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Environmental bisimulations for higherorder languages
 In TwentySecond Annual IEEE Symposium on Logic in Computer Science
, 2007
"... Developing a theory of bisimulation in higherorder languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with “upto context ” techniques, and (2) obtaining definitions and results that scale to languages with d ..."
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Developing a theory of bisimulation in higherorder languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with “upto context ” techniques, and (2) obtaining definitions and results that scale to languages with different features. To meet these challenges, we present environmental bisimulations, a form of bisimulation for higherorder languages, and its basic theory. We consider four representative calculi: pure λcalculi (callbyname and callbyvalue), callbyvalue λcalculus with higherorder store, and then HigherOrder πcalculus. In each case: we present the basic properties of environmental bisimilarity, including congruence; we show that it coincides with contextual equivalence; we develop some upto techniques, including upto context, as examples of possible enhancements of the associated bisimulation method. Unlike previous approaches (such as applicative bisimulations, logical relations, SumiiPierceKoutavasWand), our method does not require induction/indices on evaluation derivation/steps (which may complicate the proofs of congruence, transitivity, and the combination with upto techniques), or sophisticated methods such as Howe’s for proving congruence. It also scales from the pure λcalculi to the richer calculi with simple congruence proofs. 1
On the Expressiveness and Decidability of HigherOrder Process Calculi
, 2008
"... In higherorder process calculi the values exchanged in communications may contain processes. A core calculus of higherorder concurrency is studied; it has only the operators necessary to express higherorder communications: input prefix, process output, and parallel composition. By exhibiting a ne ..."
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Cited by 19 (8 self)
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In higherorder process calculi the values exchanged in communications may contain processes. A core calculus of higherorder concurrency is studied; it has only the operators necessary to express higherorder communications: input prefix, process output, and parallel composition. By exhibiting a nearly deterministic encoding of Minsky Machines, the calculus is shown to be Turing Complete and therefore its termination problem is undecidable. Strong bisimilarity, however, is proved to be decidable. Further, the main forms of strong bisimilarity for higherorder processes (higherorder bisimilarity, context bisimilarity, normal bisimilarity, barbed congruence) coincide. They also coincide with their asynchronous versions. A sound and complete axiomatization of bisimilarity is given. Finally, bisimilarity is shown to become undecidable if at least four static (i.e., toplevel) restrictions are added to the calculus.
Howe’s Method for Calculi with Passivation
"... Abstract. We show how to apply Howe’s method for the proof of congruence of early bisimilarities in a higherorder process calculus with passivation. This involves the introduction of a proof technique based on a new kind of transition system and bisimilarity, called complementary semantics. We show ..."
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Abstract. We show how to apply Howe’s method for the proof of congruence of early bisimilarities in a higherorder process calculus with passivation. This involves the introduction of a proof technique based on a new kind of transition system and bisimilarity, called complementary semantics. We show that complementary semantics is equivalent to contextual semantics, originally introduced by Sangiorgi, that relies on classical transition systems for higherorder calculi and context bisimilarity. We apply this technique to obtain the first characterization of weak barbed congruence for such a higherorder calculus with passivation. 1
Characterizing contextual equivalence in calculi with passivation
 INFORMATION AND COMPUTATION
, 2011
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Congruence Proofs For Weak Bisimulation on Higherorder Processes: Results for Typed omegaorder Calculi
, 1996
"... Congruence proofs for bisimulation on higherorder process calculi tend to be significantly more complex than their counterparts in firstorder process algebra frameworks. Moreover, a standard technique that allows us to cover strong forms of bisimulation on higherorder calculi seems to fail for th ..."
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Cited by 4 (1 self)
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Congruence proofs for bisimulation on higherorder process calculi tend to be significantly more complex than their counterparts in firstorder process algebra frameworks. Moreover, a standard technique that allows us to cover strong forms of bisimulation on higherorder calculi seems to fail for the corresponding weak forms. Similar problems are posed by applicative simulation on calculi and our starting point is a general and elegant technique for solving them that has been invented by Howe. We adapt and extend this technique to prove two new congruence results for !order process calculi. In the first case, where we use a static scoping discipline for action names, we treat a delay variant of late weak context bisimulation; in the second case, where we use a dynamic scoping discipline, we treat an early weak higherorder bisimulation. The present paper supersedes parts of our technical report [BF95], where we have considered secondorder processes.
On the Bisimulation Theory and Axiomatization of Higherorder Process Calculi
"... Higherorder process calculi, for its abstraction capability and theoretical significance, have constantly been receiving much attention in the field of process calculi, and stand as a mathematical tool for describing and analyzing mobile systems with dynamically changing interconnection structures ..."
