We investigate the extension of modal logics by bisimulation quantifiers and present a class of modal logics which is decidable when augmented with bisimulation quantifiers. These logics are refered to as the idempotent transduction logics and are defined using the programs of propositional dynamic logic including converse and tests. This is a nontrivial extension of the decidability of the pos...

We initiate a theory of locally eventually positive operator semigroups on Banach lattices. Intuitively this means: given initial datum, the solution corresponding Cauchy problem becomes (and stays) in part domain, after sufficiently large time. A drawback present C0-semigroups is that it applicable only when leading eigenvalue semigroup generator has strongly eigenvector. weaken requirement an...

We introduce the notion of idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of B-module coalgebras, then every B-module coalgebra contains a unique maximal B-submodule coalgebra in R. Moreover, a B-module coalgebra C is a member of R if, and only if, DB is in R for every simple subcoalgebra D of C. The collection of B-cocleft co...

Suppose that G is a locally compact abelian group, and write M(G) for the algebra of bounded, regular, complex-valued measures under convolution. A measure μ ∈ M(G) is said to be idempotent if μ ∗ μ = μ, or alternatively if μ̂ takes only the values 0 and 1. The Cohen-Helson-Rudin idempotent theorem states that a measure μ is idempotent if and only if the set {γ ∈ Ĝ : μ̂(γ) = 1} belongs to the cos...

In this article, we discuss the family of cellular automata generated by so-called idempotent cellular automata (CA G such that G 2 = G) on the full shift. We prove a characterization of products of idempotent CA, and show examples of CA which are not easy to directly decompose into a product of idempotents, but which are trivially seen to satisfy the conditions of the characterization. Our pro...