A correct, precise and efficient integration of set-sharing, freeness and linearity for the analysis of finite and rational tree languages

It is well known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper, we present a novel combination of set-sharing with freeness and linearity information, which is characterized by an improved abstract unification operator. We provide a new abstraction function and prove the correctness of the analysis for both the finite tree and the rational tree cases. Moreover, we show that the same notion of redundant information as identified in Bagnara et al. (2000) and Zaffanella et al. (2002) also applies to this abstract domain combination: this allows for the implementation of an abstract unification operator running in polynomial time and achieving the same precision on all the considered observable properties

Decidability of the Clark's Completion Semantics for Monadic Programs and Queries

There are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable. To obtain decidability one needs to put additional restrictions on programs and queries. In logic programming it is natural to put restrictions on the underlying first-order language. In this note we show the decidability of the Clark's completion semantics for monadic general programs and queries. To appear in Theory and Practice of Logic Programming (TPLP

Straightening warped cones

We provide the converses to two results of J. Roe (Geom. Topol. 2005): first, the warped cone associated to a free action of an a-T-menable group admits a fibred coarse embedding into a Hilbert space, and second, a free action yielding a warped cone with property A must be amenable. We construct examples showing that in both cases the freeness assumption is necessary. The first equivalence is obtained also for other classes of Banach spaces, in particular for $L^p$-spaces.Comment: Final authors' version of the article published by JTA. Changes since v2: the proof of Lem. 3.8 (now Prop. 3.10) is split between several lemmata, the proof of Thm 4.2 simplified and more detaile

Separations of Matroid Freeness Properties

Properties of Boolean functions on the hypercube invariant with respect to linear transformations of the domain are among the most well-studied properties in the context of property testing. In this paper, we study the fundamental class of linear-invariant properties called matroid freeness properties. These properties have been conjectured to essentially coincide with all testable linear-invariant properties, and a recent sequence of works has established testability for increasingly larger subclasses. One question left open, however, is whether the infinitely many syntactically different properties recently shown testable in fact correspond to new, semantically distinct ones. This is a crucial issue since it has also been shown that there exist subclasses of these properties for which an infinite set of syntactically different representations collapse into one of a small, finite set of properties, all previously known to be testable. An important question is therefore to understand the semantics of matroid freeness properties, and in particular when two syntactically different properties are truly distinct. We shed light on this problem by developing a method for determining the relation between two matroid freeness properties P and Q. Furthermore, we show that there is a natural subclass of matroid freeness properties such that for any two properties P and Q from this subclass, a strong dichotomy must hold: either P is contained in Q or the two properties are "well separated." As an application of this method, we exhibit new, infinite hierarchies of testable matroid freeness properties such that at each level of the hierarchy, there are functions that are far from all functions lying in lower levels of the hierarchy. Our key technical tool is an apparently new notion of maps between linear matroids, called matroid homomorphisms, that might be of independent interest

Communication Complexity of Discrete Fair Division

We initiate the study of the communication complexity of fair division with indivisible goods. We focus on some of the most well-studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive and unrestricted). Within these parameters, our results completely resolve whether the communication complexity of computing a fair allocation (or determining that none exist) is polynomial or exponential (in the number of goods), for every combination of fairness notion, valuation class, and number of players, for both deterministic and randomized protocols.Comment: Accepted to SODA 201