Results 1 
7 of
7
Inverse entailment and Progol
, 1995
"... This paper firstly provides a reappraisal of the development of techniques for inverting deduction, secondly introduces ModeDirected Inverse Entailment (MDIE) as a generalisation and enhancement of previous approaches and thirdly describes an implementation of MDIE in the Progol system. Progol ..."
Abstract

Cited by 631 (59 self)
 Add to MetaCart
This paper firstly provides a reappraisal of the development of techniques for inverting deduction, secondly introduces ModeDirected Inverse Entailment (MDIE) as a generalisation and enhancement of previous approaches and thirdly describes an implementation of MDIE in the Progol system. Progol is implemented in C and available by anonymous ftp. The reassessment of previous techniques in terms of inverse entailment leads to new results for learning from positive data and inverting implication between pairs of clauses.
Recursive and Combinatorial Properties of Schubert Polynomials
 SEM. LOTH. COMB. B38C
, 1995
"... We describe two recursive methods for the calculation of Schubert polynomials and use them to give new relatively simple proofs of their basic properties. Moreover, ..."
Abstract

Cited by 10 (10 self)
 Add to MetaCart
We describe two recursive methods for the calculation of Schubert polynomials and use them to give new relatively simple proofs of their basic properties. Moreover,
Performance Evaluation of Nested Transactions on Locally Distributed Database Systems
 In Proceedings of 2nd International Symposium on Parallel Architectures, Algorithms, and Networks, 1SPAN, IEEE
, 1996
"... This paper describes an execution time estimating model for nested transactions running on locally distributed database systems. At first the model of nested transactions and the model of a locally distributed database system are established. The performance evaluation model of nested transactions i ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper describes an execution time estimating model for nested transactions running on locally distributed database systems. At first the model of nested transactions and the model of a locally distributed database system are established. The performance evaluation model of nested transactions is then built in three steps. The first step describes a nondeterministic algorithm that evaluates the execution time of a nested transaction using general routing strategies. The second step gives explicit form solutions for a few special cases. The last step uses some approximate methods to develop the lower and upper bounds of the general form solution. Key Words: Nested transaction; Locally distributed database systems, Performance evaluation, Combinatorics. 1 Introduction The demand for high transaction processing rate has motivated the development of multiprocessor or locally distributed database systems [9]. A locally distributed database system has a tightly interconnection among it...
Deriving laws from ordering relations
 In press: Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Jackson Hole WY
, 2003
"... Abstract. The effect of Richard T. Cox’s contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product ru ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. The effect of Richard T. Cox’s contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes ’ Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox’s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.
Two examples of hypergraph edgecoloring, and their connections with other topics in Combinatorics
, 2002
"... This thesis consists of two independent parts, whose common root is the notion of hypergraph edgecoloring. In the first part we deal with a class of nondirected hypergraphs. A particular kind of edgecoloring is defined and studied in Chapter 2. The analysis of such coloring leads to a different t ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This thesis consists of two independent parts, whose common root is the notion of hypergraph edgecoloring. In the first part we deal with a class of nondirected hypergraphs. A particular kind of edgecoloring is defined and studied in Chapter 2. The analysis of such coloring leads to a different topic in Chapter 3, namely total weight orders over monomials of fixed degree. We remark that our results on weight orders are not related to Chapter 2. Indeed, the edgecoloring has provided nothing more than a motivation for subsequently focusing on the main topic. Nevertheless, some combinatorial properties of these hypergraphs seemed nice to us. This is the reason why we have dedicated the whole Chapter 2 to them. On the contrary, the second notion of edgecoloring has a fundamental role in Part II. In this context, every edge of a hypergraph consists of a tail (a subset of the vertices) and a head (one vertex). Following the current terminology, edges and vertices are renamed as arcs and nodes respectively, whereas the hypergraph is said to be directed. We define a notion of coloring for the arcs. Our definition is an extension of the existing notion of arccoloring for directed graphs. We enlight some relationships between the incidence structure and the coloring properties. In particular, we analyze the question of minimizing the number of colors. We are led to consider some combinatorial properties of adjacency matrices for hypergraphs. Such matrices generalize the intuitive concept of a wall made of bricks. In our rephrasing, coloring the arcs corresponds to adequately coloring each brick of the wall. 1 Contents I Greedy edgecoloring for a class of hypergraphs, as an ingenuous introduction to total weight orders over monomials of fixed degree 3
Enumerative Aspects of Certain Subclasses of Perfect Graphs
"... We investigate the enumerative aspects of various classes of perfect graphs like cographs, split graphs, trivially perfect graphs and threshold graphs. For subclasses of permutation graphs like cographs and threshold graphs we also determine the number of permutations ß of f1; 2; : : : ; ng such tha ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We investigate the enumerative aspects of various classes of perfect graphs like cographs, split graphs, trivially perfect graphs and threshold graphs. For subclasses of permutation graphs like cographs and threshold graphs we also determine the number of permutations ß of f1; 2; : : : ; ng such that the permutation graph G[ß] belongs to that class. We establish an interesting bijection between permutations whose permutation graphs are cographs (P4 free graphs) and permutations that are obtainable using an outputrestricted deque [9] and thereby enumerate such permutations. We also prove that the asymptotic number of permutations of f1; 2; : : : ; ng whose permutation graphs are split graphs is \Theta(4 n = p n). We also introduce a new class of graphs called C5 split graphs, characterize and enumerate them. C5 split graphs form a superclass of split graphs and are not necessarily perfect. All the classes of graphs that we enumerate have a finite family of small forbidden induc...
ON SUMS OF POWERS OF ZEROS OF POLYNOMIALS 1
, 1997
"... Due to Girard’s (sometimes called Waring’s) formula the sum of the r−th power of the zeros of every one variable polynomial of degree N, PN(x), can be given explicitly in terms of the coefficients of the monic ˜ PN(x) polynomial. This formula is closely related to a known N − 1 variable generalizati ..."
Abstract
 Add to MetaCart
Due to Girard’s (sometimes called Waring’s) formula the sum of the r−th power of the zeros of every one variable polynomial of degree N, PN(x), can be given explicitly in terms of the coefficients of the monic ˜ PN(x) polynomial. This formula is closely related to a known N − 1 variable generalization of Chebyshev’s polynomials of the first kind, T (N−1) r. The generating function of these power sums (or moments) is known to involve the logarithmic derivative of the considered polynomial. This entails a simple formula for the Stieltjes transform of the distribution of zeros. PerronStieltjes inversion can be used to find this distribution, e.g. for N → ∞. Classical orthogonal polynomials are taken as examples. The results for ordinary Chebyshev TN(x) and UN(x) polynomials are presented in detail. This will correct a statement about power sums of zeros of Chebyshev’s T −polynomials found in the literature. For the various cases (Jacobi, Laguerre, Hermite) these moment generating functions provide solutions to certain Riccati equations. 1