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Refinement of Actions and Equivalence Notions for Concurrent Systems
 Acta Informatica
, 1998
"... This paper combines and extends the material of [GGa/c/d/e], except for the part in [GGc] on refinement of transitions in Petri nets and the discussion of TCSPlike parallel composition in [GGe]. An informal presentation of some basic ingredients of this paper appeared as [GGb]. Among others, th ..."
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Cited by 63 (4 self)
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This paper combines and extends the material of [GGa/c/d/e], except for the part in [GGc] on refinement of transitions in Petri nets and the discussion of TCSPlike parallel composition in [GGe]. An informal presentation of some basic ingredients of this paper appeared as [GGb]. Among others, the treatment of action refinement in stable and nonstable event structures is new. The research reported here was supported by Esprit project 432 (METEOR), Esprit Basic Research Action 3148 (DEMON), Sonderforschungsbereich 342 of the TU Munchen, ONR grant N0001492J1974 and the Human Capital and Mobility Cooperation Network EXPRESS (Expressiveness of Languages for Concurrency). Contents
Categorical Logic of Names and Abstraction in Action Calculi
, 1993
"... ion elimination Definition 3.1. A monoidal category where every object has a commutative comonoid structure is said to be semicartesian. An action category is a K\Omega category with a distinguished admissible commutative comonoid structure on every object. A semicartesian category is cartesi ..."
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Cited by 27 (14 self)
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ion elimination Definition 3.1. A monoidal category where every object has a commutative comonoid structure is said to be semicartesian. An action category is a K\Omega category with a distinguished admissible commutative comonoid structure on every object. A semicartesian category is cartesian if and only if each object carries a unique comonoid structure, and such structures form two natural families, \Delta and !. The naturality means that all morphisms of the category must be comonoid homomorphisms. In action categories, the property of semicartesianness is fixed as structure: on each object, a particular comonoid structure is chosen. This choice may be constrained by some given graphic operations, with respect to which the structures must be admissible. The proof of proposition 2.6 shows that such structures determine the abstraction operators, and are determined by them. This is the essence of the equivalence of action categories and action calculi. As the embodiment of 2...
Interaction as a Framework for Modeling
"... The irreducibility of interactive to algorithmic computing requires fundamental questions concerning models of computation to be reexamined. This paper reviews singlestream and multiplestream interaction machines, extensions of set theory and algebra for models of sequential interaction, and int ..."
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Cited by 17 (6 self)
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The irreducibility of interactive to algorithmic computing requires fundamental questions concerning models of computation to be reexamined. This paper reviews singlestream and multiplestream interaction machines, extensions of set theory and algebra for models of sequential interaction, and interactive extensions of the Turing test. It motivates the use of interactive models as a basis for applications to computer architecture, software engineering, and artificial intelligence.
Approximable concepts, Chu spaces, and information systems
"... This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cros ..."
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Cited by 13 (8 self)
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This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of crossdisciplinary connections. Among other results, we show that the notion of state in Scott’s information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation corresponds to “association rules”. We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work [Hitzler and Zhang, 2004] in which a new notion of morphism on formal contexts results in a category equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings.
Mathematical Models of Interactive Computing
, 1999
"... : Finite computing agents that interact with an environment are shown to be more expressive than Turing machines according to a notion of expressiveness that measures problemsolving ability and is specified by observation equivalence. Sequential interactive models of objects, agents, and embedded s ..."
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Cited by 11 (1 self)
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: Finite computing agents that interact with an environment are shown to be more expressive than Turing machines according to a notion of expressiveness that measures problemsolving ability and is specified by observation equivalence. Sequential interactive models of objects, agents, and embedded systems are shown to be more expressive than algorithms. Multiagent (distributed) models of coordination, collaboration, and true concurrency are shown to be more expressive than sequential models. The technology shift from algorithms to interaction is expressed by a mathematical paradigm shift that extends inductive definition and reasoning methods for finite agents to coinductive methods of set theory and algebra. An introduction to models of interactive computing is followed by an account of mathematical models of sequential interaction in terms of coinductive methods of nonwellfounded set theory, coalgebras, and bisimulation. Models of distributed information flow and multiagent inter...
