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Recursive Definitions in Z
 ZUMâ€™98: The Z Formal Specification Notation, volume 1493 of Lecture Notes in Computer Science
, 1998
"... This paper considers some issues in the theory and practice of defining functions over recursive data types in Z. Principles justifying such definitions are formulated. Z free types are contrasted with the free algebras of universal algebra: the notions turn out to be related but not isomorphic. ..."
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Cited by 5 (0 self)
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This paper considers some issues in the theory and practice of defining functions over recursive data types in Z. Principles justifying such definitions are formulated. Z free types are contrasted with the free algebras of universal algebra: the notions turn out to be related but not isomorphic.
A Transformation System for Developing Recursive Programs
, 1977
"... A system of rules for transforming programs is described, with the programs in the form of recursion equations An initially very simple, lucid. and hopefully correct program IS transformed into a more efficient one by altering the recursion structure Illustrative examples of program transformations ..."
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Cited by 653 (3 self)
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A system of rules for transforming programs is described, with the programs in the form of recursion equations An initially very simple, lucid. and hopefully correct program IS transformed into a more efficient one by altering the recursion structure Illustrative examples of program transformations
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
 in Conference Record of The TwentySeventh Asilomar Conference on Signals, Systems and Computers
, 1993
"... In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang (199 ..."
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Cited by 622 (1 self)
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recursively. where fk is the current approximation, and Rkf the current residual (error). Using initial values ofR0f = 1, fo = 0, and k = 1, the MP algorithm is comprised of the following steps,.,.41) Compute the innerproducts {(Rkf,z)}. (H) Find flki such that (III) Set, I(R*f,1:n 1+,)l asupl(Rkf,z
Recursive Distributed Representations
 Artificial Intelligence
, 1990
"... A longstanding difficulty for connectionist modeling has been how to represent variablesized recursive data structures, such as trees and lists, in fixedwidth patterns. This paper presents a connectionist architecture which automatically develops compact distributed representations for such compo ..."
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Cited by 409 (9 self)
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A longstanding difficulty for connectionist modeling has been how to represent variablesized recursive data structures, such as trees and lists, in fixedwidth patterns. This paper presents a connectionist architecture which automatically develops compact distributed representations
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 to Stanford University where John McCarthy has been since 1962. Copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. Current address, John McCarthy, Computer Science Depa ..."
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Cited by 452 (3 self)
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applications of our recursive function formalism to mathematical logic and to the problem of mechanical theorem proving. 2 Functions and Function Definitions
ZTree: Zurich Toolbox for Readymade Economic Experiments, Working paper No
, 1999
"... 2.2.2 Startup of the Experimenter PC............................................................................................... 9 2.2.3 Startup of the Subject PCs....................................................................................................... 9 ..."
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Cited by 1956 (33 self)
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2.2.2 Startup of the Experimenter PC............................................................................................... 9 2.2.3 Startup of the Subject PCs....................................................................................................... 9
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
Algebraic laws for nondeterminism and concurrency
 Journal of the ACM
, 1985
"... Abstract. Since a nondeterministic and concurrent program may, in general, communicate repeatedly with its environment, its meaning cannot be presented naturally as an input/output function (as is often done in the denotational approach to semantics). In this paper, an alternative is put forth. Firs ..."
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Cited by 600 (13 self)
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. First, a definition is given of what it is for two programs or program parts to be equivalent for all observers; then two program parts are said to be observation congruent iff they are, in all program contexts, equivalent. The behavior of a program part, that is, its meaning, is defined to be its
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