We study the canonical weak distributive law $\delta$ of powerset monad over semimodule for a certain class semirings containing, in particular, positive semifields. For this subclass we characterise as convex closure free set. Using abstract theory laws, compose and monads via $\delta$, obtaining subsets semimodule.

Paredaens and Van Gucht proved that the at relational algebra has the same expressive power as the nested relational algebra as far as queries over at relations and with at results are concerned We provide a new very direct proof of this fact using a simulation technique Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of evaluat...

Monads are used for various applications in computer science, and well-known is e.g. the interpretation of morphisms in the Kleisli category of the term monad as variable substitutions assigning variables to terms. An application building upon this observation is the equivalence between most general unifiers and co-equalizers in this category [13]. In this paper we will use monads with addition...

In the context of standard abstract interpretation theory, we deene and study a systematic operator of reduced relative power for composing functionally abstract domains. The reduced relative power of two abstract domains D1 (the exponent) and D2 (the base) consists in a suitably deened lattice of monotone functions from D1 to D2, called dependencies, and it is a generalization of the Cousot an...

We consider the structure of JordanH-pseudoalgebras which are linearly finitely generated over a Hopf algebra H . There are two cases under consideration: H = U(h) and H = U(h)#C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits–Kantor–Koecher construction for finite Jordan pseudoalgebras and des...

We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class γ (that is, γ is weak, Büchi, co-Büchi, Rabin, or Streett), deterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same deterministic structure, nondeterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same structure, and γ...

Most existing studies on the expressive power of query languages have focused on what queries can be expressed and what queries cannot be expressed in a query language. They do not tell us much about whether a query can be implemented efficiently in a query language. Yet, paradoxically, efficiency is of primary concern in computer science. In this paper, the efficiency of queries in NRC(powerse...

This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. characterise compare resulting to definitions of appearing in literature. Most our results are based on exciting interplay between mona...

(Q,≦,∨) is a complete join semilattice (Q,・,e) is a monoid (∨S)・a=∨{b・a | b∈S} for a∈Q, S⊆Q a・(∨S)=∨{a・b | b∈S} for a∈Q, S⊆Q 2 Background: An Example of Quantale (Rel(A),≦,∨,・,e) is a quantale where Rel(A) is the set of all binary relations on A ≦ is the inclusion ∨ is the union ・ is the composition Q・R={ (a,c) | ∃b. (a,b)∈Q, (b,c)∈R } e is the identity relation 3 Our Goal: Relational Represent...