Showing papers on "Completeness (order theory) published in 1983"
TL;DR: It is proved that self-reducible sets are not polynomial-time Turing reducible to these sets, and weakly p -selective sets are introduced as a generalization of p - selective sets based on this characterization.
176 citations
TL;DR: In this article, it was shown that a theorem proving system consisting of resolution, paramodulation, factoring, equality reversal, simplification, and subsumption removal is complete in first-order logic with equality.
Abstract: It is proved that an automatic theorem proving system consisting of resolution, paramodulation, factoring, equality reversal, simplification, and subsumption removal is complete in first-order logic with equality. When restricted to equality units, the system is similar to the Knuth-Bendix procedure for deriving consequences from equalities. However, our proofs of completeness are restricted to the case in which the ordering on words (terms or atoms) that is required in this type of process is order-isomorphic to the positive integers. The completeness of resolution and paramodulation without the functionally reflexive axioms is a simple corollary of our result. The methods used are based upon the familiar ideas associated with semantic trees, and should be helpful in showing that other theorem proving systems with equality are complete.
99 citations
70 citations
TL;DR: Two issues concerning completeness of Hoare-like proof systems which seem unrelated at first sight are brought together: Expressiveness of the assertion language and the Rule of Adaptation.
59 citations
52 citations
42 citations
39 citations
TL;DR: The fine structure of completeness and basis properties of complex exponentials has been studied in this article, where Paley and Wiener gave new criteria for two sequences to have the same excess in the sense of Paley's completeness criterion as in this paper, and new examples and counterexamples pertaining to Riesz bases.
Abstract: This paper is concerned with what might be termed the "fine structure" of the completeness and basis properties of complex exponentials. We give new criteria for two sequences to have the same excess in the sense of Paley and Wiener, a result that illuminates and supplements a well-known completeness criterion of Levinson, and new examples and counterexamples pertaining to Riesz bases.
34 citations
06 Jun 1983
TL;DR: In this article, a formal proof system for dynamic networks of processes is presented, which has been shown to be sound and completeness of the system has been established by the authors.
Abstract: We introduced a formal proof system for dynamic networks of processes, which has been shown to be sound. Future work will consider the completeness of the system.
25 citations
TL;DR: In this article, the authors studied properties of the univariate generalized Waring distribution such as infinite divisibility, discrete self-decomposability, completeness and regression.
Abstract: This paper is concerned with properties of the univariate generalized Waring distribution such as infinite divisibility, discrete self-decomposability, completeness and regression.
23 citations
TL;DR: A model of non-sequential processes and a generalization of Dedekind's definition of the continuity (completeness) of the reals which is applicable to both totally and partially ordered sets as also to both dense and discrete structures is proposed.
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TL;DR: The first-order theory of algebraically closed fields, although not complete, possesses a property closely related to completeness as mentioned in this paper, and Fraisse-Ehrenfeucht games are used to determine whether two structures satisfy the same sentences of a given quantifier rank.
Abstract: Publisher Summary This chapter focuses on rich words. A structure consists of a set, called the universe of the structure, together with some relations, operations, and distinguished elements or constants from that set. The term structure is from model theory. A substructure of a structure A is a structure whose universe is a subset of the universe of A and whose relations, operations, and constants agree with those of A on this subset. A logic is a model of mathematical language. The sentence of each logic is composed of two types of symbols: (1) those that correspond to the various constants, relations, and operations within a class of structures; and (2) those particular to the logic—the logical symbols. Every shift invariant Borel set is meager or comeager. Fraisse–Ehrenfeucht games are used to determine whether two structures satisfy the same sentences of a given quantifier rank. The chapter discusses the monadic second-order theory of rich words. The first-order theory of algebraically closed fields, although not complete, possesses a property closely related to completeness.
IBM1
TL;DR: A (semantically) complete alternative method for verifying a family of properties of programs, called product (and power) properties, for which the verification method of Floyd and Hoare are inconvenient.
Abstract: The paper presents a family of properties of programs, called product (and power) properties, for which the verification method of Floyd and Hoare are inconvenient. A (semantically) complete alternative method is proposed' The paper presents the method in both the endogenous and exogenous versions and applies them to examples. Semantic completeness and soundness are shown. The method is particularly useful for some second-order programs, having procedures as parameters.
