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45
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 298 (31 self)
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In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken
Integration of Sequential Scenarios
 IEEE Transactions on Software Engineering
, 1998
"... Abstract—We give a formal relationbased definition of scenarios and we show how different scenarios can be integrated to obtain a more global view of usersystem interactions. We restrict ourselves to the sequential case, meaning that we suppose that there is only one user (thus, the scenarios we w ..."
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Cited by 18 (2 self)
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Abstract—We give a formal relationbased definition of scenarios and we show how different scenarios can be integrated to obtain a more global view of usersystem interactions. We restrict ourselves to the sequential case, meaning that we suppose that there is only one user (thus, the scenarios we wish to integrate cannot occur concurrently). Our view of scenarios is statebased, rather than eventbased, like most of the other approaches, and can be grafted to the wellestablished specification language Z. Also, the end product of scenario integration, the specification of the functional aspects of the system, is given as a relation; this specification can be refined using independently developed methods. Our formal description is coupled with a diagrambased, transitionsystem like, presentation of scenarios, which is better suited to communication between clients and specifiers. Index Terms—Scenario, integration, usersystem interaction, requirements elicitation, relational approach, statebased approach. 1
Foundations of the Trace Assertion Method of Module Interface Specification
, 2000
"... The trace assertion method is a formal state machine based method for specifying module interfaces. A module interface specification treats the module as a blackbox, identifying all module's ..."
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Cited by 17 (1 self)
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The trace assertion method is a formal state machine based method for specifying module interfaces. A module interface specification treats the module as a blackbox, identifying all module's
Answering Conceptual Queries with Ferret
, 2008
"... Programmers seek to answer questions as they investigate the functioning of a software system, such as “which execution path is being taken in this case?” Programmers attempt to answer these questions, which we call conceptual queries, using a variety of tools. Each type of tool typically highlights ..."
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Cited by 16 (1 self)
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Programmers seek to answer questions as they investigate the functioning of a software system, such as “which execution path is being taken in this case?” Programmers attempt to answer these questions, which we call conceptual queries, using a variety of tools. Each type of tool typically highlights one kind of information about the system, such as static structural information or controlflow information. Unfortunately for the programmer, the tools seldom directly answer the programmer’s conceptual queries. Instead, the programmer must piece together results from different tools to determine an answer to the initial query. At best, this process is time consuming and at worst, this process can lead to data overload and disorientation. In this paper, we present a model that supports the integration of different sources of information about a program. This model enables the results of concrete queries in separate tools to be brought together to directly answer many of a programmer’s conceptual queries. In addition to presenting this model, we present a tool that implements the model, demonstrate the range of conceptual queries supported by this tool, and present the results of use of the conceptual queries in a small field study.
An Algebraic Formalization of Fuzzy Relations
 Fuzzy Sets and Systems 101
, 1995
"... This paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with supmin composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom has been given by G. Schmidt and T. Strohlein. Unlike Boolean ..."
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Cited by 9 (5 self)
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This paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with supmin composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom has been given by G. Schmidt and T. Strohlein. Unlike Boolean relation algebras, fuzzy relation algebras are not Boolean but equipped with semiscalar multiplication. First we present a set of axioms for fuzzy relation algebras and improve the definition of point relations. Then by using relational calculus a representation theorem for such relation algebras is deduced without Tarski rule. Keywords : fuzzy relations, relation algebras, relational calculus, representation theorem. 1 Introduction Since Zadeh's invention the concept of fuzzy sets has been extensively investigated in mathematics, science and engineering. The notion of fuzzy relations is also a basic one in processing fuzzy information in relational structures, see e.g. Pedrycz [9]. Gogue...
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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Cited by 9 (3 self)
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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...
Algorithm and architecturelevel design space exploration using hierarchical data flows
 in: IEEE International Conference on ApplicationsSpecific Systems, Architectures and Processors
, 1997
"... Incorporating algorithm and architecture level design space exploration in the early phases of the design process can have a dramatic impact on the area, speed, and power consumption of the resulting systems. This paper proposes a framework for supporting systemlevel design space exploration and di ..."
