The Experts below are selected from a list of 201588 Experts worldwide ranked by ideXlab platform

Roger David Braddock - One of the best experts on this subject based on the ideXlab platform.

Sten Agerholm - One of the best experts on this subject based on the ideXlab platform.

  • Non-primitive Recursive Function Definitions
    BRICS Report Series, 1995
    Co-Authors: Sten Agerholm
    Abstract:

    This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a Domain Theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved termination, the original specification can be derived easily. A collection of algorithms are presented which hide the Domain Theory from a user. Hence, the derivation of a Domain Theory specification has been automated completely, and for well-founded recursive function specifications the process of deriving the original specification from the Domain Theory one has been automated as well, though a user must supply a well-founded relation and prove certain termination properties of the specification. There are constructions for building well-founded relations easily.

  • TPHOLs - Non-primitive Recursive Function Definitions
    Higher Order Logic Theorem Proving and Its Applications, 1995
    Co-Authors: Sten Agerholm
    Abstract:

    This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a Domain Theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved termination, the original specification can be derived easily. A collection of algorithms are presented which hide the Domain Theory from a user. Hence, the derivation of a Domain Theory specification has been automated completely, and for well-founded recursive function specifications the process of deriving the original specification from the Domain Theory one has been automated as well, though a user must supply a well-founded relation and prove certain termination properties of the specification. There are constructions for building well-founded relations easily.

J.-y. Parlange - One of the best experts on this subject based on the ideXlab platform.

Abbas Edalat - One of the best experts on this subject based on the ideXlab platform.

  • dynamical systems measures and fractals via Domain Theory
    Information & Computation, 1995
    Co-Authors: Abbas Edalat
    Abstract:

    Abstract We introduce Domain Theory in dynamical systems, iterated function systems (fractals), and measure Theory. For a discrete dynamical system given by the action of a continuous map f : X → X on a metric space X , we study the extended dynamical systems ( VX , Vf ), ( UX , Uf ), and ( LX , Lf ), where V , U , and L are respectively the Vietoris hyperspace, the upper hyperspace, and the lower hyperspace functors. We show that if ( X , f ) is chaotic, then so is ( UX , Uf ). When X is locally compact UX , is a continuous bounded complete dcpo. If X is second countable as well, then UX will be ω-continuous and can be given an effective structure. We show how strange attractors, attractors of iterated function systems (fractals) and Julia sets are obtained effectively as fixed points of deterministic functions on UX or fixed points of non-deterministic functions on CUX where C is the convex (Plotkin) power Domain. We also show that the set, M ( X ), of finite Borel measures on X can be embedded in PUX , where P is the probabilistic power Domain. This provides an effective framework for measure Theory. We then prove that the invariant measure of an hyperbolic iterated function system with probabilities can he obtained as the unique fixed point of an associated continuous function on PUX .

  • MFPS - Domain Theory in Learning Processes
    Electronic Notes in Theoretical Computer Science, 1995
    Co-Authors: Abbas Edalat
    Abstract:

    AbstractWe present applications of Domain Theory in stochastic learning automata and in neural nets. We show that a basic probabilistic algorithm, the so-called linear reward-penalty scheme, for the binary-state stochastic learning automata can be modelled by the dynamics of an iterated function system on a probabilistic power Domain and we compute the expected value of any continuous function in the learning process. We then consider a general class of, so-called forgetful, neural nets in which pattern learning takes place by a local iterative scheme, and we present a Domain-theoretic framework for the distribution of synaptic couplings in these networks using the action of an iterated function system on a probabilistic power Domain. We then obtain algorithms to compute the decay of the embedding strength of the stored patterns

  • dynamical systems measures and fractals via Domain Theory
    Formal Methods, 1993
    Co-Authors: Abbas Edalat
    Abstract:

    We introduce Domain Theory in the computation of dynamical systems, iterated function systems (fractals) and measures. For a discrete dynamical system (X, f), given by the action of a continuous map f: X → X on a metric space X, we study the extended dynamical systems (VX, Vf) and (UX, Uf) where V is the Vietoris functor and U is the upper space functor. In fact, from the point of view of computing the attractors of (X, f), it is natural to study the other two systems: A compact attractor of (X, f) is a fixed point of (VX, Vf) and a fixed point of (UX, Uf). We show that if (X, f) is chaotic, then so is (UX, Uf). When X is locally compact UX is a continuous bounded complete dcpo. If X is second countable as well, then UX will be ω-continuous and can be given an effective structure. We show how strange attractors, attractors of iterated function systems (fractals) and Julia sets are obtained effectively as fixed points of deterministic functions on UX or fixed points of non-deterministic functions on CUX where C is the convex (Plotkin) power Domain. We also establish an interesting link between measure Theory and Domain Theory. We show that the set, M(X), of Borel measures on X can be embedded in PUX, where P is the probabilistic power Domain. This provides an effective way of obtaining measures on X. We then prove that the invariant measure of an hyperbolic iterated function system with probabilities can be obtained as the unique fixed point of an associated continuous function on PUX.

  • LICS - Domain Theory and differential calculus (functions of one variable)
    Proceedings 17th Annual IEEE Symposium on Logic in Computer Science, 1
    Co-Authors: Abbas Edalat, André Lieutier
    Abstract:

    A data-type for differential calculus is introduced, which is based on Domain Theory. We define the integral and also the derivative of a Scott continuous function on the Domain of intervals, and present a Domain-theoretic generalization of the fundamental theorem of calculus. We then construct a Domain for differentiable real valued functions of a real variable. The set of classical C/sup 1/ functions, equipped with its C/sup 1/ norm, is embedded into the set of maximal elements of this Domain, which is a countably based bounded complete continuous Domain. This gives a data type for differential calculus. The construction can be generalized to C/sup k/ and C/sup /spl infin// functions. As an immediate application, we present a Domain-theoretic generalization of Picard's theorem, which provides a data type for solving differential equations.

Olav Geil - One of the best experts on this subject based on the ideXlab platform.

  • Evaluation codes from order Domain Theory
    Finite Fields and Their Applications, 2008
    Co-Authors: Henning Ejnar Andersen, Olav Geil
    Abstract:

    The celebrated Feng-Rao bound estimates the minimum distance of codes defined by means of their parity check matrices. From the Feng-Rao bound it is clear how to improve a large family of codes by leaving out certain rows in their parity check matrices. In this paper we derive a simple lower bound on the minimum distance of codes defined by means of their generator matrices. From our bound it is clear how to improve a large family of codes by adding certain rows to their generator matrices. The new bound is very much related to the Feng-Rao bound as well as to Shibuya and Sakaniwa's bound in [T. Shibuya, K. Sakaniwa, A dual of well-behaving type designed minimum distance, IEICE Trans. Fund. E84-A (2001) 647-652]. Our bound is easily extended to deal with any generalized Hamming weights. We interpret our methods into the setting of order Domain Theory. In this way we fill in an obvious gap in the Theory of order Domains.

  • ISIT - The missing evaluation codes from order Domain Theory
    International Symposium onInformation Theory 2004. ISIT 2004. Proceedings., 1
    Co-Authors: Henning Ejnar Andersen, Olav Geil
    Abstract:

    This paper presents the missing codes evaluation map in the order Domain Theory is a generalization of the code construction E(s) to order Domains of arbitrary transcendence degree and the introduction of a class of improved codes E/spl tilde/(s). The code construction to the order Domain setting, the minimum distance estimation and the generalized Hamming weights of the new codes are also discussed.