Showing papers on "Completeness (order theory) published in 2011"
TL;DR: In this paper, a nonparametric model between the two variables with additive separability and a large support condition is considered, and different versions of completeness are obtained, depending on which regularity conditions are imposed.
Abstract: The notion of completeness between two random elements has been considered recently to provide identification in nonparametric instrumental problems. This condition is quite abstract, however, and characterizations have been obtained only in special cases. This paper considers a nonparametric model between the two variables with an additive separability and a large support condition. In this framework, different versions of completeness are obtained, depending on which regularity conditions are imposed. This result allows one to establish identification in an instrumental nonparametric regression with limited endogenous regressor, a case where the control variate approach breaks down.
165 citations
Proceedings Article•
12 Dec 2011TL;DR: This paper introduces a formal definition of lifted inference that allows us to reason about the completeness of lifting inference algorithms relative to a particular class of probabilistic models, and shows how to obtain a completeness result using a first-order knowledge compilation approach for theories of formulae containing up to two logical variables.
Abstract: Probabilistic logics are receiving a lot of attention today because of their expressive power for knowledge representation and learning. However, this expressivity is detrimental to the tractability of inference, when done at the propositional level. To solve this problem, various lifted inference algorithms have been proposed that reason at the first-order level, about groups of objects as a whole. Despite the existence of various lifted inference approaches, there are currently no completeness results about these algorithms. The key contribution of this paper is that we introduce a formal definition of lifted inference that allows us to reason about the completeness of lifted inference algorithms relative to a particular class of probabilistic models. We then show how to obtain a completeness result using a first-order knowledge compilation approach for theories of formulae containing up to two logical variables.
108 citations
Posted Content•
TL;DR: In this paper, the authors consider an L2-completeness condition that lies between completeness and bounded completeness, and construct broad classes of distributions that are L2complete and boundedly complete.
Abstract: Completeness and bounded-completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non-classical measurement error models. However, distributions that are known to be complete or boundedly complete are somewhat scarce. In this paper, we consider an L2-completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L2-complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L2-incomplete distributions also are provided.
89 citations
21 Jun 2011
TL;DR: dlPCF is not only able to precisely capture the functional behaviour of PCF programs but also some of their intensional properties, namely the complexity of evaluating them with Krivine's Machine.
Abstract: A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely capture the functional behaviour of PCF programs (i.e. how the output relates to the input) but also some of their intensional properties, namely the complexity of evaluating them with Krivine's Machine. dlPCF is designed around dependent types and linear logic and is parametrized on the underlying language of index terms, which can be tuned so as to sacrifice completeness for tractability.
84 citations
01 Aug 2011
TL;DR: It is shown that in important cases weakest preconditions for query completeness can be expressed in terms of table completeness statements, which means that these statements identify precisely the parts of a database that are critical for the completeness of a query.
Abstract: Data completeness is an important aspect of data quality as in many scenarios it is crucial to guarantee completeness of query answers. We develop techniques to conclude the completeness of query answers from information about the completeness of parts of a generally incomplete database. In our framework, completeness of a database can be described in two ways: by table completeness (TC) statements, which say that certain parts of a relation are complete, and by query completeness (QC) statements, which say that the set of answers of a query is complete. We identify as core problem to decide whether table completeness entails query completeness (TC-QC). We develop decision procedures and assess the complexity of TC-QC inferences depending on the languages of the TC and QC statements. We show that in important cases weakest preconditions for query completeness can be expressed in terms of table completeness statements, which means that these statements identify precisely the parts of a database that are critical for the completeness of a query. For the related problem of QC-QC entailment, we discuss its connection to query determinacy. Moreover, we show how to use the concrete state of a database to enable further completeness inferences.
67 citations
TL;DR: dlPCF is not only able to precisely capture the functional behaviour of PCF programs but also some of their intensional properties, namely the complexity of evaluating them with Krivine's Machine.
Abstract: A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely capture the functional behaviour of PCF programs (i.e. how the output relates to the input) but also some of their intensional properties, namely the complexity of evaluating them with Krivine's Machine. dlPCF is designed around dependent types and linear logic and is parametrized on the underlying language of index terms, which can be tuned so as to sacrifice completeness for tractability.
