Showing papers on "Completeness (order theory) published in 2003"

Complexity and Completeness of Finding Another Solution and Its Application to Puzzles

Abstract: The Another Solution Problem (ASP) of a problem Π is the following problem: for a given instance x of Π and a solution s to it, find a solution to x other than s. (The notion of ASP as a new class of problems was first introduced by Ueda and Nagao.) In this paper we consider n-ASP, the problem to find another solution when n solutions are given. In particular we consider ASP-completeness, the completeness with respect to the parsimonious reductions which allow polynomial-time transformation

Asymptotic stability of N-soliton states of NLS

Abstract: We prove the asymptotic stability and asymptotic completeness of an arbitrary number of weakly interacting solitons for NLS.

On the interplay between consistency, completeness, and correctness in requirements evolution

Abstract: The initial expression of requirements for a computer-based system is often informal and possibly vague. Requirements engineers need to examine this often incomplete and inconsistent brief expression of needs. Based on the available knowledge and expertise, assumptions are made and conclusions are deduced to transform this \rough sketch" into more complete, consistent, and hence correct requirements. This paper addresses the question of how to characterize these properties in an evolutionary framework, and what relationships link these properties to a customer’s view of correctness. Moreover, we describe in rigorous terms the dieren t kinds of validation checks that must be performed on dieren t parts of a requirements specication in order to ensure that errors (i.e., cases of inconsistency and incompleteness) are detected and marked as such, leading to better quality requirements.

Byzantine Fault Detectors for Solving Consensus

Abstract: Unreliable fault detectors can be defined in terms of completeness and accuracy properties and can be used to solve the consensus problem in asynchronous distributed systems that are subject to crash faults. We extend this result to asynchronous distributed systems that are subject to Byzantine faults. First, we define and categorize Byzantine faults. We then define two new completeness properties, eventual strong completeness and eventual weak completeness. We use these completeness properties and previously defined accuracy properties to define four new classes of unreliable Byzantine fault detectors. Next, we present an algorithm that uses a Byzantine fault detector to solve the consensus problem in an asynchronous distributed system of n processes in which the number k of Byzantine faults satisfies k ≤� (n − 1)/3� . We also give algorithms that implement a Byzantine fault detector in a model of partial synchrony. Finally, we prove the correctness of the consensus algorithm and analyze its complexity.

Loop Formulas for Disjunctive Logic Programs

Abstract: We extend Clark’s definition of a completed program and the definition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completion that satisfy the loop formulas. The concept of a tight program and Fages’ theorem are extended to disjunctive programs as well.

Lower bounds for non-black-box zero knowledge

Abstract: We show new lower bounds and impossibility results for general (possibly non-black-box) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a constant-round zero-knowledge strong proof (or argument) of knowledge (as defined by Goldreich, 2001) for a nontrivial language; 2. There does not exist a two-round zero-knowledge proof system with perfect completeness for an NP-complete language; 3. There does not exist a constant-round public-coin proof system for a nontrivial language that is resettable zero knowledge. This result also extends to bounded resettable zero knowledge. In contrast, we show that under reasonable assumptions, there does exist such a (computationally sound) argument system that is bounded-resettable zero knowledge.

A Unified Approach To The Concept Of Fuzzy L-Uniform Space

Abstract: The theory of uniform structures is an important area of topology which in a certain sense can be viewed as a bridge linking metrics as well as topological groups with general topological structures. In particular, uniformities form, the widest natural context where such concepts as uniform continuity of functions, completeness and precompactness can be extended from the metric case. Therefore, it is not surprising that the attention of mathematicians interested in fuzzy topology constantly addressed the problem to give an appropriate definition of a uniformity in fuzzy context and to develop the corresponding theory. Already by the late 1970’s and early 1080’s, this problem was studied (independently at the first stage) by three authors: B. Hutton [21], U. Hohle [11, 12], and R. Lowen [30]. Each of these authors used in the fuzzy context a different aspect of the filter theory of traditional uniformities as a starting point, related in part to the different approaches to traditional unformities as seen in [37, 2] vis-a-vis [36, 22]; and consequently, the applied techniques and the obtained results of these authors are essentially different. Therefore it seems natural and urgent to find a common context as broad as necessary for these theories and to develop a general approach containing the previously obtained results as special cases—it was probably S. E. Rodabaugh [31] who first stated this problem explicitly.

The Basic Algebra of Game Equivalences

Abstract: We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.

Compositional circular assume-guarantee rules cannot be sound and complete

Abstract: Circular assume-guarantee reasoning is used for the compositional verification of concurrent systems. Its soundness has been studied in depth, perhaps because circularity makes it anything but obvious. In this paper, we investigate completeness. We show that compositional circular assume-guarantee rules cannot be both sound and complete.

Elementary Fixed Point Theorems

Abstract: In this chapter we provide an introduction to those topics of fixed point theory that for the most part involve only the notions of completeness, order, and convexity. In spite of their elementary character, the results given here have a number of significant applications. Some of these are presented at the end of the chapter.

Deriving Use Cases from Business Process Models

Abstract: Use cases are intended to capture the functional requirements of an information system. The problem of identifying use cases is however not satisfactorily resolved yet. The approach presented in this paper is to derive use cases from the business system models that are produced by applying DEMO (Demo Engineering Methodology for Organizations). These models have three attractive properties: essence, atomicity and completeness. Essence means that the real business things are identified, clearly distinguished from informational things. Atomic means that one ends up with things that are units from the business point of view. Complete means that no business things are overlooked and that the models do not contain irrelevant things. A three-step procedure is proposed for deriving use cases from these models, such that they do possess the same properties of essence, atomicity and completeness.

Kleene Algebra with Tests and the Static Analysis of Programs

Abstract: We propose a general framework for the static analysis of programs based on Kleene algebra with tests (KAT). We show how KAT can be used to statically verify compliance with safety policies specified by security automata. We prove soundness and completeness over relational interpretations. We illustrate the method on an example involving the correctness of a device driver.

Completeness of a fact extractor

Abstract: The process of software reverse engineering commonlyuses an extractor, which parses source code and extractsfacts about the code. The level of detail in these factsvaries from extractor to extractor. This paper describesfour levels of increasingly detailed completeness of thesefacts: (semantic completeness, compiler completeness,syntax completeness and source completeness) andintroduces the concept of relative completeness ofextractors. Validating that an extractor correctlyproduces facts at a given level of completeness is ingeneral very challenging. This paper gives a method forvalidating the semantic completeness of an extractor, anddescribes the application of this method to CPPX, anextractor for C or C++ based on GCC.

Geometric Completeness of Distribution Spaces

Abstract: This paper introduces a notion of geometric completeness for spaces of distributions, modelled after the notion of a complete variety in algebraic geometry. It is related to the following elimination problem for systems of PDE: consider the set of homogeneous solutions of a system of PDE in some space of distributions. When is the projection of this set onto some of its coordinates also the set of homogeneous solutions of a system of PDE?

Global Hyperbolicity of Sliced Spaces

Abstract: We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced spaces are timelike and null geodesically complete if and only if space is a complete Riemannian manifold.

On the NP-completeness of the Slither Link Puzzle

Abstract: For many of the widely played games and puzzles, their computational complexities have been analyzed. In this paper, we consider a sort of puzzle “Slither Link” and prove that the problem which determines whether or not a given instance of puzzle has any solutions is NP-complete, by using a polynomial time reduction from the Hamilton Path Problem with respect to restricted graphs. In addition we consider Another Solution Problem for the puzzle, the problem which determines, for a given instance and its solution, whether there is another solution for the instance. We provide a strategy to prove its NP-completeness.

Closure operators and complete embeddings of residuated lattices

Abstract: In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.

Subspaces with Equal Closure

Abstract: We take a new and unifying approach toward polynomial and trigonometric approximation in topological vector spaces used in analysis on R n . The idea is to show in considerable generality that in such a space a module, which is generated over the polynomials or trigonometric functions by some set, necessarily has the same closure as the module which is generated by this same set, but now over the compactly supported smooth functions. The particular properties of the ambient space or generating set are, to a large degree, irrelevant for these subspaces to have equal closure. This translation—which goes in fact beyond modules—allows us, by what is now essentially a straightforward check of a few properties, to replace many classical results in various spaces by more general statements of a hitherto unknown type. Even in the case of modules with one generator the resulting theorems on, e.g., completeness of polynomials are then significantly stronger than the classical statements. This extra precision stems from the use of quasi-analytic methods (in several variables) rather than holomorphic methods, combined with the classification of quasi-analytic weights. In one dimension this classification, which then involves the logarithmic integral, states that two well-known families of weights are essentially equal. As a side result we also obtain an integral criterion for the determinacy of multidimensional measures which is less stringent than the classical version. The approach can be formulated for Lie groups and this interpretation then shows that many classical approximation theorems are “actually” theorems on the unitary dual of R n , thus inviting to a change of paradigm. In this interpretation polynomials correspond to the universal enveloping algebra of R n and trigonometric functions correspond to the group algebra. It should be emphasized that the point of view, combined with the use of quasi-analytic methods, yields a rather general and precise ready-to-use tool, which can very easily be applied in new situations of interest which are not covered by this paper.

