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Rewriting Logic as a Semantic Framework for Concurrency: a Progress Report
, 1996
"... . This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency mod ..."
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Cited by 83 (23 self)
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. This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency models, each on its own terms, avoiding any encodings or translations. Bringing very different models under a common semantic framework makes easier to understand what different models have in common and how they differ, to find deep connections between them, and to reason across their different formalisms. It becomes also much easier to achieve in a rigorous way the integration and interoperation of different models and languages whose combination offers attractive advantages. The logic and model theory of rewriting logic are also summarized, a number of current research directions are surveyed, and some concluding remarks about future directions are made. Table of Contents 1 In...
The Tile Model
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1996
"... In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the ..."
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Cited by 65 (24 self)
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In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the others, the structured operational semantics [Plo81], the context systems [LX90] and the structured transition systems [CM92] approaches. Our model recollects many properties of these sources: first, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Second, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. Finally, an equivalence relation over sequences of transitions is defined, equipping the system under analysis with a concurrent semantics, ...
Internal Strategies in a Rewriting Implementation of Tile Systems
 Rewriting Logic and its Applications, volume 15 of Electronic Notes in Theoretical Computer Science. Elsevier Sciences
, 1998
"... Tile logic extends rewriting logic, taking into account rewriting with sideeffects and rewriting synchronization. Since rewriting logic is the semantic basis of several language implementation efforts, it is interesting to map tile logic back into rewriting logic in a conservative way, to obtain ex ..."
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Cited by 16 (11 self)
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Tile logic extends rewriting logic, taking into account rewriting with sideeffects and rewriting synchronization. Since rewriting logic is the semantic basis of several language implementation efforts, it is interesting to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. The resulting implementation requires a metalayer to control the rewritings, so that only tile proofs are accepted. However, by exploiting the reflective capabilities of the Maude language, such metalayer can be specified as a kernel of internal strategies. It turns out that the required strategies are very general and can be reformulated in terms of search algorithms for nonconfluent systems equipped with a notion of success. We formalize such strategies, giving their detailed description in Maude, and showing their application to modeling uniform tile systems. 1 Introduction The evolution of a process in a concurrent system often depends on the ...
Executable Tile Specifications for Process Calculi
, 1999
"... . Tile logic extends rewriting logic by taking into account sideeffects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and "the rest of the world". Since rewriting log ..."
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Cited by 14 (10 self)
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. Tile logic extends rewriting logic by taking into account sideeffects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and "the rest of the world". Since rewriting logic is the semantic basis of several language implementation efforts, an executable specification of tile systems can be obtained by mapping tile logic back into rewriting logic, in a conservative way. However, a correct rewriting implementation of tile logic requires the development of a metalayer to control rewritings, i.e., to discard computations that do not correspond to any deduction in tile logic. We show how such methodology can be applied to term tile systems that cover and extend a wideclass of SOS formats for the specification of process calculi. The wellknown casestudy of full CCS, where the term tile format is needed to deal with recursion (in the form of the replicator operator), is di...
Tiles, Rewriting Rules and CCS
"... In [12] we introduced the tile model, a framework encompassing a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting and of concurrency theory, and our formalism recollects many properties ..."
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Cited by 14 (8 self)
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In [12] we introduced the tile model, a framework encompassing a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting and of concurrency theory, and our formalism recollects many properties of these sources. For example, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Moreover, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. In this work we narrow our scope, presenting a restricted version of our tile model and focussing our attention on its expressive power. To this aim, we recall the basic definitions of the process algebras paradigm [3,24], centering the paper on the recasting of this framework in our formalism.
An Opfibration Account of Typed DPO and DPB Graph Transformation: Injective Productions
, 1996
"... : The "in the large" properties of typed graph transformation systems in the double pushout framework and a double pullback variation of it, are reexamined for injective productions (for which the theory is strictly richer than in the general case). Preceding accounts utilising a fixed cho ..."
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Cited by 3 (2 self)
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: The "in the large" properties of typed graph transformation systems in the double pushout framework and a double pullback variation of it, are reexamined for injective productions (for which the theory is strictly richer than in the general case). Preceding accounts utilising a fixed choice of pullbacks (whether adopted directly or via partial morphisms) are seen to be excessively sensitive to the precise graphs involved for comfort. The properties of a fixed choice of pullbacks are seen to be analogous to those of a splitting of an opfibration, and so a framework of graph transformations utilising unsplit opfibrations is constructed, which proves to be free of the excessive sensitivity noted. The new formulation exploits a triple category whose existence depends crucially on the injectivity of productions. In the new framework, graph grammars graph transition systems and graph derivation systems, computation grammars computation systems and computation sequence systems, are all cons...