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Higherorder process calculi, for its abstraction capability and theoretical significance, have constantly been receiving much attention in the field of process calculi, and stand as a mathematical tool for describing and analyzing mobile systems with dynamically changing interconnection structures. In this thesis we contribute to the higherorder paradigm in several aspects. • Higherorder πcalculus with mismatch: the bisimulation theory. Linear fragment of higherorder πcalculus with mismatch: the axiomatization. The problem of the axiomatization of higherorder process calculi, such as higherorder πcalculus, is always a nontrivial one. However, it is important, both in theory and practice, to be able to decide whether two higherorder processes are equivalent with respect to some bisimulation, which needs an algorithm that can effectively analyze and give an answer efficiently. We further the available work by considering the higherorder πcalculus with mismatch, which is a useful operator in bisimulation theory and especially the axiomatization, from algorithmic point of view. We first formulate the bisimulation theory, where the bisimulation we define is called open weak higherorder bisimulation, which is a nondelayed
Toward a Bisimulation Theory for Linear HigherOrder πCalculus
, 2007
"... Abstract. Higherorder process calculi have been receiving much attention in recent years for its significance in both theorey and practice. Work on bisimulations has never ceased evolving, typically represented by Thomsen and Sangiorgi for their work on bisimulation theory and encoding to and from ..."
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Abstract. Higherorder process calculi have been receiving much attention in recent years for its significance in both theorey and practice. Work on bisimulations has never ceased evolving, typically represented by Thomsen and Sangiorgi for their work on bisimulation theory and encoding to and from firstorder process calculi. Fu puts forth linear higherorder πcalculus, and makes improvement to previous work on bisimulation and builds a sound and complete equation system by exploitng linearity of processes, which takes resource sensitiveness into account. In this paper, we establish some recent result on bisimulation theory in linear higherorder πcalculus. By exploiting the properties of linear highorder processes, we work out two simpler variants than local bisimulation, which is an intuitive observational equivalence, and they both coincide with local bisimilarity. The first variant, called local linear bisimulation, simplifies the matching of higherorder input and higherorder output based on the feature of checking equivalence with some special processes (in input or output) instead of general ones. The second variant, called local linear variant bisimulation, rewrites the firstorder bound output clause in local bisimulation in some more suitable form for some application on it, by harnessing the congruence properties. We also mention some future work in the conclusion. Key words: Bisimulation, Linear, Higherorder, πCalculus, Process calculi 1
Bisimulation Congruences for HigherOrder Mobile Embedded Resources
"... We present a calculus of HigherOrder Mobile Embedded Resources (Homer), extending Thomsen’s Plain CHOCS, a higherorder calculus with local names, to allow for strongly mobile computing resources in nested locations. We provide labelled transition semantics and strong and weak late labelled transit ..."
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We present a calculus of HigherOrder Mobile Embedded Resources (Homer), extending Thomsen’s Plain CHOCS, a higherorder calculus with local names, to allow for strongly mobile computing resources in nested locations. We provide labelled transition semantics and strong and weak late labelled transition bisimulation congruences, which is proven to be sound with respect to respectively strong and weak barbed bisimulation congruence. The heritage to Plain CHOCS gives a simple reduction and labelled transition semantics, and applicability of Howe’s method for proving contextual bisimulation to be a congruence. The main technical contribution is the successful application of Howe’s method to a calculus with nested, strongly mobile resources with local names and static scoping. We demonstrate the expressiveness of the calculus by giving several examples, in particular we provide a novel encoding of πcalculus namepassing.
Characterizing Contextual Equivalence in Calculi with
"... We study the problem of characterizing contextual equivalence in higherorder languages with passivation. To overcome the difficulties arising in the proof of congruence of candidate bisimilarities, we introduce a new form of labelled transition semantics together with its associated notion of bisim ..."
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We study the problem of characterizing contextual equivalence in higherorder languages with passivation. To overcome the difficulties arising in the proof of congruence of candidate bisimilarities, we introduce a new form of labelled transition semantics together with its associated notion of bisimulation, which we call complementary semantics. Complementary semantics allows to apply the wellknown Howe’s method for proving the congruence of bisimilarities in a higherorder setting, even in presence of an early form of bisimulation. We use complementary semantics to provide a coinductive characterization of contextual equivalence in the HOπP calculus, an extension of the higherorder πcalculus with passivation, obtaining the first result of this kind. We then study the problem of defining a more effective variant of bisimilarity that still characterizes contextual equivalence, along the lines of Sangiorgi’s notion of normal bisimilarity. We provide partial results on this difficult problem: we show that a large class of test processes cannot be used to derive a normal bisimilarity in HOπP, but we show that a form of normal bisimilarity can be defined for HOπP without restriction. 1.
Added entries UNIVERSITY OF NEWCASTLE UPON TYNE
, 1117
"... Petri nets are a wellestablished model of concurrent and distributed computation featuring a wealth of tools for the analysis and verification of their behavioural properties. Like membrane systems, Petri nets are in essence multiset rewriting systems. Using this key commonality we describe a faith ..."
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Petri nets are a wellestablished model of concurrent and distributed computation featuring a wealth of tools for the analysis and verification of their behavioural properties. Like membrane systems, Petri nets are in essence multiset rewriting systems. Using this key commonality we describe a faithful translation from basic membrane systems to Petri nets. We also sketch the changes required to deal with promoters and inhibitors and with dynamically changing membrane structures. To capture the compartmentisation of membrane systems, the Petri net model is extended with localities and we show how to adapt the notion of a Petri net process accordingly. This makes it possible to describe ongoing concurrent behaviour of membrane systems in terms of causalities between the reactions that are taking place. © 2008 University of Newcastle upon Tyne.