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Some Algebraic Laws for Spans (and Their Connections With MultiRelations)
 Proceedings of RelMiS 2001, Workshop on Relational Methods in Software. Electronic Notes in Theoretical Computer Science, n.44 v.3, Elsevier Science (2001
, 2001
"... This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets. O ..."
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This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets. Our results nd analogous counterparts in (and are partly inspired by) the theory of relational algebras, thus our paper also shed some light on the relationship between (co)spans and the categories of (multi)relations and of equivalence relations. And, since (co)spans yields an intuitive presentation in terms of dynamical system with input and output interfaces, our results introduce an expressive, twofold algebra that can serve as a specication formalism for rewriting systems and for composing software modules and open programs. Key words: Spans, multirelations, monoidal categories, system specications. Introduction The use of spans [1,6] (and of the dual notion of cospans) have been...
Controlflow semantics for assemblylevel dataflow graphs
 8th Intl. Seminar on Relational Methods in Computer Science, RelMiCS 2005, volume 3929 of LNCS
, 2006
"... Abstract. As part of a larger project, we have built a declarative assembly language that enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. Since the key design poi ..."
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Cited by 8 (2 self)
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Abstract. As part of a larger project, we have built a declarative assembly language that enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. Since the key design points for this language are to only describe data flow, have builtin facilities for redundancies, and still have code that looks like assembler, by virtue of consisting mainly of assembly instructions, we are basing the theoretical foundations on dataflow graph theory, and have to accommodate also relational aspects. Using functorial semantics into a Kleene category of “hyperpaths”, we formally capture the dataflowwithchoice aspects of this language and its implementation, providing also the framework for the necessary correctness proofs. 1
Functorial Semantics for Multialgebras
 Recent Trends in Algebraic Development Techniques, volume 1589 of LNCS
, 1998
"... . Multialgebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multialgebras and partial algebras, analogous to the classical pre ..."
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Cited by 7 (4 self)
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. Multialgebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multialgebras and partial algebras, analogous to the classical presentation of algebras over a signature \Sigma as cartesian functors from the algebraic theory of \Sigma , Th(\Sigma), to Set. The functors we introduce are based on variations of the notion of theory, having a structure weaker than cartesian, and their target is Rel, the category of sets and relations. We argue that this functorial presentation provides an original abstract syntax for partial and multialgebras. 1 Introduction Nondeterminism is a fundamental concept in Computer Science. It arises not only from the study of intrinsically nondeterministic computational models, like Turing machines and various kinds of automata, but also in the study of the behaviour of deterministic sys...
Normal Forms for Algebras of Connections
 Theoretical Computer Science
, 2000
"... Recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards the application to the `distributed and concurrent systems' field, ..."
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Cited by 5 (4 self)
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Recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards the application to the `distributed and concurrent systems' field, but an exhaustive comparison between them is sometimes difficult, because their presentations can be quite dissimilar. This work is a first step towards a unified view: Focusing on the primitive ingredients of distributed spaces (namely interfaces, links and basic modules), we introduce a general schema for describing a normal form presentation of many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable monoidal categories.
Term Graph Syntax for MultiAlgebras
, 2000
"... Multialgebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. Starting from a functorial presentation of multialgebras based on gsmonoidal theories, we argue that speci cations for multialgebras ..."
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Cited by 5 (4 self)
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Multialgebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. Starting from a functorial presentation of multialgebras based on gsmonoidal theories, we argue that speci cations for multialgebras should be based on the notion of term graphs instead of on standard terms. We consider the simplest case of (term graph) equational specification, showing that it enjoys an unrestricted form of substitutivity. We discuss the expressive power of equational specification for multialgebras, and we sketch possible extensions of the calculus.
A Decentralized Implementation Of Mobile Ambients
, 2008
"... We present a graphical implementation for finite processes of the mobile ambients calculus. Our encoding uses unstructured (i.e., non hierarchical) graphs and it is sound and complete with respect to the structural congruence of the calculus (that is, two processes are equivalent iff they are mapp ..."
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Cited by 4 (4 self)
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We present a graphical implementation for finite processes of the mobile ambients calculus. Our encoding uses unstructured (i.e., non hierarchical) graphs and it is sound and complete with respect to the structural congruence of the calculus (that is, two processes are equivalent iff they are mapped into isomorphic graphs). With respect to alternative proposals for the graphical implementation of mobile ambients, our encoding distinguishes the syntactic structure of a process from the activation order of a process components. Our solution faithfully captures a basic feature of the calculus (ambients can be nested and reductions are propagated across ambient nesting) and it allows to model the reduction semantics via a graph transformation system containing just three rules.
Rewriting on Cyclic Structures
 EXTENDED ABSTRACT IN FIXED POINTS IN COMPUTER SCIENCE, SATELLITE WORKSHOP OF MFCS'98
, 1998
"... We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the wellaccepted operational definition proposed in [3]  but for the case of circular redexes, for which we propose (and justify formally) a different treatm ..."
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Cited by 4 (3 self)
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We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the wellaccepted operational definition proposed in [3]  but for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework, based on suitable 2categories, allows to model also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures. Furthermore, it can be used for defining various extensions of term graph rewriting, and for relating it to other rewriting formalisms.
Declarative Assembler
, 2004
"... Abstract. As part of a larger project, we have built a declarative assembly language. This language enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. The instructio ..."
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Abstract. As part of a larger project, we have built a declarative assembly language. This language enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. The instruction scheduler is also innovative in that it includes aggressive pipelining, and exhaustive (but lazy) search for optimal instruction schedules. We present some examples where our approach has produced very promising results. 1
A.: Graphical encoding of a spatial logic for the πcalculus
, 2007
"... Abstract. This paper extends our graphbased approach to the verification of spatial properties of πcalculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped with respect to the usual structural congruence, i.e., two processes are equivalent exac ..."
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Cited by 3 (3 self)
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Abstract. This paper extends our graphbased approach to the verification of spatial properties of πcalculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield isomorphic graphs. Behavioral and structural properties of πcalculus processes expressed in a spatial logic can then be verified on the graphical encoding of a process rather than on its textual representation. In this paper we introduce a modal logic for graphs and define a translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula. 1