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Reverse mathematics of some topics from algorithmic graph theory

100%

Clote P. G. , Hirst J. L.

Fundamenta Mathematicae

1998

tom 157

nr 1

1-13

This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.

UPSILON: Universal Programming System with Incomplete Lazy Object Notation

88%

Postow B. , Regan K. , Smith C. H.

Fundamenta Informaticae

2002

tom Vol. 50, nr 3,4

325-359

This paper presents a new model of computation that differs from prior models in that it emphasizes data over flow control, has no named variables and has an object-oriented flavor. We prove that this model is a complete and confluent acceptable programming system and has a usable type theory. A new data synchronization primitive is introduced in order to achieve the above properties. Subtle variations of the model are shown to fall short of having all these necessary properties.

Proof Methods for Corecursive Programs

75%

Gibbons J. , Hutton G.

Fundamenta Informaticae

2005

tom Vol. 66, nr 4

353--366

Recursion is a well-known and powerful programming technique, with a wide variety of applications. The dual technique of corecursion is less well-known, but is increasingly proving to be just as useful. This article is a tutorial on the four main methods for proving properties of corecursive programs: fixpoint induction, the approximation (or take) lemma, coinduction, and fusion.

Recurrent Construction of MacWilliams and Chebyshev Matrices

63%

Gogin N. , Hirvensalo M.

Fundamenta Informaticae

2012

tom Vol. 116, nr 1-4

93-110

We give two recursive expressions for both MacWilliams and Chebyshev matrices. The expressions give rise to simple recursive algorithms for constructing the matrices. In order to derive the second recursion for the Chebyshev matrices we find out the Krawtchouk coefficients of the discrete Chebyshev polynomials, a task interesting on its own.