Towards Semantics of SelfAdaptive Software
, 2000
"... When people perform computations, they routinely monitor their results, and try to adapt and improve their algorithms when a need arises. The idea of selfadaptive software is to implement this common facility of human mind within the framework of the standard logical methods of software engineering ..."
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Cited by 9 (1 self)
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When people perform computations, they routinely monitor their results, and try to adapt and improve their algorithms when a need arises. The idea of selfadaptive software is to implement this common facility of human mind within the framework of the standard logical methods of software engineering. The ubiquitous practice of testing, debugging and improving programs at the design time should be automated, and established as a continuing run time routine. Technically, the task thus requires combining functionalities of automated software development tools and of runtime environments. Such combinations lead not just to challenging engineering problems, but also to novel theoretical questions. Formal methods are needed, and the standard techniques do not suffice. As a first contribution in this direction, we present a basic mathematical framework suitable for describing selfadaptive software at a high level of semantical abstraction. A static view leads to a structure akin...
CATEGORIES ENRICHED OVER A QUANTALOID: ISBELL ADJUNCTIONS AND KAN ADJUNCTIONS
"... Abstract. Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads. These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in ..."
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Cited by 3 (2 self)
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Abstract. Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads. These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in category theory. It is proved that these two processes are functorial with infomorphisms playing as morphisms between distributors; and that the free cocompletion functor of Qcategories factors through both of these functors. 1.
Interaction, Computability, and Church's Thesis
, 1999
"... : This article formalizes the claim that interactive finite computing agents are more expressive than Turing machines. The impact of models of interaction on Church's thesis and Godel's incompleteness result is explored. The evolution from algorithmic to interactive models of computation i ..."
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Cited by 3 (1 self)
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: This article formalizes the claim that interactive finite computing agents are more expressive than Turing machines. The impact of models of interaction on Church's thesis and Godel's incompleteness result is explored. The evolution from algorithmic to interactive models of computation in computer architecture, software engineering, and AI is considered in a final section. Contents 1. Interaction Machines 1.1. Sequential Interaction Machines (SIMs) 1.2. Interactive Behavior and Expressiveness 1.3. MultiStream Interaction Machines (MIMs) 2. Extensions of Expressiveness 2.1. Interactive Extensions of Machines, Sets, and Algebras 2.2. Interactive Extensions of the ChurchTuring Thesis 3. Mathematical Models of Interaction 3.1. NonWellFounded Set Theory 3.2. Coalgebras 3.3. Beyond NonWellFounded Sets 4. From Induction to Coinduction 4.1. The Inductive Modeling Paradigm 4.2. Coinduction and Greatest Fixed Points 5. Metamathematics of Coinduction 5.1. From Formal Mode...
Chu Spaces  A New Approach to Diagnostic Information Fusion
 Proceedings of the 2nd International Conference on Information Fusion FUSION'99
, 1999
"... This paper is rather theoretical. Its aim is to describe a general algebraic framework, known as Chu spaces, in which different type of information can be transformed into the same form, so that fusion procedures can be investigated in a single general framework. Keywords: Chu spaces, data fusion, f ..."
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Cited by 3 (3 self)
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This paper is rather theoretical. Its aim is to describe a general algebraic framework, known as Chu spaces, in which different type of information can be transformed into the same form, so that fusion procedures can be investigated in a single general framework. Keywords: Chu spaces, data fusion, fuzziness, probability 1 A Motivating Example Data fusion means that we combine ("fuse") several pieces of information (measurement results, expert estimates) about one or several objects. To describe our new approach to formalizing data fusion, we will start with a physically meaningful (and mathematically simple) example. In order to find the location of distant radio sources, we measure the signals from these sources received on different radiotelescopes, and then fuse the measurement results. The larger the telescope, the more accurate the measurements. Therefore, to achieve maximum accuracy, antennas forming a radiotelescope are placed as far away from each other as possible: ideally, o...