Knowledge bases theory provide an important example of the field where applications of universal algebra and algebraic logic look very natural, and their interaction with practical problems arising in computer science might be very productive. In this paper we study the equivalence problem for knowledge bases. Our interest is to find out how the informational equivalence is related to the logic...

We establish some results in the theory of standard bases of differential ideals (also known as differential Gröbner bases) in differential polynomial rings. This work was stimulated by some articles of V. Weispfenning, devoted to the classification of term-orders and parametric Gröbner bases of ideals generated by monomials and binomials.

the present study has dealt with studying the coaching model in training of human resource based on grounded theory. this study has done on qualitative bases and has utilized grounded theory approach besides semi-structured interviews for data collecting. in this study, interview was conducted, by using purposive and chain sampling, 7 training experts who were familiar with coaching. this quali...

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Gröbner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.

Recently, Zharkov and Blinkov introduced the notion of involutive bases of polynomial ideals. This involutive approach has its origin in the theory of partial di erential equations and is a translation of results of Janet and Pommaret. In this paper we present a pure algebraic foundation of involutive bases of Pommaret type. In fact, they turn out to be generalized left Grobner bases of ideals...

Involutive bases are a special kind of non-reduced Gröbner bases. They have been introduced by Gerdt and collaborators for polynomial ideals (see e.g. Zharkov and Blinkov, 1993; Gerdt and Blinkov, 1998a,b) based on ideas from the Janet–Riquier theory of differential equations (Janet, 1929; Riquier, 1910). Involutive bases possess special combinatorial properties: in particular, they define Stan...

We discuss canonical bases in theories with a rudimentary notion of independence. We characterize when canonical bases exist for an ominimal theory, and we also study germs of definable multi-functions at definable types in the general case.

Bases in sets and groups and their extremal problems have been studied in additive number theory such as the postage stamp problem. On the other hand, Cayley graphs based on specific finite groups have been studied in algebraic graph theory and applied to construct efficient communication networks such as circulant networks with minimum diameter (or transmission delay). In this paper we establi...

We give the generating function for the index of integer lattice points, relative to a finite order ideal. The index is an important concept in the theory of border bases, an alternative to Gröbner bases.

We introduce Fibonacci gates as a polynomial time computable primitive, and develop a theory of holographic algorithms based on these gates. The Fibonacci gates play the role of matchgates in Valiant’s theory [16]. We develop a signature theory and characterize all realizable signatures for Fibonacci gates. For bases of arbitrary dimensions we prove a universal bases collapse theorem. We apply ...