Showing papers on "Completeness (order theory) published in 2004"

Type error slicing in implicitly typed higher-order languages

Abstract: Previous methods have generally identified the location of a type error as a particular program point or the program subtree rooted at that point. We present a new approach that identifies the location of a type error as a set of program points (a slice) all of which are necessary for the type error. We identify the criteria of completeness and minimality for type error slices. We discuss the advantages of complete and minimal type error slices over previous methods of presenting type errors. We present and prove the correctness of algorithms for finding complete and minimal type error slices for implicitly typed higher-order languages like Standard ML.

Asymptotic behaviour of the Einstein-Vlasov system with a positive cosmological constant

Abstract: We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic behaviour of solutions in the future time is investigated in various aspects.

Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach

Abstract: This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a finite universe of objects and an a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. Very few properties of this quadernary relation are assumed (beside completeness, transitivity and a very natural form of symmetry). The two rules that we characterize are the maxi-max criterion and the lexi-max criterion. The maxi-max criterion considers that a set is more diverse than another if and only if the two objects that are the most dissimilar in the former are weakly as dissimilar as the two most dissimilar objects in the later. The lexi-max criterion is defined as usual as the lexicographic extension of the maxi-max criterion. Some connections with the broader issue of measuring freedom of choice are also provided.

Exploring Relational Structures Via FLE

Abstract: Designing ontologies and specifying axioms of the described domains is an expensive and error-prone task. Thus, we propose a method originating from Formal Concept Analysis which uses empirical data to systematically generate hypothetical axioms about the domain, which are represented to an ontology engineer for decision. In this paper, we focus on axioms that can be expressed as entailment statements in the description logic FLE . The proposed technique is an incremental one, therefore, in every new step we have to reuse the ax- iomatic information acquired so far. We present a sound and complete deduction calculus for FLE entailment statements. We give a detailed description of this multistep algorithm including a technique called empirical attribute reduction and demonstrate the pro- posed technique using an example from mathematics. We give a completeness result on the explored information and address the question of algorithm termination. Finally, we discuss possible appli- cations of our method.

An empirical assessment of completeness in UML designs

Abstract: Delivering high quality software in an economic way requires advanced control over the software development process and the product in all stages of its life-cycle. The use of metrics as means of control and improvement plays an important role in software engineering. Interviews with industrial software engineers identified incompleteness of UML designs as a potential problem for subsequent stages of development. In this paper we propose a definition of completeness of a UML model and present a set of rules to assess model completeness. We report results from industrial case studies to assess the level of completeness in practice. The amount of completeness and consistency rule violations was very high. Different case studies showed large variations in conformance to and violations of rules.

Algebraic Aspects of Cut Elimination

Abstract: We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17].

Strong Preservation as Completeness in Abstract Interpretation

Abstract: Many algorithms have been proposed to minimally refine abstract transition systems in order to get strong preservation relatively to a given temporal specification language. These algorithms compute a state equivalence, namely they work on abstractions which are partitions of system states. This is restrictive because, in a generic abstract interpretation-based view, state partitions are just one particular type of abstraction, and therefore it could well happen that the refined partition constructed by the algorithm is not the optimal generic abstraction. On the other hand, it has been already noted that the well-known concept of complete abstract interpretation is related to strong preservation of abstract model checking. This paper establishes a precise correspondence between complete abstract interpretation and strongly preserving abstract model checking, by showing that the problem of minimally refining an abstract model checking in order to get strong preservation can be formulated as a complete domain refinement in abstract interpretation, which always admits a fixpoint solution. As a consequence of these results, we show that some well-known behavioural equivalences used in process algebra like simulation and bisimulation can be elegantly characterized in pure abstract interpretation as completeness properties.

