Related papers: The algebra of non-deterministic programs: demonic…
Binary logic programs can be obtained from ordinary logic programs by a binarizing transformation. In most cases, binary programs obtained this way are less efficient than the original programs. (Demoen, 1992) showed an interesting example…
We find conditions on ideals of an algebra under which the algebra is dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the real numbers. We introduce a concept of bq-homomorphism (which is given by two linear maps $f,…
We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More…
Programs that combine I/O and countable probabilistic choice, modulo either bisimilarity or trace equivalence, can be seen as describing a probabilistic strategy. For well-founded programs, we might expect to axiomatize bisimilarity via a…
Kleene Algebra with Tests (KAT) provides an elegant algebraic framework for describing non-deterministic finite-state computations. Using a small finite set of non-deterministic programming constructs (sequencing, non-deterministic choice,…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
A binarization of a bounded variable $x$ is a linear formulation with variables $x$ and additional binary variables $y_1,\dots, y_k$, so that integrality of $x$ is implied by the integrality of $y_1,\dots, y_k$. A binary extended…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Composition is an important feature of a specification language, as it enables the design of a complex system in terms of a product of its parts. Decomposition is equally important in order to reason about structural properties of a system.…
We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from…
We introduce a framework for proving statements about linear operators by verification of ideal membership in a free algebra. More specifically, arbitrary first-order statements about identities of morphisms in preadditive semicategories…
Discrete optimisation problems arise in many different areas and are studied under many different names. In many such problems the quantity to be optimised can be expressed as a sum of functions of a restricted form. Here we present a…
Our concern is the axiomatisation problem for modal and algebraic logics that correspond to various fragments of two-variable first-order logic with counting quantifiers. In particular, we consider modal products with Diff, the…
We introduce the notion of relation type of an affine algebra and prove that it is well defined by using the Jacobi-Zariski exact sequence of Andr\'e-Quillen homology. In particular, the relation type is an invariant of an affine algebraic…
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive…
Probabilistic programming combines general computer programming, statistical inference, and formal semantics to help systems make decisions when facing uncertainty. Probabilistic programs are ubiquitous, including having a significant…
In this note we prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.
We consider the decidability of the verification problem of programs \emph{modulo axioms} --- that is, verifying whether programs satisfy their assertions, when the functions and relations it uses are assumed to interpreted by arbitrary…
We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposition of such sets with respect to the Zariski topology as…