The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it “quotient complexity”. The problem of ...

in this paper, we investigate the existence of positive solutions for the ellipticequation $delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $omega$ of $r^{n}$, $ngeq2$, with navier boundary conditions. we show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

We relate the existence problem of universal objects to the properties of corresponding enriched categories (lifts or expansions). In particular, extending earlier results, we prove that for every regular set F of finite connected structures there exists a (countable) ω-categorical universal structure U for the class Forbh(F) (of all countable structures not containing any homomorphic image of ...

circuits are used for formalizing regular hardware structures which can ] be expressed by means of primitive recursion. In general, . . . . . . . regular circuit structures lead to regular signal structures. If for example, a structure is described, that con~ ~ sists of n combinational circuits connected in parallel, then it would be appropriate to use the type list for : grouping together the ...

We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by game automata. In particular this algorithm is applicable to all deterministic automata. We then use the algorithm to prove through examples three properties of measure: ...

We study the space complexity of querying regular languages over data streams in the sliding window model. The algorithm has to answer at any point of time whether the content of the sliding window belongs to a fixed regular language. A trichotomy is shown: For every regular language the optimal space requirement is either in Θ(n), Θ(logn), or constant, where n is the size of the sliding window...

Let F be a function from Fpn to itself and δ a positive integer. F is called zerodifference δ-balanced if the equation F (x+a)−F (x) = 0 has exactly δ solutions for all nonzero a ∈ Fpn . As a particular case, all known quadratic planar functions are zero-difference 1-balanced; and some quadratic APN functions over F2n are zerodifference 2-balanced. In this paper, we study the relationship betwe...

The circular ow number F c (G) of a graph G = (V; E) is the minimum r 2 Q such that G admits a ow with 1 (e) r ? 1, for each e 2 E. We determine the circular ow number of some regular multigraphs. In particular, we characterize the bipartite (2t + 1)-regular graphs (t 1). Our results imply that there are gaps for possible circular ow numbers for (2t + 1)-regular graphs, e.g. there is no cubic g...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

Salomaa ((1969) Theory of Automata, page 143) asked whether the equational theory of regular expressions over a singleton alphabet has a finite equational base. In this paper, we provide a negative answer to this long standing question. The proof of our main result rests upon a modeltheoretic argument. For every finite collection of equations, that are sound in the algebra of regular expression...