Omega-regular algebras axiomatise the equational theory of omega-regular expressions as induced by omega-regular language identity. Wagner presented an omega-regular algebra which requires recursively defined side conditions in some of its axioms. We introduce a first-order Horn axiomatisation for which such conditions can be avoided because additive and multiplicative units are absent. We prov...

In this paper, we introduce a variant of the Ehrenfeucht-Fräıssé game from logic which is useful for analyzing the expressive power of classes of generalized regular expressions. An extension of the game to generalized ω-regular expressions is also established. To gain insight into how the game can be applied to attack the long-standing generalized star height 2 problem, we propose and solve a ...

in the present paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. further, we also study the pairwise weakly lindelof subspaces and subsets, and investigate some of their properties. it was proved that a pairwise weakly lindelof property is not a hereditary property.