The paper studies language equations of the type X ⋄ L = R and L ⋄ Y = R, where L and R are given languages and ⋄ is an invertible binary word(language) operation. For most of the considered insertion and deletion operations, the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular L and R. In case L is a context-free language and R i...

in methods presented to calculate the voltage collapse point, the transmission system is usually the only part of the power system that is completely modeled. distribution systems are often replaced by aggregate load models because the use of the detailed model of distribution systems in voltage stability analysis not only increases the computation time, but also decreases the probability of co...

Word equation in a special form X = A, where X is a sequence of variables and A is a sequence of constants, is considered. The problem whether X = A has a solution over a free monoid (PatternEquation problem) is shown to be NP–complete. It is also shown that disjunction of a special type equation systems and conjunction of the general ones can be eliminated. Finally, the case of stuttering equa...

Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words string variables and constants. Its solution amounts to function mapping constant strings that equate left right hand sides equation. While problem is decidable, decidability with length (i.e., relating lengths equation) has remained long-standing open problem...

Word use presents regular oscillations mounted over slowly varying trends. These have been recently interpreted in terms of fashion-like cycles interest and saturation, modelled using a logistic equation with distributed delay. Here we show that the communities semantically related words are partially synchronized. To account for this, model each community equations connected Kuramoto coupling....

The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented recompression technique of the second author. He ...

We study the monadic case of a decision problem know as simultaneous rigid E-uni cation. We show its equivalence to an extension of word equations. We prove decidability and complexity results for special cases of this problem.

We study the monadic case of a decision problem know as simultaneous rigid E-uni cation. We show its equivalence to an extension of word equations. We prove decidability and complexity results for special cases of this problem. 1 Section

Parikh matrix of a word gives numerical information of the word in terms of its subwords. In this Paper an algorithm for finding Parikh matrix of a binary word is introduced. With the help of this algorithm Parikh matrix of a binary word, however large it may be can be found out. M-ambiguous words are the problem of Parikh matrix. In this paper an algorithm is shown to find the Mambiguous words...