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Designing Programs That Check Their Work
, 1989
"... A program correctness checker is an algorithm for checking the output of a computation. That is, given a program and an instance on which the program is run, the checker certifies whether the output of the program on that instance is correct. This paper defines the concept of a program checker. It d ..."
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Cited by 305 (17 self)
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A program correctness checker is an algorithm for checking the output of a computation. That is, given a program and an instance on which the program is run, the checker certifies whether the output of the program on that instance is correct. This paper defines the concept of a program checker. It designs program checkers for a few specific and carefully chosen problems in the class FP of functions computable in polynomial time. Problems in FP for which checkers are presented in this paper include Sorting, Matrix Rank and GCD. It also applies methods of modern cryptography, especially the idea of a probabilistic interactive proof, to the design of program checkers for group theoretic computations. Two strucural theorems are proven here. One is a characterization of problems that can be checked. The other theorem establishes equivalence classes of problems such that whenever one problem in a class is checkable, all problems in the class are checkable.
Exploiting orbits in symmetric ilp
 Mathematical Programming
"... This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an authorized administrator of Research Showcase. For more information, please contact kbehrman@andrew.cmu.edu. Mathematical Programming manuscript No. (wi ..."
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Cited by 23 (0 self)
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This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an authorized administrator of Research Showcase. For more information, please contact kbehrman@andrew.cmu.edu. Mathematical Programming manuscript No. (will be inserted by the editor)
Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (Cellular) Algebras.
, 1997
"... ..."
Symmetric ILP: coloring and small integers
 Discrete Optimization
"... This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an ..."
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Cited by 6 (0 self)
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This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an
The Preliminary Design Of An ObjectOriented Framework For Combinatorial Enumeration
 in proceedings of the Colloquium on Object Orientation in Databases and Software Engineering, 62nd Congress of ACFAS
, 1994
"... The design of an objectoriented framework for combinatorial enumeration is described. Combinatorial enumeration requires a subtle interplay between the search mechanism, the ordering of the space of combinatorial objects, and the symmetries used to prune equivalent cases from the search. Efficiency ..."
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Cited by 1 (1 self)
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The design of an objectoriented framework for combinatorial enumeration is described. Combinatorial enumeration requires a subtle interplay between the search mechanism, the ordering of the space of combinatorial objects, and the symmetries used to prune equivalent cases from the search. Efficiency requires that pruning be used as much as possible, while correctness requires the pruning not be used more than is provably correct. The framework is the product of an evolutionary process of modelling and of attempts at precise (but not formal) mathematical specification of the framework. Our approach to specifying the framework, and documenting how it should be instantiated for a particular combinatorial enumeration, is to list the proof obligations that must be satisfied by the usersupplied components. This work reports our preliminary objectoriented design of the framework, with only brief mention of the use of proof obligations. 1. Introduction The design of an objectoriented frame...
Construction of Combinatorial Objects
, 1995
"... Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, u ..."
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Cited by 1 (1 self)
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Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way. The exposition is based on graph theoretic concepts to give an easy explanation of data structures for group actions.
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"... . In this paper we approximate large sets of univariate data by piecewise linear functions which interpolate subsets of the data, using adaptive thinning strategies. Rather than minimize the global error at each removal (AT0), we propose a much cheaper thinning strategy (AT1) which only minimize ..."
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. In this paper we approximate large sets of univariate data by piecewise linear functions which interpolate subsets of the data, using adaptive thinning strategies. Rather than minimize the global error at each removal (AT0), we propose a much cheaper thinning strategy (AT1) which only minimizes errors locally. Interestingly, the two strategies are equivalent in all our numerical tests and we prove this to be true for convex data. We also compare with nonadaptive thinning strategies. x1. Introduction In applications such as visualization, it is often desirable to generate a hierarchy of coarser and coarser representations of a given discrete data set. Though we are primarily interested in hierarchies of scattered data sets, and in particular piecewise linear approximations over triangulations in the plane [1], we focus in this paper on univariate data sets and propose several adaptive thinning strategies. Thinning algorithms generate hierarchies of subsets by removing points ...
DUMMY  A Package to Find the Canonical Form of Expressions Involving Dummy Variables  Version 1.1
"... Introduction The possibility to handle dummy variables and to manipulate dummy summations are important features in many applications. In particular, in theoretical physics, the possibility to represent complicated expressions concisely and to realize simplifications e#ciently depend on both capabi ..."
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Introduction The possibility to handle dummy variables and to manipulate dummy summations are important features in many applications. In particular, in theoretical physics, the possibility to represent complicated expressions concisely and to realize simplifications e#ciently depend on both capabilities. However, when dummy variables are used, there are many more ways to express a given mathematical objects since the names of dummy variables may be chosen almost arbitrarily. Therefore, from the point of view of computer algebra the simplification problem is much more di#cult. Given a definite ordering, one is, at least, to find a representation which is independent of the names chosen for the dummy variables otherwise, simplifications are 1 2 DUMMY VARIABLES AND DUMMY SUMMATIONS 2 impossible. The package does handle any number of dummy variables and summations present in expressions which are arbitrary multivariate polynomials and which have operator objects ev