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18
Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting
, 2004
"... Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to solve this problem in the DPO (doublepushout) approach to graph rewriting. Unlike in previous approaches, we consider graphs as objects, instead of arrows, ..."
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Cited by 78 (16 self)
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Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to solve this problem in the DPO (doublepushout) approach to graph rewriting. Unlike in previous approaches, we consider graphs as objects, instead of arrows, of the category under consideration. This allows us to present a very simple way of deriving labelled transitions (called rewriting steps with borrowed context) which smoothly integrates with the DPO approach, has a very constructive nature and requires only a minimum of category theory. The core part of this paper is the proof sketch that the bisimilarity based on rewriting with borrowed contexts is a congruence relation.
On the expressiveness of internal mobility in namepassing calculi
, 1998
"... We consider the language rI, a namepassing calculus introduced by Sangiorgi, where only private names can be exchanged among processes (internal mobility). The calculus 7cI has simple mathematical theory, very close to that of CCS. We provide an encoding from (an asynchronous variant of) the ~rca ..."
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Cited by 43 (0 self)
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We consider the language rI, a namepassing calculus introduced by Sangiorgi, where only private names can be exchanged among processes (internal mobility). The calculus 7cI has simple mathematical theory, very close to that of CCS. We provide an encoding from (an asynchronous variant of) the ~rcalculus to IrI, which is fully abstract on the reduction relations of the two calculi. The result shows that, in namepassing calculi, internal mobility is the essential ingredient as far as expressiveness i concerned. 1 In t roduct ion By now, the 7rcalculus [13] is generally recognized as the prototypical algebraic language for describing concurrent systems with dynamically evolving communication linkage. The latter phenomenon, known as mobility, is modelled through the passing of channel names among processes (namepassing). The expressive power of the ~rcalculus is demonstrated by the existence of simple and fully abstract ranslations into it for a variety of computational formalisms, including Acalculus [12], higherorder process calculi [15] and calculi which permits reasoning on the causal or spatial structure of the systems [4, 17]. The price to pay for this expressiveness i a rather complex mathematical theory of the rcalculus. A source of complications i, above all, the need to take name instantiation (otherwise called substitution) into account. Input and output at a of a tuple of names b are written, respectively, asa(b).P (input prefix) and ~(b).P (output prefix), with P representing the continuation of the prefix. An input and an output prefix can be consumed in a communication, where a tuple of names is passed and used to instantiate the formal parameters of the input prefix, thus: a(c).P]5<b>.Q ~, P{b/~}]Q (,) with {b~} denoting the instantiation ofnames in ~'with names in b. Name instantiation is a central aspect in the mathematical treatment of certain behavioural relations.
Solos in concert
 IN ICALP’99, LNCS 1644:513–523
, 1999
"... We present a calculus of mobile processes without prefix or summation, and using two different encodings we show that it can express both action prefix and guarded summation. One encoding gives a strong correspondence but uses a match operator; the other yields a slightly weaker correspondence but u ..."
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Cited by 21 (4 self)
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We present a calculus of mobile processes without prefix or summation, and using two different encodings we show that it can express both action prefix and guarded summation. One encoding gives a strong correspondence but uses a match operator; the other yields a slightly weaker correspondence but uses no additional operators.
ProofChecking Protocols using Bisimulations
 IN PROC. CONCUR’99, LNCS 1664
, 1999
"... We report on our experience in using the Isabelle/HOL theorem prover to mechanize proofs of observation equivalence for systems with infinitely many states, and for parameterized systems. We follow the direct approach: An infinite relation containing the pair of systems to be shown equivalent is def ..."
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Cited by 12 (2 self)
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We report on our experience in using the Isabelle/HOL theorem prover to mechanize proofs of observation equivalence for systems with infinitely many states, and for parameterized systems. We follow the direct approach: An infinite relation containing the pair of systems to be shown equivalent is defined, and then proved to be a weak bisimulation. The weak bisimilarity proof is split into many cases, corresponding to the derivatives of the pairs in the relation. Isabelle/HOL automatically proves simple cases, and guarantees that no case is forgotten. The strengths and weaknesses of the approach are discussed.