01 Jan 1983
TL;DR: In this paper, the authors considered the set of all the subsequences of a linearly independent sequence of a Banach space and described the elementary types of this set, that is some types of subsequences such that all the other subsequences are union of these elementary types.
Abstract: The subject of the Note is the set of all the subsequences of a linearly independent sequence of a Banach space. There are described the elementary types of this set, that is some types of subsequences such that all the other subsequences are union of these elementary types. Moreover there is a research of the most regular element in this set, in particular a research of the most regular element which keeps the completeness.
TL;DR: In this paper, the generalized Kundt solution with λ is shown to be completeness, and the symmetries of the studied metric are presented, as well as the demonstration of completeness.
Abstract: The demonstration of completeness of the generalized Kundt solution with λ is given. The symmetries of the studied metric are presented.
Proceedings Article•
08 Aug 1983TL;DR: A new strategy for semantic paramodulation for Horn sets is presented and it is proved that either both parents be false positive units or one parent and the paramodulant both be false relative to an interpretation.
Abstract: We present a new strategy for semantic paramodulation for Horn sets and prove its completeness The strategy requires for each paramoduiation that either both parents be false positive units or that one parent and the paramodulant both be false relative to an interpretation We also discuss some of the issues involved in choosing an interpretation that has a chance of giving better performance that simple set-of-support paramoduiation.
09 Mar 1983
TL;DR: The aim of this paper is to extend the above results to a language including also Cartesian product and disjoint sum, and a semantic characterization of typed terms is given.
Abstract: An interesting notion of polymorphism is the one introduced in the language ML (/GMW/). Its soundness has been proved in /MIL/ for a subset of ML based on λ-calculus plus constants. A partial completeness result for the same language has been given in /COP/. The aim of this paper is to extend the above results to a language including also Cartesian product and disjoint sum. The extension is not trivial, owing to difficulties introduced mainly by disjoint sum. Moreover a semantic characterization of typed terms is given.
01 May 1983
TL;DR: In this article, the progress towards an effective completeness criterion for uniformly delayed multiple-valued combinatorial circuits is reported, and the work is extended to the case of periodic closed spectra.
Abstract: : The paper reports on the progress towards an effective completeness criterion for uniformly delayed multiple-valued combinatorial circuits In view of previous work by Hikita & Nazaki and Hikita it suffices to study periodic closed spectra
TL;DR: In this article, the convergence properties of the extended block-pulse functions have been studied and it has been shown that the set of extended block pulse functions is complete and complete.
Abstract: In this paper, block-pulse functions have been extended to multidimension. The convergence properties of the extended block-pulse functions have been studied. It has been shown that the set of extended block-pulse functions is complete
TL;DR: In this article, it was shown that the mixture of a strongly complete distribution is complete if and only if the mixing distribution of the distribution is also complete. But this is not the case for all strongly complete distributions.
Abstract: In this article, we first introduce the concept of strong completeness and then show that the mixture of every strongly complete distribution is complete if the mixing distribution is complete. This, in effect, reveals the completeness of several well-known mixtures. For instance, Xekalaki (1983,Ann. Inst. Statist. Math., to appear) showed that the Univariate Generalized Waring Distribution is boundedly complete only relative to one of its three parameters. Now, as a consequence of our result, it follows that this distribution is actually complete relative to any of its parameters.
TL;DR: In this article, an elementary approach to NP-completeness is presented, with a focus on the problem of NP-completeness in the elementary setting. The American Mathematical Monthly: Vol. 90, No. 6, pp. 398-399.
Abstract: (1983). An Elementary Approach to NP-Completeness. The American Mathematical Monthly: Vol. 90, No. 6, pp. 398-399.
06 Jun 1983
TL;DR: A first-order theory is called PC-compact if each asserted program which is true in all models of the theory is also true in a finite subset of a theory as mentioned in this paper.
Abstract: A first order theory is called PC-compact if each asserted program which is true in all models of the theory is true in all models of a finite subset of the theory. If a structure has a complete Hoare's logic then its first order theory must be PC-compact; moreover, its partial correctness theory must be decidable relative to this first order theory.