55 citations
01 Jan 2011
TL;DR: In this article, the authors considered the long time behavior of continuous time random walks on infinite graphs and characterized the stochastic completeness of the random walk in terms of function-theoretic and geometric properties of the underlying graph.
Abstract: In this thesis we are concerned with the long time behavior of continuous time random walks on infinite graphs. The following three related problems are considered.
1. Stochastic completeness of the random walk. We characterize the stochastic completeness of the random walk in terms of function-theoretic and geometric properties of the underlying graph.
2. Uniqueness of the Cauchy problem for the discrete heat equation in certain function classes. We provide a uniqueness class on an arbitrary graph in terms of the growth of the L2-norm of solutions and show its sharpness. An application of this results to bounded solutions yields a criterion for stochastic completeness in terms of the volume growth with respect to a so-called adapted distance. In special cases, this leads to a volume growth criterion with respect to the graph distance as well.
3. Escape rate of the random walk. We provide upper rate functions for stochastically complete random walks in terms of the volume growth function.
51 citations
TL;DR: In this article, the authors introduce the concept of the square-mean pseudo almost automorphy for a stochastic process and introduce the properties on the completeness and the composition of the space that consists of such processes.
50 citations
TL;DR: In this paper, a set of complete addition laws for arbitrary Edwards curves is given, where the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension.
48 citations
TL;DR: The dual characterization of the corresponding submodelinjection map is given, as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel.
48 citations
TL;DR: In this article, double sequence spaces of fuzzy real numbers defined by Orlicz function are introduced and some properties like solidness, symmetricity, completeness, and inclusion results are proved.
Posted Content•
TL;DR: In this article, the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs were studied, and for a class of graphs with a very weak spherical symmetry, it was shown that the spectral properties of these graphs imply both the incompleteness and the discreteness of the spectrum.
Abstract: We study the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic incompleteness and discreteness of the spectrum. We then use these graphs to give some comparison results for both stochastic completeness and estimates on the bottom of the spectrum for general locally finite graphs.
TL;DR: In this paper, an analogue of the weak Omori-Yau maximum principle and Khasʼminskii's criterion for graphs in the general setting of Keller and Lenz is presented.
TL;DR: A variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall is presented, and an axiomatic system is proposed and its completeness for a rather expressive subset is proved.
Abstract: We present a variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall. The cooperation modalities assume the use the distributed knowledge of coalitions and accordingly refer to perfect recall incomplete information strategies. We propose a model-checking algorithm for the logic. It is based on techniques for games with imperfect information and partially observable objectives, and involves deciding emptiness for automata on infinite trees. We also propose an axiomatic system and prove its completeness for a rather expressive subset. As for the constructs left outside this completely axiomatised subset, we present axioms by which they can be defined in the subset on the class of models in which every state has finitely many successors and give a complete axiomatisation for a “flat” subset of the logic with these constructs included.
TL;DR: In this paper, the authors present the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete, obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theory.
Abstract: This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic completeness, provided by this theory, are adopted in the present investigation.
TL;DR: A survey of methods for constructing covering arrays used in generation of tests for interfaces with a great number of parameters, and heuristics are presented that allow one to reduce arrays without loss of completeness.
Abstract: The paper presents a survey of methods for constructing covering arrays used in generation of tests for interfaces with a great number of parameters. The application domain of these methods and algorithms used in them are analyzed. Specific characteristics of the methods, including time complexity and estimates of the required memory, are presented. Various--direct, recursive, optimization, genetic, and backtracking--algorithms used for constructing covering arrays are presented. Heuristics are presented that allow one to reduce arrays without loss of completeness, and application domains of these heuristics are outlined.
14 Jul 2011
TL;DR: If the Buchi automaton associated with an LTL formula is cliquey, i.e., can be decomposed into clique-shaped strongly connected components, then the associated completeness threshold is linear in the recurrence diameter of the Kripke model under consideration, which strengthens earlier results, which report manageable thresholds only for elementary formulas of the form F p and G q.
