Bisimulations on data graphs

Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called “data graphs”), and where observers can test for equality or inequality of data values (e.g., asking the attribute ‘name’ of a node to be different from that of all its neighbors). The present work constitutes a first investigation of “data aware” bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath —a language that extends modal logics like PDL with tests for data equality— with and without transitive closure operators. We show that in general the problem is PSPACE-complete, but identify several restrictions that yield better complexity bounds (CO- NP, PTIME) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.Fil: Abriola, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; ArgentinaFil: Barceló, Pablo. Universidad de Chile; ChileFil: Figueira, Diego. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentin

A logical framework to study concept-learning biases in the presence of multiple explanations

When people seek to understand concepts from an incomplete set of examples and counterexamples, there is usually an exponentially large number of classification rules that can correctly classify the observed data, depending on which features of the examples are used to construct these rules. A mechanistic approximation of human concept-learning should help to explain how humans prefer some rules over others when there are many that can be used to correctly classify the observed data. Here, we exploit the tools of propositional logic to develop an experimental framework that controls the minimal rules that are simultaneously consistent with the presented examples. For example, our framework allows us to present participants with concepts consistent with a disjunction and also with a conjunction, depending on which features are used to build the rule. Similarly, it allows us to present concepts that are simultaneously consistent with two or more rules of different complexity and using different features. Importantly, our framework fully controls which minimal rules compete to explain the examples and is able to recover the features used by the participant to build the classification rule, without relying on supplementary attention-tracking mechanisms (e.g. eye-tracking). We exploit our framework in an experiment with a sequence of such competitive trials, illustrating the emergence of various transfer effects that bias participants’ prior attention to specific sets of features during learning.Fil: Abriola, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Tano, Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Romano, Sergio Gaston. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentin

Model theory of XPath on data trees. Part II: Binary bisimulation and definability

We study the expressive power of the downward and vertical fragments of XPath equipped with (in)equality tests over possibly infinite data trees. We introduce a suitable notion of saturation with respect to node expressions, and show that over saturated data trees, the already studied notion of (unary) bisimulation coincides with the idea of ‘indistinguishability by means of node expressions’. We also prove definability and separation theorems for classes of pointed data trees. We introduce new notions of binary bisimulations, which relate two pairs of nodes of data trees. We show that over finitely branching data trees, these notions correspond to the idea of ‘indistinguishability by means of path expressions’. We prove a characterization theorem, which describes when a first-order formula with two free variables is expressible in the downward fragment. We show definability and separation theorems, for classes of two-pointed data trees and in the context of path expressions.Fil: Abriola, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Descotte, María Emilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación; Argentin

Linearizing well quasi-orders and bounding the length of bad sequences

We study the length functions of controlled bad sequences over some well quasi-orders (wqo's) and classify them in the Fast Growing Hierarchy. We develop a new and self-contained study of the length of bad sequences over the disjoint product in Nn (Dickson's Lemma), which leads to recently discovered upper bounds but through a simpler argument. We also give a tight upper bound for the length of controlled decreasing sequences of multisets of Nn with the underlying lexicographic ordering, and use it to give an upper bound for the length of controlled bad sequences in the majoring ordering with the underlying disjoint product ordering. We apply this last result to attain complexity upper bounds for the emptiness problem of itca and atra automata. For the case of the product and majoring wqo's the idea is to linearize bad sequences, i.e. to transform a bad sequence over a wqo into a decreasing one over a well-order, for which upper bounds can be more easily handled.Fil: Abriola, Sergio Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Senno, Gabriel Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Definability for Downward and Vertical XPath on Data Trees

We study the expressive power of the downward and vertical fragments of XPath equipped with (in)equality tests over data trees. We give necessary and sufficient conditions for a class of pointed data trees to be definable by a set of formulas or by a single formula of each of the studied logics. To do so, we introduce a notion of saturation, and show that over saturated data trees bisimulation coincides with logical equivalence.Fil: Abriola, Sergio Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Descotte, María Emilia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentin