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13
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, ..."
Abstract

Cited by 64 (12 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.
Cartesian Closed Double Categories, their LambdaNotation, and the PiCalculus
, 1999
"... We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between s ..."
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Cited by 20 (12 self)
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We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between simply typed calculus and cartesian closed categories, we define a new typed framework, called double notation, which is able to express the abstraction /application and pairing/projection operations in all dimensions. In this development, we take the categorical presentation as a guidance in the interpretation of the formalism. A case study of the ßcalculus, where the double  notation straightforwardly handles name passing and creation, concludes the presentation.
A General Framework for Types in Graph Rewriting
, 2000
"... . A general framework for typing graph rewriting systems is presented: the idea is to statically derive a type graph from a given graph. In contrast to the original graph, the type graph is invariant under reduction, but still contains meaningful behaviour information. We present conditions, a t ..."
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Cited by 10 (3 self)
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. A general framework for typing graph rewriting systems is presented: the idea is to statically derive a type graph from a given graph. In contrast to the original graph, the type graph is invariant under reduction, but still contains meaningful behaviour information. We present conditions, a type system for graph rewriting should satisfy, and a methodology for proving these conditions. In two case studies it is shown how to incorporate existing type systems (for the polyadic  calculus and for a concurrent objectoriented calculus) into the general framework. 1 Introduction In the past, many formalisms for the specication of concurrent and distributed systems have emerged. Some of them are aimed at providing an encompassing theory: a very general framework in which to describe and reason about interconnected processes. Examples are action calculi [18], rewriting logic [16] and graph rewriting [3] (for a comparison see [4]). They all contain a method of building terms (or ...
A Rewriting Logic Approach to Operational Semantics – Extended Abstract Abstract
, 2007
"... This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: bigstep and smallstep structural operational semantics (SOS), modular SOS, reductio ..."
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Cited by 1 (0 self)
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This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: bigstep and smallstep structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, and continuationbased semantics. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a onetoone correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or preimpose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles. 1
Cartesian Closed Double Categories,
"... their LambdaNotation, and the PiCalculus We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. ..."
Abstract
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their LambdaNotation, and the PiCalculus We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between simply typed ¢calculus and cartesian closed categories, we define a new typed framework, called double ¢notation, which is able to express the abstraction/application and pairing/projection operations in all dimensions. In this development, we take the categorical presentation as a guidance in the interpretation of the formalism. A case study of the £calculus, where the double ¢notation straightforwardly handles name passing and creation, concludes the presentation.
Deriving Bisimulation Congruences with Borrowed Contexts (Abstract)
, 2007
"... In the last few years the problem of deriving labelled transitions and bisimulation congruences from unlabelled reaction or rewriting rules has received great attention. This line of research was motivated by the theory of bisimulation congruences for process calculi, such as the πcalculus [19, 14] ..."
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In the last few years the problem of deriving labelled transitions and bisimulation congruences from unlabelled reaction or rewriting rules has received great attention. This line of research was motivated by the theory of bisimulation congruences for process calculi, such as the πcalculus [19, 14]. A bisimilarity defined on unlabelled reduction rules is usually not a congruence, that is, it is not closed under the operators of the process calculus. Congruence is a desirable property since it allows one to replace a subsystem with an equivalent one without changing the behaviour of the overall system and futhermore helps to make bisimilarity proofs modular. Previous solutions have been to either require that two processes are related if and only if they are bisimilar under all possible contexts [15] or to derive a labelled transition system manually. Since the first solution needs quantification over all possible contexts, proofs of bisimilarity can be very complicated. In the second solution, proofs tend to be much easier, but it is necessary to show that the labelled variant of the transition system is equivalent to the unlabelled
Analysis and Verification of Systems with Dynamically Evolving Structure
"... This thesis is concerned with verification and analysis techniques for software systems characterized by dynamically evolving structure, such as dynamic creation and deletion of objects, mobility and variable topology. Examples for such systems are pointer structures, objectbased systems and commun ..."
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This thesis is concerned with verification and analysis techniques for software systems characterized by dynamically evolving structure, such as dynamic creation and deletion of objects, mobility and variable topology. Examples for such systems are pointer structures, objectbased systems and communication protocols in which the number of participants is not constant. The approach taken here is based on graph transformation systems, an intuitive and—at the same time—powerful formalism for the modelling of distributed and mobile systems. So far there exists comparatively little research concerning the verification of graph rewriting. We will—in the first part of this thesis—introduce graph transformations and give an overview of existing analysis and verification methods, with a focus on the verification of systems with dynamically evolving structure. Then we will describe three original lines of research: behavioural equivalences, type systems and approximation by Petri nets, all of them concerned with the analysis of
Some Algebraic Properties of (Co)Spans
, 2000
"... The paper investigates the algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions. We analyze the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets, show ..."
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The paper investigates the algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions. We analyze the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets, showing that they characterize dierent selfdual algebraic structures. Furthermore, our results shed some light on their relationship with the categories of (multi)relations and of equivalence relations. Introduction Recent years have seen a large diusion of equational presentations for dierent graphlike structures. The motivations underlying these works are quite varied, and dicult to recast in a unitary thread, even if they could be roughly divided into two halves, albeit tightly intertwined. On the one hand, there have been the studies regarding the syntax for diagrammatic presentations of, e.g., nets and circuits. The initial works can be considered those introducing the ownomial c...
unknown title
, 2004
"... www.elsevier.com/locate/tcs Observational congruences for dynamically reconfigurable tile systems � ..."
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www.elsevier.com/locate/tcs Observational congruences for dynamically reconfigurable tile systems �