Paradigm-based approaches to word processing/learning assume that word forms are not acquired in isolation, but through associative relations linking members of the same word family (e.g. a paradigm, or a set of forms filling the same paradigm cell). Principles of correlative learning offer a set of dynamic equations that are key to modelling this complex dynamic at a considerable level of deta...

We give NSPACE(n logn) algorithms solving the following decision problems.Satisfiability: Is the given equation over a free partially commutative monoid with involution(resp. a free partially commutative group) solvable? Finiteness: Are there only finitely manysolutions of such an equation? PSPACE algorithms with worse complexities for the first problemare known, but so far, a P...

For every symmetric (“palindromic”) word S(A,B) in two positive definite letters and for each fixed n-by-n positive definite B and P , it is shown that the symmetric word equation S(A,B) = P has an n-by-n positive definite solution A. Moreover, if B and P are real, there is a real solution A. The notion of symmetric word is generalized to allow non-integer exponents, with certain limitations. I...

is not always true for square integer matricesM and N . The most basic example of a semigroup is the set, Σ∗, of strings over an alphabet, Σ, where the binary operation is concatenation. In fact, we take the associativity of concatenation so much for granted that we typically write xyz for the concatenation of x, y, z ∈ Σ∗, without bothering to indicate whether they were concatenated as (x ◦ y)...

In this article we introduce the functions Fi(x1, x2)λ1,..., λs and Th(x1, x2, x3)iλ1,..., λ2s (i = 1, 2, 3), of the word variables xi and of the natural number variables λi, where s ≥ 0. By means of these functions, we give exactly the general solution (i.e. the set of all the solutions) of the first basic parametric equation: x1x2x3x4 = x3x1λx2x5, in a free monoid.

The numerical investigation of computing the rate of radiated solar-energy requires equations as a function of solar-time according to the radiation angle of the sun (β) in the latitude 37°N and the shape. This paper implements the Lagrange interpolation to obtain the equations of normal diagram of elements based on data obtained from surveying. Also the method of Hann-window equation ...

Parikh matrix is a numerical property of a word on an ordered alphabet. It is used for studying word in terms of its sub words. It was introduced by Mateescu et al. in 2000. Since then it has been being studied for various ordered alphabets. In this paper Parikh Matrices over tertiary alphabet are investigated. Algorithm is developed to display Parikh Matrices of words over tertiary alphabet. T...

We present a decision procedure for a logic that combines (i) word equations over string variables denoting words of arbitrary lengths, together with (ii) constraints on the length of words, and on (iii) the regular languages to which words belong. Decidability of this general logic is still open. Our procedure is sound for the general logic, and a decision procedure for a particularly rich fra...