We propose a natural subclass of regular languages (Alphabetic Pattern Constraints, APC) which is effectively closed under permutation rewriting, i.e., under iterative application of rules of the form ab ! ba. It is well-known that regular languages do not have this closure property, in general. Our result can be applied for example to regular model checking , for verifying properties of parame...

The complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are represented by NFAs (DFAs), the isomorphism problem for regular trees turns out to be EXPTIME-complete (resp. P-complete). In case the input automata are acyclic NFAs (acy...

The basic querying mechanism over semistructured data, namely regular path queries, asks for all pairs of objects that are connected by a path conforming to a regular expression. We consider conjunctive two-way regular path queries (C2RPQ ’s), which extend regular path queries with two features. First, they add the inverse operator, which allows for expressing navigations in the database that t...

in this paper we investigate the green‎ ‎graphs for the regular and inverse semigroups by considering the‎ ‎green classes of them‎. ‎and by using the properties of these‎ ‎semigroups‎, ‎we prove that all of the five green graphs for the‎ ‎inverse semigroups are isomorphic complete graphs‎, ‎while this‎ ‎doesn't hold for the regular semigroups‎. ‎in other words‎, ‎we prove‎ ‎that in a regular se...

We examine the influence of heterogeneous curing rates for a SIS model, used for malware spreading on the Internet, information dissemination in unreliable networks, and propagation of failures in networks. The topology structures considered are the regular graph which represents the homogenous network structures and the complete bi-partite graph which represents the hierarchical network struct...

In this paper the problem of regular language decomposition as a concatenation of given regular languages is considered. We prove that the problem is decidable in unary case when all the languages are in single-letter alphabet. This result may be used to give a negative answer in some cases of the general problem.

In this paper, we study the achromatic indices of the regular complete multipartite graphs and obtain the following results: (1) A good upper bound for the achromatic index of the regular complete multipartite graph which gives the exact values of an infinite family of graphs and solves a problem posed by Bouchet. (2) An improved Bouchet coloring which gives the achromatic indices of another in...