Completeness in Two-Party Secure Computation - A Computational View

Abstract: A Secure Function Evaluation (SFE) of a two-variable function f(·,·) is a protocol that allows two parties with inputs x and y to evaluate f(x,y) in a manner where neither party learns "more than is necessary". A rich body of work deals with the study of completeness for secure two-party computation. A function f is complete for SFE if a protocol for securely evaluating f allows the secure evaluation of all (efficiently computable) functions. The questions investigated are which functions are complete for SFE, which functions have SFE protocols unconditionally and whether there are functions that are neither complete nor have efficient SFE protocols. The previous study of these questions was mainly conducted from an information theoretic point of view and provided strong answers in the form of combinatorial properties. However, we show that there are major differences between the information theoretic and computational settings. In particular, we show functions that are considered as having SFE unconditionally by the combinatorial criteria but are actually complete in the computational setting. We initiate the fully computational study of these fundamental questions. Somewhat surprisingly, we manage to provide an almost full characterization of the complete functions in this model as well. More precisely, we present a computational criterion (called computational row non-transitivity) for a function f to be complete for the asymmetric case. Furthermore, we show a matching criterion called computational row transitivity for f to have a simple SFE (based on no additional assumptions). This criterion is close to the negation of the computational row non-transitivity and thus we essentially characterize all "nice" functions as either complete or having SFE unconditionally.

Unknown input observers for singular systems designed by eigenstructure assignment

Abstract: In this paper, any unknown input observers with orders between minimum and full orders can be established for singular systems by eigenstructure assignment method. The complete and parametric solutions for the observer matrices and for the generalized eigenvectors are obtained. The completeness and parametric forms of the solutions and the flexibility in selecting the observer order allow the designer to choose a suitable observer according to the control purposes; hence, the solutions are quite suitable for advanced applications.

A complete and stable set of affine-invariant Fourier descriptors

Abstract: We propose here a study of a new affine-invariant Fourier descriptors (Ghorbel (1998)) which are computed on the projection of a given curve that is assumed to be evolving on three dimensional space and supposed to be far enough from the camera. This set of descriptors is compared to the well known affine curvature. These invariants satisfy the completeness and stability properties.

Global Existence of Solutions to the Coupled Einstein and Maxwell-Higgs System in the Spherical Symmetry

Abstract: We prove the global unique existence of classical solutions to the Einstein equations coupled with Maxwell-Higgs system for small initial data under the spherical symmetry We also obtain the decay estimates of the solutions, and find that the corresponding space-time is time-like and null geodesically complete toward the future For the proof we reduce the system to a single first order integrodifferential equation, and use the contraction mapping theorem in the appropriate function spaces We also obtain the completeness of space-time along the future directed time-like lines exterior to a region which resembles the even horizon of the Reissner-Nordstrom black hole

Construction of Complete and Independent Systems of Rotation Moment Invariants

Abstract: The problem of independence and completeness of rotation moment invariants is addressed in this paper. General method for constructing invariants of arbitrary orders by means of complex moments is described. It is shown that for any set of invariants there exists relatively small basis by means of which all other invariants can be generated. The method how to construct such a basis is presented. Moreover, it is proved that all moments involved can be recovered from this basis. The basis of the 3rd order moment invariants is constructed explicitly and its relationship to Hu’s invariants is studied. Based on this study, Hu’s invariants are shown to be dependent and incomplete.

Method and system for checking consistency and completeness of selection conditions in a product configuration system

Abstract: Embodiments of the present invention relate to a method and system for evaluating selection conditions associated with variants of components of a multi-component configurable product for consistency and completeness.

On completeness of multi-dimensional first-order temporal logics

Abstract: In this paper, we show that first-order temporal logics form a proper expressiveness hierarchy with respect to dimensionality and quantifier depth of temporal connectives. This result resolves (negatively) the open question concerning the existence of an expressively complete first-order temporal logic, even when allowing multidimensional temporal connectives.

A Catalog ofWeak Many-Valued Modal Axioms and their Corresponding Frame Classes

Abstract: In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fitting's many-valued modal languages. These languages were introduced by M. Fitting in the early '90s and are built on Heyting algebras which serve as the space of truth values. The possible-worlds frames interpreting these languages are directed graphs whose edges are labelled with an element of the underlying Heyting algebra, providing us a form of many-valued accessibility relation. Weak axioms of the form we treat here have been examined from the completeness perspective and further explored for applications in non-monotonic reasoning. Here, we introduce more weak many-valued modal axioms and prove a frame correspondence result for all of them. The classes of corresponding labelled frames possess algebraic properties which are strongly reminiscent of many classical ones, such as the Church-Rosser property, reflexivity, transitivity, partial functionality, etc.

Alternating signs of quiver coefficients

Abstract: We prove K-theoretic generalizations of the component formulas of Knutson, Miller, and Shimozono, and deduce that K-theoretic quiver coefficients have alternating signs. We also prove new variants of the factor sequences conjecture, and a conjecture of Knutson, Miller, and Shimozono stating that the double ratio formula agrees with the original quiver formulas. For completeness we include a short proof of the ratio formula for quiver varieties.

Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time

Abstract: This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and machine-independent affine reductions.