We prove that there exists an ACD-ground theory | an equational theory deened by a set of ground equations plus the associativity and commutativity of two binary symbols and +, and the distributivity of over + | for which the word problem is undecidable.

We show that AI–matching (AI denotes the theory of an associative and idempotent function symbol), which is solving matching word equations in free idempotent semigroups, is NP-complete. Note: this is a full version of the paper [9] and a revision of [8].

We study the special class of equations in words of type (R,w), where R is a two variable generalized regular expression, without constant, and where w is a constant word. We show that the problem may be solved by applying a O(|w| ln |w|) time algorithm.

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Two-dimensional Haar wavelets are applied for solution of the partial differential equations (PDEs). The pro...

Makanin's algorithm Ma77] shows that it is decidable whether a word equation has a solution. The original description was hard to understand and not designed for implementation. Since words represent a fundamental data type, various authors have given improved descriptions P e81, Ab87, Sc90, Ja90]. In this paper we present a version of the algorithm which probably cannot be further simpliied wi...

The word2vec model and application by Mikolov et al. have attracted a great amount of attention in recent two years. The vector representations of words learned by word2vec models have been shown to carry semantic meanings and are useful in various NLP tasks. As an increasing number of researchers would like to experiment with word2vec or similar techniques, I notice that there lacks a material...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t We extend the stability criterion in distribution as in Yuan and Mao [C. Yuan and X. Mao. Asymptotic stabili...

We study a weak variant of omega algebra, where one of the usual star induction axioms is absent, in the context of recursive regular equations. We present abstract conditions for explicitly defining the omega operation and use them for proving an algebraic variant of Arden’s rule for solving such equations. We instantiate these results in concrete models—languages, traces and relations—showing...

This study focused mainly on the derivation of the 2 and 3-point block methods with constant coefficients for solving special second order ordinary differential equations directly based on Newton-Gregory backward interpolation formula. The performance of the new methods was compared with the conventional 1-point method using a standard set of test problems. Numerical results were presented to i...

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on linear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and investigate its implications to pot...