In 2007, B. Poonen (unpublished) studied the p–adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Belläıche asked the same question for the special case of Abelian varieties. These problems are p–adic analogues of a question raised earlier by B. Mazur on the density of rational points for the real topology. For a simple Abelian variety over the fie...

In this paper, we discuss an adjustable strategy for the transitive closure compression to support graph reachability queries, asking whether a given node u in a directed graph G is reachable from another node v through a path. The main idea behind it is to define a series of graph deductions G0(V0, E0) (= G), G1(V1, E1), ..., Gk(Vk, Ek) with ni > ni+1 (i = 0, ..., k 1), where ni = |Vi|. Each n...

It is a classical result of Mortimer that L 2 , rst-order logic with two variables, is decidable for satissability. We show that going beyond L 2 by adding any one of the following leads to an undecidable logic: very weak forms of recursion, viz. (i) transitive closure operations (ii) (restricted) monadic xed-point operations weak access to cardinalities, through the HH artig (or equicardinalit...

Let R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke (1992) states that if R is excellent, then the absolute integral closure of R is a big Cohen-Macaulay algebra. We prove that if R is the homomorphic image of a Gorenstein local ring, then all the local cohomology (below the dimension) of such a ring maps to zero in a finite extension of the ring. The...

Query processing in the presence of recursively defined views usually involves some form of iteration. For example, computing the transitive closure of a tree involves iterating N times, where N is the depth of the tree, each time computing pairs of vertices that are one edge further apart than the pairs produced in the previous iteration. Applying a divide and conquer technique we devise algor...

Modular Structural Operational Semantics (MSOS) is a variant of Structural Operational Semantics (SOS). It allows language constructs to be specified independently, such that no reformulation of existing rules in an MSOS specification is required when a language is extended with new constructs and features. Introducing the Prolog MSOS tool, we first recall how to synthesize executable interpret...

It is proved deenability in FO+IFP of a global linear ordering on vertices of strongly extensional (SE) nitely-branching graphs. In the case of nite SE graphs this also holds for FO+LFP. This gives capturing results for PTIME computability on the latter class of graphs by FO+LFP and FO+IFP, and also on the corresponding anti-founded universe HFA of hereditarily-nite sets by a language of a boun...

We provide a generic work-list algorithm to compute the (reflexive-)transitive closure of relations where only successors of newly detected states are generated. In contrast to our previous work [2], the relations do not have to be finite, but each element must only have finitely many (indirect) successors. Moreover, a subsumption relation can be used instead of pure equality. An executable var...

Where do new markets come from? I construct a network model in which national markets are nodes and flows of recorded music between them are links and conduct a longitudinal analysis of the global pattern of trade in the period 1976 to 2010. I hypothesize that new export markets are developed through a process of transitive closure in the network of international trade. When two countries’ mark...

We investigate the polyhedral structure of the Periodic Event Scheduling Problem (PESP), which is commonly used in periodic railway timetable optimization. This is the first investigation of Chvátal closures and of the Chvátal rank of PESP instances. In most detail, we first provide a PESP instance on only two events, whose Chvátal rank is very large. Second, we identify an instance for which w...