In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems...

We study the extension of the full logic CaRet with the unary regular modality N (which reads “from now on”) which allows to model forgettable past. For such an extension, denoted NCaRet, we show the following: (1) NCaRet is expressively complete for the first-order fragment of MSOμ, which extend MSO over words with a binary matching predicate, (2) satisfiability and pushdown model checking are...

We call a positive definite Hermitian lattice regular if it represents all integers, which can be represented locally by the lattice. We investigate binary regular Hermitian lattices over imaginary quadratic fields Q( √ −m) and provide a complete list of the (normal) binary regular Hermitian lattices.

The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless ...

In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (1) The axiom of dependent choice. (2) Products of compact Hausdorff spaces are Baire. (3) Products of pseudocompact spaces are Baire. (4) Products of countably compact, regular spaces are Baire. (5) Products of regular-closed spaces are Baire. (6) Products of Čech-complete...

We combine Steiner systems with Hadamard matrices to produce a new class of equiangular tight frames. This in turn leads to new constructions of strongly regular graphs and distance-regular antipodal covers of the complete graph.