We use both Abel’s lemma on summation by parts and Zeilberger’s algorithm to find recurrence relations for definite summations. The role of Abel’s lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger alg...

We derive linear inequality characterizations for sets of the form conv{(x, q) ∈ R×R : q ≥ Q(x), x ∈ R − int(P )} where Q is convex and differentiable and P ⊂ R. We show that in several cases our characterization leads to polynomial-time separation algorithms that operate in the original space of variables, in particular when Q is a positive-definite quadratic and P is a polyhedron or an ellips...

Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and a...

Growing interest in visual languages has triggered new extended research into the specification and parsing of multi-dimensional structures. The paper discusses the need for a visual specification formalism and introduces such a technique by augmenting logic programming with picture terms which can be considered as partially specified pictures. We define how to match picture terms and how to in...

A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a diff...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Hassan Ait-Kaci introduced the #/-term, an informational structure resembling feature-based functional structures but which also includes taxonomic inheritance (Ait-Kaci, 1984). We describe e-terms and how they have been incorporated into the Logic Grammar formalism. The result, which we call Inheritance Grammar, is a proper superset of DCG and includes many features of PATR-II. Its taxo-nomic ...

This paper describes a system in PROLOG for the automatic transforination of a grammar, written in LFG formalism, into a DCG-based parser. It demonstrates the main principles of the transformation, the representation of f-structures and constraints, the treatment of long-distance dependencies, and left rccursion. Finally some problem areas of the system and possibilities for overcoming them are...

This paper presents the design and implementation of an intelligent document understanding and reproduction system. The system analyses a printed document to create an electronic document. The electronic document is written in a standard type-setting language (L w), and is thus human usable. The output from processing the electronic document closely resembles the original printed document. A ne...