In the last WSML phone conference we had a brief discussion about the expressivity of First-order Logic and Datalog resp. the relation between the expressiveness of those two languages. In particular, there has been some confusion around the description of the transitive closure R of some binary relation R. In this short document, we want to clarify the situation and hope to remedy the confusion.

Using a method of R. McKenzie, we construct a finitely generated semisimple variety of infinite type, and a finitely generated nonsemisimple variety of finite type, both having arbitrarily large finite but no infinite simple members. This amplifies M. Valeriote’s negative solution to Problem 11 from [1]. R. McKenzie [2] has constructed a finitely generated variety having arbitrarily large finit...

The “standard” method of implementing composition is to perform join and projection as one combined operation and then to remove the duplicates from the result of this operation as a separate step. When a hash-based or sort-merge algorithm is used for the join operation and the size of the result is large, duplicates cannot be eliminated at the same time the join is being performed. In this pap...

We study modular fibers of elliptic differentials, i.e. investigate spaces of coverings (Y, τ) → (C/Z ⊕ Zi, dz). For genus 2 torus covers with fixed degree we show, that the modular fibers Fd(1, 1) are connected torus covers with Veech group SL2(Z). Using results of Eskin, Masur and Schmoll [EMS] we calculate χ(Fd(1, 1)) and the parity of the spin structure of the quadratic differential (Fd(1, ...

Let C = (C, ^ ) be a linear ordering, E a subset of {(x,y):x < y in C} whose transitive closure is the linear ordering C, and let 9:E->G be a map from £ to a finite group G = (G>). We showed with M. Pouzet that, when C is countable, there is F^ E whose transitive closure is still C, and such that 6(p) = 6(xo,x1).d(xvx2),....8(xn_1,xn)eG depends only upon the extremities xo,xn of p, where p = (x...

Transitive closures of binary relations and relations α with the property that any two α-sequences connecting two given elements are of the same length are investigated. Vyšetřuj́ı se tranzitivńı uzávěry binárńıch relaćı a relaćı α s vlastnost́ı, že každé dvě α-posloupnosti spojuj́ıćı dané dva prvky maj́ı stejnou délku. The present short note collects a few elementary observations concerning the tr...

PROOF: One implication follows from Lemmas 3 and 4. To prove the remaining implication, we show that the domain of all preference profiles that do not admit n-cycles, n= 2 3 satisfies R1 and R2. Fix a profile A that does not admit n-cycles, n= 2 3 To prove that R1 is satisfied, we construct an extension of the partial ordering constructed in the proof of Lemma 5 (the construction did not rely o...

This paper presents a new approach for computing the transitive closure of a union of relations describing all the dependences in both uniform and quasi-uniform perfectly-nested parameterized loops. This approach is based on calculating the basis of a dependence distance vectors set. The procedure has polynomial time complexity for most steps of calculations. This allows us to effectively extra...

Let C A n be a geometrically irreducible aane curve of (geometric) genus 0 deened over Z such that C(Z) is an innnite set. We use elementary methods to describe the distribution of C(Z) in C(R) relative to the real topology. The study of integral points on aane curves has a long history. The deenitive niteness theorem, due to Siegel 5], says that a geometrically irreducible aane curve C has onl...

Boolean affine relations, which combine affine inequalities by boolean connectives are ubiquitous in all kind of static program analyzes. One of the crucial operations on such relations is transitive closure, which is closely related to the construction of loop inductive invariants. I present here a new over-approximation algorithm, which has the interesting property of being extendible for inc...