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Cited by 8 (0 self)
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Incorporating algorithm and architecture level design space exploration in the early phases of the design process can have a dramatic impact on the area, speed, and power consumption of the resulting systems. This paper proposes a framework for supporting systemlevel design space exploration and discusses the three fundamental issues involved in effectively supporting such an early design space exploration: dejinition of an adequate level of abstraction: definition of goodfidelity systemlevel metrics; and definition of mechanisms for automating the exploration process. Thejirst issue, the definition of an adequate level of abstraction is then addressed in detail. Specifically, an algorithmlevel model, an architecturelevel model, and a set of operations on these models, are proposed, aiming at efficiently supporting an early, aggressive systemlevel design space exploration. A discussion on work in progress in the other two topics, metrics and automation, concludes the papel: 1
On Automating the Calculus of Relations
 In: Proc. IJCAR. Vol. 5195. LNCS
, 2008
"... Abstract. Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer science. We prove more than hundred theorems of relation algebras with offtheshelf automated theorem provers. This ..."
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Cited by 7 (2 self)
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Abstract. Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer science. We prove more than hundred theorems of relation algebras with offtheshelf automated theorem provers. This yields a basic calculus from which more advance applications can be explored. Here, we present two examples from the formal methods literature. Our experiments not only further underline the feasibility of automated deduction in complex algebraic structures and provide theorem proving benchmarks, they also pave the way for lifting established formal methods such as B or Z to a new level of automation. 1
Relational Set Theory
 Lecture Notes in Computer Science
, 1995
"... This article presents a relational formalization of axiomatic set theory, including socalled ZFC and the antifoundation axiom (AFA) due to P. Aczel. The relational framework of set theory provides a general methodology for the fundamental study on computer and information sciences such as theory of ..."
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Cited by 6 (4 self)
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This article presents a relational formalization of axiomatic set theory, including socalled ZFC and the antifoundation axiom (AFA) due to P. Aczel. The relational framework of set theory provides a general methodology for the fundamental study on computer and information sciences such as theory of graph transformation, situation semantics and analysis of knowledge dynamics in distributed systems. To demonstrate the feasibility of relational set theory some fundamental theorems of set theory, for example, CantorBernstein Schroder theorem, Cantor's theorem, Rieger's theorem and Mostowski's collapsing lemma are proved. 1 Introduction The study on (binary) relations on sets has been begun together with the pioneering works of set theory and since then theory of relations has been extensively investigated by many mathematicians from the view points of logic, algebra, topology and computer science. For more detailed history of studies on relations the reader refer to R.D. Muddux [14] and...
Categorical Representation Theorems of Fuzzy Relations
 Proceedings of 4th International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (RSFD 96) 190197
, 1996
"... This paper provides a notion of Zadeh categories as a categorical structure formed by fuzzy relations with supmin composition, and proves two representation theorems for Dedekind categories (relation categories) with a unit object analogous to onepoint set, and for Zadeh categories without unit ob ..."
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Cited by 6 (6 self)
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This paper provides a notion of Zadeh categories as a categorical structure formed by fuzzy relations with supmin composition, and proves two representation theorems for Dedekind categories (relation categories) with a unit object analogous to onepoint set, and for Zadeh categories without unit objects. Keywords: fuzzy relations, relation algebras, representation theorem, Dedekind categories, Zadeh category. 1 Introduction Since Zadeh's invention the concept of fuzzy sets has been extensively investigated in mathematics, science and engineering. The notion of fuzzy relations is also a basic one in processing fuzzy information in relational structures, see e.g. Pedrycz [10]. Goguen [2] generalized the concepts of fuzzy sets and relations taking values on partially ordered sets. Fuzzy relational equations were initiated and applied to medical models of diagnosis by Sanchez [12]. On the other hand theory of relations, namely relational calculus, has a long history, see [8, 13, 14] for...