We show how to provide a structure of probability space to the set of execution traces on a nonconfluent abstract rewrite system, by defining a variant of a Lebesgue measure on the space of traces. Then, we show how to use this probability space to transform a non-deterministic calculus into a probabilistic one. We use as example λ+, a recently introduced calculus defined through type isomorphi...

Two important aspects of computation are reduction, hence the current infatuation with termrewriting systems (TI~Ss), and abstraction, hence the study of A-calculus. In his groundbreaking thesis, Klop [10] combined both areas in the framework of combinatory reduction systems (ClaSs) and lifted many results from the A-calculus to the CRS-level. More recently [15], we proposed a different althoug...

1. I n t r o d u c t i o n Many term rewriting systems and their modifications are considered in logic, automated theorem proving, and programming language [2,3,4,6,8,9]. A fundamental property of term rewriting systems is the confluence property. A few sufficient criteria for the confluence are well known [2,3,4,5,8,9]. However, if a term rewriting system is nonterminating and nonlinear, we kn...

In this thesis, we explore different algorithms for the inversion of Vandermonde matrices and the corresponding suitable architectures for implement in FPGA. The inversion of Vandermonde matrix is one of the three master projects of the topic, Implementation of a digital error correction algorithm for time-interleaved analog-to-digital converters. The project is divided into two major parts: al...

We have implemented a Matlab code to compute Discrete Extremal Sets (of Fekete and Leja type) on convex or concave polygons, together with the corresponding interpolatory cubature formulas. The method works by QR and LU factorizations of rectangular Vandermonde matrices on Weakly Admissible Meshes (WAMs) of polygons, constructed by polygon quadrangulation. 2000 AMS subject classification: 65D05...

The P systems are a class of distributed parallel computing devices of a biochemical type. In this note, we show that by using membrane separation to obtain exponential workspace, SAT problem can be solved in linear time in a uniform and confluent way by active P systems without polarizations. This improves some results already obtained by A. Alhazov, T.-O. Ishdorj. A universality result relate...

The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein-Vandermonde matrix is considered. Bernstein-Vandermonde matrices are a generalization of Vandermonde matrices arising when considering for the space of the algebraic polynomials o...

Several identification and control problems present nonlinearities that cannot be neglected and are often approximated by polynomials. In some previous works optimal set of interpolation nodes that minimizes the uncertainties of the approximation have been derived for the Vandermonde base that, however, can lead to ill-conditioned numerical problems. In this paper the conditions under which pol...

The Vandermonde and con uent Vandermonde matrices are of fundamental signi cance in matrix theory. A further generalization of the Vandermonde matrix called the q-adic coe cient matrix was introduced in [V. Mani and R. E. Hartwig, Lin. Algebra Appl., to appear]. It was demonstrated there that the q-adic coe cient matrix reduces the Bezout matrix of two polynomials by congruence. This extended t...