Observational Equivalence for Synchronized Graph Rewriting with Mobility
, 2001
"... We introduce a notion of bisimulation for graph rewriting systems, allowing us to prove observational equivalence for dynamically evolving graphs and networks. We use the framework of synchronized graph rewriting with mobility which we describe in two different, but operationally equivalent ways: on ..."
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Cited by 10 (7 self)
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We introduce a notion of bisimulation for graph rewriting systems, allowing us to prove observational equivalence for dynamically evolving graphs and networks. We use the framework of synchronized graph rewriting with mobility which we describe in two different, but operationally equivalent ways: on graphs defined as syntactic judgements and by using tile logic. One of the main results of the paper says that bisimilarity for synchronized graph rewriting is a congruence whenever the rewriting rules satisfy the basic source property. Furthermore we introduce an upto technique simplifying bisimilarity proofs and use it in an example to show the equivalence of a communication network and its specification.
Behavioural Equivalences for Dynamic Web Data
, 2004
"... We study behavioural equivalences for dynamic web data in Xd#, a model for reasoning about behaviour found in (for example) dynamic web page programming, applet interaction, and webservice orchestration. Xd# is based on an idealised model of semistructured data, and an extension of the #calculus ..."
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Cited by 6 (3 self)
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We study behavioural equivalences for dynamic web data in Xd#, a model for reasoning about behaviour found in (for example) dynamic web page programming, applet interaction, and webservice orchestration. Xd# is based on an idealised model of semistructured data, and an extension of the #calculus with locations and operations for interacting with data. The equivalences are nonstandard due to the integration of data and processes, and the presence of locations. Contents 1
Description and Verification of Mobile Processes with Graph Rewriting Techniques
"... The aim of this thesis is to describe the semantics of a process calculus by means of hypergraph rewriting, creating a specification mechanism combining modularity of process calculi and locality of graph transformation. Verification of processes is addressed by presenting two methods: barbed congru ..."
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Cited by 5 (5 self)
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The aim of this thesis is to describe the semantics of a process calculus by means of hypergraph rewriting, creating a specification mechanism combining modularity of process calculi and locality of graph transformation. Verification of processes is addressed by presenting two methods: barbed congruence for relating processes displaying the same behaviour and generic type systems, forming a central part of this work. Based on existing work in graph rewriting...
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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Cited by 4 (0 self)
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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
A πcalculus process semantics of concurrent idealised ALGOL
 In Proc. FOSSACS'99, volume 1578 of LNCS
, 1999
"... We study the use of the πcalculus for semantical descriptions of languages such as Concurrent Idealised ALGOL (CIA), combining imperative, functional and concurrent features. We first present an operational semantics for CIA, given by SOS rules and a contextual form of behavioural equivalence; th ..."
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Cited by 3 (0 self)
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We study the use of the πcalculus for semantical descriptions of languages such as Concurrent Idealised ALGOL (CIA), combining imperative, functional and concurrent features. We first present an operational semantics for CIA, given by SOS rules and a contextual form of behavioural equivalence; then a πcalculus semantics. As behavioural equivalence on πcalculus processes we choose the standard (weak early) bisimilarity. We compare the two semantics, demonstrating that there is a close operational correspondence between them and that the πcalculus semantics is sound. This allows for applying thecalculus theory in proving behavioural properties of CIA phrases. We discuss laws and examples which have served as benchmarks to various semantics, and a more complex example involving procedures of higher order.
Proving Write Invalidate Cache Coherence with Bisimulations in Isabelle/HOL
, 2000
"... The aim of this paper is to advocate the use of bisimulation relations in the verification of infinitestate or parameterized systems, and demonstrates the support that generalpurpose theorem provers can offer. A powerful proof technique, known as up to expansion, is discussed and applied in a case ..."
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Cited by 2 (1 self)
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The aim of this paper is to advocate the use of bisimulation relations in the verification of infinitestate or parameterized systems, and demonstrates the support that generalpurpose theorem provers can offer. A powerful proof technique, known as up to expansion, is discussed and applied in a case study about write invalidate cache coherence. This example is of interest, as the system is parameterized in the number of its components, and the bisimulation relation reflects the coherence of the caches with the main memory.