Abstract diagrams and an opfibration account of typed graph transformation
, 1999
"... Abstract: The “in the large ” properties of typed graph transformation systems in the double pushout framework and a double pullback variation of it, are reexamined. Preceding accounts utilising a fixed choice of pullbacks (whether adopted directly or via partial morphisms) are seen diagrams is deve ..."
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Cited by 2 (0 self)
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Abstract: The “in the large ” properties of typed graph transformation systems in the double pushout framework and a double pullback variation of it, are reexamined. Preceding accounts utilising a fixed choice of pullbacks (whether adopted directly or via partial morphisms) are seen diagrams is developed, that allows the smooth formulation of an abstract version of the theory.
The Concurrency Column
"... in organizing a thematic research workshop, a strategic meeting charting new research agenda or an advanced school on a theme related to concurrency theory to consider the University Residential Centre of Bertinoro, Bertinoro (Forl), Italy, as a possible location for it. Activities taking place in ..."
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in organizing a thematic research workshop, a strategic meeting charting new research agenda or an advanced school on a theme related to concurrency theory to consider the University Residential Centre of Bertinoro, Bertinoro (Forl), Italy, as a possible location for it. Activities taking place in that beautiful conference location are held under the organization and sponsorship of BICI (Bertinoro International Center for Informatics). On behalf of the concurrency theory community, I welcome the establishment of such an association devoted to the development of research in Computer Science via the sponsorship of high quality events in an environment that offers excellent support, and a congenial atmosphere, for the hosting of research activities. P###### ####### ##### ##### ########### Wan Fokkink, Jan Friso Groote, Michel Reniers Dep. of Mathematics and Computer Science, Eindhoven University of Technology P.O. Box 513, 5600 MB Eindhoven, The Netherlands CWI, P.O. Box 94079, 109
A Fibration Semantics for PiCalculus Modules via Abstract MONSTR . . .
, 1996
"... MONSTR Rule Systems R. Banach UMCS9673 Computer Science University of Manchester Technical Report Series University of Manchester Department of Computer Science ISSN 1361  6161 2 A Fibration Semantics for PiCalculus Modules via Abstract MONSTR Rule Systems* R. Banach Department of ..."
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MONSTR Rule Systems R. Banach UMCS9673 Computer Science University of Manchester Technical Report Series University of Manchester Department of Computer Science ISSN 1361  6161 2 A Fibration Semantics for PiCalculus Modules via Abstract MONSTR Rule Systems* R. Banach Department of Computer Science University of Manchester Oxford Road, Manchester, U.K. banach@cs.man.ac.uk 31 July 1996 Copyright 1996. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that: (1) this copyright notice is included, (2) proper attribution to the author or authors is made, and (3) no commercial gain is involved. Recent technical reports issued by the Department of Computer Science, Manchester University, are available by anonymous ftp from ftp.cs.man.ac.uk in the directory pub/TR. The files are stored as PostScript, in compressed form, with the report number as filename. They can also be obtained on WWW via ...
COMPLEX NONLINEAR BIODYNAMICS IN CATEGORIES, HIGHER DIMENSIONAL ALGEBRA AND ŁUKASIEWICZ– MOISIL TOPOS: TRANSFORMATIONS OF NEURONAL,
"... ABSTRACT. A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of nonlinear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz– Moisil Algebraic–Logic models of neural, genetic and neoplastic cell ..."
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ABSTRACT. A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of nonlinear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz– Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of nonlinear dynamic systems with nstate components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘nextstate functions ’ is extended to a Łukasiewicz–Moisil Topos with an nvalued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents nonrandom and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, noncommutative quantum logics are considered in the context of an emerging Quantum Relational Biology. KEY WORDS: adjoint functors and dynamically analogous systems, biogroupoids and organismal development, biological principles, nuclear equivalence and cell differentiation, categories, nvalued logics and higher dimensional algebra in neuroscience and genetics, cognitive and anticipatory processes, learning and quantum wavepattern recognition, colimits, limits and adjointness relations in biology, generalized (M,R)systems, neurocategories and consciousness, quantum automata and relational biology, quantum bionetworks and their underlying quantum logics, quantum computers 1.