Abstract: Bounded model checking is a symbolic bug-finding method that examines paths of bounded length for violations of a given LTL formula. Its rapid adoption in industry owes much to advances in SAT technology over the past 10-15 years. More recently, there have been increasing efforts to apply SAT-based methods to unbounded model checking. One such approach is based on computing a completeness threshold: a bound k such that, if no counterexample of length k or less to a given LTL formula is found, then the formula in fact holds over all infinite paths in the model. The key challenge lies in determining sufficiently small completeness thresholds. In this paper, we show that if the Buchi automaton associated with an LTL formula is cliquey, i.e., can be decomposed into clique-shaped strongly connected components, then the associated completeness threshold is linear in the recurrence diameter of the Kripke model under consideration. We moreover establish that all unary temporal logic formulas give rise to cliquey automata, and observe that this group includes a vast range of specifications used in practice, considerably strengthening earlier results, which report manageable thresholds only for elementary formulas of the form F p and G q.
TL;DR: This article will show the usefulness and elegance of strict intersection types for the Lambda Calculus, that are strict in the sense that they are the representatives of equivalence classes of types in the BCD-system.
Abstract: This article will show the usefulness and elegance of strict intersection types for the Lambda Calculus, that are strict in the sense that they are the representatives of equivalence classes of types in the BCD-system [Barendregt et al. 1983]. We will focus on the essential intersection type assignment; this system is almost syntax directed, and we will show that all major properties hold that are known to hold for other intersection systems, like the approximation theorem, the characterization of (head/strong) normalization, completeness of type assignment using filter semantics, strong normalization for cut-elimination and the principal pair property. In part, the proofs for these properties are new; we will briefly compare the essential system with other existing systems.
TL;DR: In this article, the authors proved the NP-completeness of some problems of choosing a Euclidean vector subset and reduced one of the data analysis problems to these problems.
Abstract: The NP-completeness is proved of some problems of choosing a Euclidean vector subset. One of the data analysis problems is reduced to these problems. The required subset is assumed to have a fixed cardinality and include the vectors that are “close” to each other by the criterium of the minimum sum of squares of distances.
TL;DR: In this paper, the equivalence between the Lioville property and the Khas'minskii condition is discussed, i.e., the existence of an exhaustion function which is also a supersolution for the operator outside a compact set.
Abstract: Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sense modeled after the p-Laplacian with potential. In particular, we discuss the equivalence between the Lioville property and the Khas'minskii condition, i.e. the existence of an exhaustion functions which is also a supersolution for the operator outside a compact set. This generalizes a previous result obtained by one of the authors and answers to a question in "Aspects of potential theory, linear and nonlinear" by Pigola, Rigoli and Setti.
TL;DR: Godefroy, Kalton and Li as discussed by the authors showed that a separable Banach space X with the Schur property cannot be renormed to have a certain quantitative form of weak sequential completeness.
Posted Content•
TL;DR: In this article, the authors consider an L 2 -completeness condition that lies between completeness and bounded completeness, and construct broad classes of distributions that are L 2-complete and boundedly complete.
Abstract: Completeness and bounded-completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non-classical measurement error models. However, distributions that are known to be complete or boundedly complete are somewhat scarce. In this paper, we consider an L^2-completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L^2-complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L^2-incomplete distributions also are provided.
TL;DR: An algebra, which consists of three binary and two unary operations, is able to support the specification of a large variety of integration constraints and is presented as a framework that uses the algebra for the fine-grained integration of policies expressed in XACML.
28 Mar 2011
TL;DR: Every finite deterministic 2- party function is either complete or can be considered equivalent to a noncomplete symmetric 2-party function-this assertion holds true with respect to active adversaries as well as passive adversaries.
Abstract: In this paper we present simple but comprehensive combinatorial criteria for completeness of finite deterministic 2-party functions with respect to information-theoretic security. We give a general protocol construction for efficient and statistically secure reduction of oblivious transfer to any finite deterministic 2-party function that fulfills our criteria. For the resulting protocols we prove universal composability. Our results are tight in the sense that our criteria still are necessary for any finite deterministic 2-party function to allow for implementation of oblivious transfer with statistical privacy and correctness.
