Related papers: Process Algebra with Imperfect Actions
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
I review the three principal methods to assign meaning to recursion in process algebra: the denotational, the operational and the algebraic approach, and I extend the latter to unguarded recursion.
In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter algebraic structures, inside which there are no atoms and,…
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We exhibit two relation algebra atom structures such that they are elementarily equivalent but their term algebras are not. This answers Problem 14.19 in the book Hirsch, R. and Hodkinson, I., "Relation Algebras by Games", North-Holland,…
We give the images of the adjoint representations of exceptional simple Lie algebras by matrices over complex numbers. Next, we digitalize these matrices by the use of Maxima, which is a computer algebra system. These digitalized matrices…
In decision theory an act is a function from a set of conditions to the set of real numbers. The set of conditions is a partition in some algebra of events. The expected value of an act can be calculated when a probability measure is given.…
This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…
We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\em if-then-else} and…
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
We present process-algebraic models of multi-writer multi-reader safe, regular and atomic registers. We establish the relationship between our models and alternative versions presented in the literature. We use our models to formally…
Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on star-continuous Kleene omega-algebras, we show here that energy problems can be solved by algebraic manipulations on the…
This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with time-out transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
On example of tasks of class NP the questions concerning accuracy of work of already existing and possible in the future algorithms for the solution of tasks on discrete structures are considered.
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic…