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...

This paper generalizes a method of generating shift sequences in the interleaved construction proposed by Gong. With the new shift sequences, some new families of p-ary sequences with desired properties can be obtained. A lower bound on the number of new families of binary sequences is also established.

We consider the problem of formalizing in higher-order logic the familiar notion of widening from abstract interpretation. It turns out that many axioms of widening (e.g. widening sequences are ascending) are not useful for proving correctness. After keeping only useful axioms, we give an equivalent characterization of widening as a lazily constructed wellfounded tree. In type systems supportin...

in this work, we describe an adjunction between the comma category of set-based monads under the v -powerset monad and the category of associative lax extensions of set-based monads to the category of v -relations. in the process, we give a general construction of the kleisli extension of a monad to the category of v-relations.

When analyzing a large amount of data, analysts often define groups over data elements that share certain properties. Using these groups as the unit of analysis not only reduces the data volume, but also allows detecting various patterns in the data. This involves analyzing intersection relations between these groups, and how the element attributes vary between these intersections. This kind of...

A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab + 1 of two different elements a and b of A is always a pure power, and the occurring pure powers are all coprime. We prove that each coprime Diophantine powerset A ⊂ {1, . . . , N} has |A| 8000 log N/ log log N for sufficiently large N. The proof combines results from extremal graph theory with numbe...