On the use of measure-valued strategies in bond markets

Abstract: We propose here a theory of cylindrical stochastic integration, recently developed by Mikulevicius and Rozovskii, as mathematical background to the theory of bond markets. In this theory, since there is a continuum of securities, it seems natural to define a portfolio as a measure on maturities. However, it turns out that this set of strategies is not complete, and the theory of cylindrical integration allows one to overcome this difficulty. Our approach generalizes the measure-valued strategies: this explains some known results, such as approximate completeness, but at the same time it also shows that either the optimal strategy is based on a finite number of bonds or it is not necessarily a measure-valued process.

Reasoning about common knowledge with infinitely many agents

Abstract: Complete axiomatizations and exponential-time decision procedures are provided for reasoning about knowledge and common knowledge when there are infinitely many agents. The results show that reasoning about knowledge and common knowledge with infinitely many agents is no harder than when there are finitely many agents, provided that we can check the cardinality of certain set differences G - G', where G and G' are sets of agents. Since our complexity results are independent of the cardinality of the sets G involved, they represent improvements over the previous results even when the sets of agents involved are finite. Moreover, our results make clear the extent to which issues of complexity and completeness depend on how the sets of agents involved are represented.

The Hardness of the Lemmings Game, or "Oh no, more NP-Completeness Proofs"

Abstract: In the computer game ‘Lemmings’, the player must guide a tribe of green-haired lemming creatures to safety, and save them from an untimely demise. We formulate the decision problem which is, given a level of the game, to decide whether it is possible to complete the level (and hence to find a solution to that level). Under certain limitations, this can be decided in polynomial time, but in general the problem is shown to be NP-Hard. This can hold even if there is only a single lemming to save, thus showing that it is hard to approximate the number of saved lemmings to any factor.

The Basis Properties of Some Systems of Exponential Functions, Cosines, and Sines

Abstract: We consider some systems of exponential functions, cosines, and sines with complex-valued coefficients and establish a necessary and sufficient condition for completeness and minimality of these systems in Lebesgue spaces.

Convexity in tandem queues

Abstract: We derive convexity results and related properties for the value functions of tandem queuing systems. The results for standard multiserver queues are new. For completeness, we also prove and generalize existing results on tandems of controllable queues. The results can be used to compare queuing systems. This is done for systems with and without batch arrivals and for systems with different numbers of on–off sources.

A note on completeness in large financial markets

Abstract: We study completeness in large financial markets, namely markets containing countably many assets. We investigate the relationship between asymptotic completeness in the global market and completeness in the finite submarkets, under a no-arbitrage assumption. We also suggest a way to approximate a replicating strategy in the large market by finite-dimensional portfolios. Furthermore, we find necessary and sufficient conditions for completeness to hold in a factor model.

A Note on Completeness in Large Financial Markets

Abstract: We study completeness in large financial markets, namely markets containing countably many assets. We investigate the relationship between asymptotic completeness in the global market and completeness in the finite submarkets, under a no-arbitrage assumption. We also suggest a way to approximate a replicating strategy in the large market by finite-dimensional portfolios. Furthermore, we find necessary and sufficient conditions for completeness to hold in a factor model.

Modal Kleene Algebra and partial correctness

Abstract: Modal Kleene algebra is Kleene algebra enriched by forward and backward box and diamond operators. We formalize the symmetries of these operators as Galois connections and dualities. We study their properties in the associated semirings of operators. Modal Kleene algebra provides a unifying semantics for various program calculi and enhances efficient cross-theory reasoning in this class, often in a very concise state-free style. This claim is supported by novel algebraic soundness and completeness proofs for Hoare logic.

Set comprehension in church's type theory

Abstract: Church's simple type theory allows quantification over sets and functions. This expressive power allows a natural formalization of much of mathematics. However, searching for set instantiations has not yet been well-understood. Here we study the role of set comprehension in higher-order automated theorem proving. In particular, we introduce formulations of Church's type theory which are restricted with respect to set comprehension. We then define corresponding semantics and show soundness and completeness. Using completeness, we show that some restrictions to set comprehension are complete. That is, we can prove any theorem with restricted set comprehension that could be proven with unrestricted set comprehension. We also show some restrictions are incomplete. This methodology is used to study set comprehension both in the presence and absence of extensionality. We also describe methods for automated theorem proving in extensional type theory with restricted set instantiations. The approach to automated proof search presented here extends mating search by including connections up to extensional and equational reasoning. Search procedures based on these ideas have been implemented as part of the TPS theorem prover. The procedures have also been augmented by including the ability to solve for certain sets using set constraints. We describe the implementation and include experimental results.

