitestate graph transformation systems, based on the construction of finite structures approximating their behaviour. Following a classical approach, one can construct a chain of finite underapproximations (ktruncations) of the Winskel style unfolding of a graph grammar. More interestingly, also a chain of finite overapproximations (kcoverings) of the unfolding can be constructed. The fact that ktruncations and kcoverings approximate the unfolding with arbitrary accuracy is formalised by showing that both chains converge (in a categorical sense) to the full unfolding. We discuss how the finite over and underapproximations can be used to check properties of systems modelled by graph transformation systems, illustrating this with some small examples. We also describe the Augur tool, which provides a partial implementation of the proposed constructions, and has been used for the verification of larger case studies.
Generating compiler optimization from proofs
 In POPL
, 2010
"... We present an automated technique for generating compiler optimizations from examples of concrete programs before and after improvements have been made to them. The key technical insight of our technique is that a proof of equivalence between the original and transformed concrete programs informs us ..."
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Cited by 14 (3 self)
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We present an automated technique for generating compiler optimizations from examples of concrete programs before and after improvements have been made to them. The key technical insight of our technique is that a proof of equivalence between the original and transformed concrete programs informs us which aspects of the programs are important and which can be discarded. Our technique therefore uses these proofs, which can be produced by translation validation or a proofcarrying compiler, as a guide to generalize the original and transformed programs into broadly applicable optimization rules. We present a categorytheoretic formalization of our proof generalization technique. This abstraction makes our technique applicable to logics besides our own. In particular, we demonstrate how our technique can also be used to learn query optimizations for relational databases or to aid programmers in debugging type errors. Finally, we show experimentally that our technique enables programmers to train a compiler with applicationspecific optimizations by providing concrete examples of original programs and the desired transformed programs. We also show how it enables a compiler to learn efficienttorun optimizations from expensivetorun superoptimizers.
Precategories for Combining Probabilistic Automata
 Electronic Notes in Theoretical Computer Science
, 1999
"... A relaxed notion of category is presented having in mind the categorical caracterization of the mechanisms for combining probabilistic automata, since the composition of the appropriate morphisms is not always defined. A detailed discussion of the required notion of morphism is provided. The partial ..."
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Cited by 11 (6 self)
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A relaxed notion of category is presented having in mind the categorical caracterization of the mechanisms for combining probabilistic automata, since the composition of the appropriate morphisms is not always defined. A detailed discussion of the required notion of morphism is provided. The partiality of composition of such morphisms is illustrated at the abstract level of countable probability spaces. The relevant fragment of the theory of the proposed precategories is developed, including (constrained) products and Cartesian liftings. Precategories are precisely placed in the universe of neocategories. Some classical results from category theory are shown to carry over to precategories. Other results are shown not to hold in general. As an application, the precategorical universal constructs are used for characterizing the basic mechanisms for combining probabilistic automata: aggregation, interconnection and state constraining. Mathematics Subject Classifications: 18A10 68Q75. Ke...
A Coalgebraic Perspective on Linear Weighted Automata
, 2011
"... Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either ( ..."
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Cited by 11 (6 self)
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Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either (weighted) bisimilarity or (weighted) language equivalence. Coalgebras provide a categorical framework for the uniform study of statebased systems and their behaviours. In this work, we show that coalgebras can suitably model weighted automata in two different ways: coalgebras on
HOMOTOPICAL INTERPRETATION OF GLOBULAR COMPLEX BY MULTIPOINTED DSPACE
"... Abstract. Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a ..."
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Cited by 10 (4 self)
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Abstract. Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is equivalent to the homotopy category of flows. The underlying
Distributed unfolding of petri nets
, 2006
"... Some recent Petri netbased approaches to fault diagnosis of distributed systems suggest to factor the problem into local diagnoses based on the unfoldings of local views of the system, which are then correlated with diagnoses from neighbouring supervisors. In this paper we propose a notion of syste ..."
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Cited by 9 (5 self)
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Some recent Petri netbased approaches to fault diagnosis of distributed systems suggest to factor the problem into local diagnoses based on the unfoldings of local views of the system, which are then correlated with diagnoses from neighbouring supervisors. In this paper we propose a notion of system factorisation expressed in terms of pullback decomposition. To ensure coherence of the local views and completeness of the diagnosis, data exchange among the unfolders needs to be specified with care. We introduce interleaving structures as a format for data exchange between unfolders and we propose a distributed algorithm for computing local views of the unfolding for each system component. The theory of interleaving structures is developed to prove correctness of the distributed unfolding algorithm.
NEIGHBOURHOOD STRUCTURES: BISIMILARITY AND BASIC MODEL THEORY
, 2009
"... Neighbourhood structures are the standard semantic tool used to reason about nonnormal modal logics. The logic of all neighbourhood models is called classical modal logic. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denote ..."
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Cited by 9 (2 self)
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Neighbourhood structures are the standard semantic tool used to reason about nonnormal modal logics. The logic of all neighbourhood models is called classical modal logic. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denoted by 2 2. We use this coalgebraic modelling to derive notions of equivalence between neighbourhood structures. 2 2bisimilarity and behavioural equivalence are well known coalgebraic concepts, and they are distinct, since 2 2 does not preserve weak pullbacks. We introduce a third, intermediate notion whose witnessing relations we call precocongruences (based on pushouts). We give backandforth style characterisations for 2 2bisimulations and precocongruences, we show that on a single coalgebra, precocongruences capture behavioural equivalence, and that between neighbourhood structures, precocongruences are a better approximation of behavioural equivalence than 2 2bisimulations. We also introduce a notion of modal saturation for neighbourhood models, and investigate its relationship with definability and imagefiniteness. We prove a HennessyMilner theorem for modally saturated and for imagefinite neighbourhood models. Our main results are an analogue of Van Benthem’s characterisation theorem and a modeltheoretic proof of Craig interpolation for classical modal logic.
Model Synchronization: Mappings, Tiles, and Categories
 In: GTTSE 2009, LNCS
, 2011
"... Abstract. The paper presents a novel algebraic framework for specification and design of model synchronization tools. The basic premise is that synchronization procedures, and hence algebraic operations modeling them, are diagrammatic: they take a configuration (diagram) of models and mappings as ..."
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Cited by 9 (2 self)
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Abstract. The paper presents a novel algebraic framework for specification and design of model synchronization tools. The basic premise is that synchronization procedures, and hence algebraic operations modeling them, are diagrammatic: they take a configuration (diagram) of models and mappings as their input and produce a diagram as the output. Many important synchronization scenarios are based on diagram operations of square shape. Composition of such operations amounts to their tiling, and complex synchronizers can thus be assembled by tiling together simple synchronization blocks. This gives rise to a visually suggestive yet precise notation for specifying synchronization procedures and reasoning about them. 1
A Kleislibased approach to lax algebras
 Appl. Categ. Structures
, 2007
"... By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhoodlike presentation of categories of lax algebras. A notable advantage of this approach is that it does not require the introduction of a lax extension of the associated m ..."
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Cited by 8 (2 self)
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By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhoodlike presentation of categories of lax algebras. A notable advantage of this approach is that it does not require the introduction of a lax extension of the associated monad functor. As a byproduct, the different philosophies underlying the construction of fuzzy topological spaces on one hand, and approach spaces on the other, may be simply expressed in terms of lax algebras.