We unify and generalize results of Joe Kilian (1991, 2000) in two ways. Firstly, we show that his completeness criteria also hold in the UC framework. Secondly, what is our main contribution, our criteria also cover a wide class of primitives that are not subject of previous criteria. We show that there are non-trivial examples of finite deterministic 2- party functions that are neither symmetric nor asymmetric and therefore have not been covered by existing completeness criteria so far. As a corollary of our work, every finite deterministic 2-party function is either complete or can be considered equivalent to a noncomplete symmetric 2-party function-this assertion holds true with respect to active adversaries as well as passive adversaries. Thereby known results on non-complete symmetric 2-party functions are strengthened.
TL;DR: It is proved that it is possible to extend Girard's Ludics so as to have repetitions (hence exponentials), and still have the results on semantical types which characterize Ludics in the panorama of Game Semantics.
Abstract: Ludics is peculiar in the panorama of game semantics: we first have the definition of interaction-composition and then we have semantical types, as a set of strategies which "behave well" and react in the same way to a set of tests. The semantical types which are interpretations of logical formulas enjoy a fundamental property, called internal completeness, which characterizes ludics and sets it apart also from realizability. Internal completeness entails standard full completeness as a consequence. A growing body of work start to explore the potential of this specific interactive approach. However, ludics has some limitations, which are consequence of the fact that in the original formulation, strategies are abstractions of MALL proofs. On one side, no repetitions are allowed. On the other side, the proofs tend to rely on the very specific properties of the MALL proof-like strategies, making it difficult to transfer the approach to semantical types into different settings. In this paper, we provide an extension of ludics which allows repetitions and show that one can still have interactive types and internal completeness. From this, we obtain full completeness w.r.t. a polarized version of MELL. In our extension, we use less properties than in the original formulation, which we believe is of independent interest. We hope this may open the way to applications of ludics approach to larger domains and different settings.
TL;DR: It is shown that an equation follows from the axioms of dagger compact closed categories if and only if it holds in finite dimensional Hilbert spaces.
TL;DR: In this article, the authors provide an extension of ludics which allows repetitions and show that one can still have interactive types and internal completeness w.r.t. a polarized version of MELL.
Abstract: Ludics is peculiar in the panorama of game semantics: we first have the
definition of interaction-composition and then we have semantical types, as a
set of strategies which "behave well" and react in the same way to a set of
tests. The semantical types which are interpretations of logical formulas enjoy
a fundamental property, called internal completeness, which characterizes
ludics and sets it apart also from realizability. Internal completeness entails
standard full completeness as a consequence. A growing body of work start to
explore the potential of this specific interactive approach. However, ludics
has some limitations, which are consequence of the fact that in the original
formulation, strategies are abstractions of MALL proofs. On one side, no
repetitions are allowed. On the other side, the proofs tend to rely on the very
specific properties of the MALL proof-like strategies, making it difficult to
transfer the approach to semantical types into different settings. In this
paper, we provide an extension of ludics which allows repetitions and show that
one can still have interactive types and internal completeness. From this, we
obtain full completeness w.r.t. a polarized version of MELL. In our extension,
we use less properties than in the original formulation, which we believe is of
independent interest. We hope this may open the way to applications of ludics
approach to larger domains and different settings.
Proceedings Article•
24 Jun 2011TL;DR: The method automatically extracts knowledge representations from a textbook and uses them to generate concept maps, which are evaluated according to their accuracy, completeness, and pedagogy.
Abstract: In this paper we present a methodology for creating concept map exercises for students. Concept mapping is a common pedagogical exercise in which students generate a graphical model of some domain. Our method automatically extracts knowledge representations from a textbook and uses them to generate concept maps. The purpose of the study is to generate and evaluate these concept maps according to their accuracy, completeness, and pedagogy.
TL;DR: In this article, the supergravity r-and c-maps preserve completeness, and it is shown that any component H of a hypersurface defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold, and any complete quaternionic projective manifold of negative scalar curvature.
Abstract: We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h=1} defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler manifold defines a complete quaternionic Kahler manifold of negative scalar curvature. We classify all complete quaternionic Kahler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.
TL;DR: For non-trivial preorders, it shows that, unlike the standard definitions, the weak preference relation defined in Galaabaatar and Karni (2010) allows for incomplete preferences while maintaining all the continuity properties of complete preference relations.