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FORWARD ANALYSIS FOR WSTS, PART I: COMPLETIONS
, 2009
"... Wellstructured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretic ..."
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Cited by 14 (8 self)
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Wellstructured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretical framework for manipulating downwardclosed sets was missing. We answer this problem, using insights from domain theory (dcpos and ideal completions), from topology (sobrifications), and shed new light on the notion of adequate domains of limits.
On Noetherian Spaces
"... A topological space is Noetherian iff every open is compact. Our starting point is that this notion generalizes that of wellquasi order, in the sense that an Alexandroffdiscrete space is Noetherian iff its specialization quasiordering is well. For more general spaces, this opens the way to verify ..."
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Cited by 10 (5 self)
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A topological space is Noetherian iff every open is compact. Our starting point is that this notion generalizes that of wellquasi order, in the sense that an Alexandroffdiscrete space is Noetherian iff its specialization quasiordering is well. For more general spaces, this opens the way to verifying infinite transition systems based on nonwell quasi ordered sets, but where the preimage operator satisfies an additional continuity assumption. The technical development rests heavily on techniques arising from topology and domain theory, including sobriety and the de Groot dual of a stably compact space. We show that the category Nthr of Noetherian spaces is finitely complete and finitely cocomplete. Finally, we note that if X is a Noetherian space, then the set of all (even infinite) subsets of X is again Noetherian, a result that fails for wellquasi orders. 1.
Topology, Domain Theory and Theoretical Computer Science
, 1997
"... In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from ..."
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Cited by 10 (2 self)
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In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from concerns that semantics generates. Keywords: Domain theory, Scott topology, power domains, untyped lambda calculus Subject Classification: 06B35,06F30,18B30,68N15,68Q55 1 Introduction Topology has proved to be an essential tool for certain aspects of theoretical computer science. Conversely, the problems that arise in the computational setting have provided new and interesting stimuli for topology. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra. In this paper, we outline some of these interactions between topology and theoretical computer science, focusing on those aspects that have been mo...
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
A truly concurrent semantics for a process algebra using resource pomsets
 Theoretical Computer Science
, 2002
"... In this paper we study a process algebra whose semantics is based on true concurrency. In our model, actions are defined in terms of the resources they need to execute, which allows a simple definition of a weak sequential composition operator. This operator allows actions which do not share any res ..."
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Cited by 2 (0 self)
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In this paper we study a process algebra whose semantics is based on true concurrency. In our model, actions are defined in terms of the resources they need to execute, which allows a simple definition of a weak sequential composition operator. This operator allows actions which do not share any resources to execute concurrently, while dependent actions have to occur sequentially. This weak sequential composition operator may be used to automatically parallelize a sequential process. We add the customary (strict) sequential composition and a parallel composition operator allowing synchronization on specified actions. Our language also supports a hiding operator that allows the hiding of actions and even of individual resources used by actions. Strict sequential composition and hiding require that we generalize from the realm of Mazurkiewicz traces to that of pomsets, since these operations introduce “oversynchronized ” traces – ones for which a pair of independent actions may occur sequentially. Our language also supports recursion and our semantics makes the unwinding of recursion visible by the use of special resources used to
Local DCPOs, Local CPOs and Local Completions
"... We use a subfamily of the Scottclosed sets of a poset to form a local completion of the poset. This is simultaneously a topological analogue of the ideal completion of a poset and a generalization of the sobrification of a topological space. After we show that our construction is the object level o ..."
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Cited by 2 (0 self)
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We use a subfamily of the Scottclosed sets of a poset to form a local completion of the poset. This is simultaneously a topological analogue of the ideal completion of a poset and a generalization of the sobrification of a topological space. After we show that our construction is the object level of a left adjoint to the forgetful functor from the category of local cpos to the category of posets and Scottcontinuous maps, we use this completion to show how local domains can play a role in the study of domaintheoretic models of topological spaces. Our main result shows that any topological space that is homeomorphic to the maximal elements of a continuous poset that is weak at the top also is homeomorphic to the maximal elements of a bounded complete local domain. The advantage is that continuous maps between such spaces extend to Scottcontinuous maps between the modeling local domains.
www.stacsconf.org FORWARD ANALYSIS FOR WSTS, PART I: COMPLETIONS
, 2009
"... ABSTRACT. Wellstructured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the ..."
Abstract
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ABSTRACT. Wellstructured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretical framework for manipulating downwardclosed sets was missing. We answer this problem, using insights from domain theory (dcpos and ideal completions), from topology (sobrifications), and shed new light on the notion of adequate domains of limits. 1.
RSP: A Language Supporting Synchronization Using Rendezvous
"... A language based on uninterpreted atomic actions and supporting angelic nondeterminism and parallel composition is studied. The language includes also a version of the rendezvous protocol for synchronization between processes. An operational semantics and related adequate and fully abstract denotati ..."
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A language based on uninterpreted atomic actions and supporting angelic nondeterminism and parallel composition is studied. The language includes also a version of the rendezvous protocol for synchronization between processes. An operational semantics and related adequate and fully abstract denotational semantics for the language are presented. In fact, it is shown that the operational semantics and the denotational semantics for this language are isomorphic, so that the operational semantics is compositional. The operational model is given by a transition system which is composed of two sets of rules, rewrite rules and transition rules. The rewrite rules for the language are syntactic program transformations designed to "percolate to the top" the next atomic action or rendezvous to be performed by a process. The use of a rewrite rule does not correspond to an observable step of computation, whereas the use of a transition rule does. We show that the rewrite rules are strongl...