Solving equations involving sequence variables and sequence functions

Abstract: Term equations involving individual and sequence variables, and individual and sequence function symbols are studied. Function symbols can have either fixed or flexible arity. A new unification procedure for solving such equations is presented. Decidability of unification is proved. Completeness and almost minimality of the procedure is shown.

Bergman completeness of hyperconvex manifolds

Abstract: Abstract We proved that any hyperconvex manifold has a complete Bergman metric.

On the call-by-value CPS transform and its semantics

Abstract: We investigate continuations in the context of idealized call-by-value programming languages On the semantic side, we analyze the categorical structures that arise from continuation models of call-by-value languages On the syntactic side, we study the call-by-value continuation-passing transformation as a translation between equational theories Among the novelties are an unusually simple axiomatization of control operators and a strengthened completeness result with a proof based on a delaying transform

On Notions of Completeness Weaker than Kripke Completeness.

Abstract: We are going to show that the standard notion of Kripke completeness is the strongest one among many provably distinct algebraically motivated completeness properties, some of which seem to be of intrinsic interest. More specifically, we are going to investigate notions of completeness with respect to algebras which are either atomic, complete, completely additive or admit residuals (the last notion of completeness coincides with conservativity of minimal tense extensions); we will be also interested in combinations of these properties.

Bi-immunity separates strong NP-completeness notions

Abstract: We prove that if for some e > 0, NP contains a set that is DTIME(2ne))-bi-immune, then NP contains a set that is 2-Turing complete for NP (hence 3-truth-table complete) but not 1-truth-table complete for NP. Thus this hypothesis implies a strong separation of completeness notions for NP. Lutz and Mayordomo (Theor. Comput. Sci. 164 (1996) 141-163) and Ambos-Spies and Bentzien (J. Comput. Syst. Sci. 61(3) (2000) 335-361) previously obtained the same consequence using strong hypotheses involving resource-bounded measure and/or category theory. Our hypothesis is weaker and involves no assumptions about stochastic properties of NP.

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.

On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry

Abstract: Spacetimes with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry are shown to be timelike and null geodesically complete in the expanding direction, provided the data satisfy a certain size restriction.

Letter: 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.

Exploiting functional properties of boolean functions for optimal multi-level design by bi-decomposition

Abstract: This paper introduces the theory of bi-decomposition of Boolean functions. This approach optimally exploits functional properties of a Boolean function in order to find an associated multilevel circuit representation having a very short delay by using simple two input gates. The machine learning process is based on the Boolean Differential Calculus and is focused on the aim of detecting the profitable functional properties available for the Boolean function.For clear understanding the bi-decomposition of completely specified Boolean functions is introduced first. Significantly better chance of success are given for bi-decomposition of incompletely specified Boolean functions, discussed secondly. The inclusion of the weak bidecomposition allows to prove the the completeness of the suggested decomposition method. The basic task for machine learning consists of determining the decomposition type and dedicated sets of variables. Lean on this knowledge a complete recursive design algorithm is suggested.Experimental results over MCNC benchmarks show that the bi-decomposition out-performs SIS and other BDD-based decomposition methods in terms of area and delay of the resulting circuits with comparable CPU time.By switching from the ON-set/OFF-set model of Boolean function lattices to their upper-and lower-bound model a new view to the bi-decomposition arises. This new form of the bi-decomposition theory makes a comprehensible generalization of the bi-decomposition to multivalued function possible.

On the Completeness of an Exponential Type Sequence

Abstract: We investigate the Birch's sequence YK = pαqβ ¦ p, q > 1, α, β N0, 0 ≦ β ≦ K giving a partial answer for a question of P Erdos