We extend order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The obtained signature corresponds to a finite bottom-up unranked tree automaton. We prove that regular expression order-sorted (REOS) unification is of type infinitary and decidable. The unification problem presented by us generalizes some known problems, such as, e.g...

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

In this paper, we define a novel variation on the constrained sequence alignment problem, the Sequence Alignment with Regular Expression Path Constraint problem, in which the constraint is given in the form of a regular expression. Our definition extends and generalizes the existing definitions of alignment-path constrained sequence alignments to the expressive power of regular expressions. We ...

The discriminator of an integer sequence s = (s(i))i≥0, introduced by Arnold, Benkoski, and McCabe in 1985, is the map Ds(n) that sends n ≥ 1 to the least positive integer m such that the n numbers s(0), s(1), . . . , s(n − 1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of ...

A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergent double sequence into a convergent sequence with the same limit. Firstly, Robison [G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926) 50–73] presented the necessary and sufficient conditions for regular matrix transformations of double sequences. In this paper, t...

Interest has recently intensified in the search for molecular motors and actuators capable of delivering useful work to nanodevices under the control of electrochemical or photochemical power sources. While many of these man-made molecular machines are designed to deliver rectilinear motion, very few are proposed for the controlled delivery of rotary motion on the time scale characteristic of i...