Showing papers on "Equivalence (measure theory) published in 1971"
Proceedings Article•
01 Sep 1971TL;DR: A technique is given and illustrated for proving simulation and equivalence of programs; there is an analogy with Floyd''s technique for proving correctness of programs.
Abstract: A simulation relation between programs is defined which is quasi-ordering. Mutual simulation is then an equivalence relation, and by dividing out by it we abstract from a program such details as how the sequencing is controlled and how data is represented. The equivalence classes are approxiamtions to the algorithms which are realized, or expressed, by their member programs. A technique is given and illustrated for proving simulation and equivalence of programs; there is an analogy with Floyd''s technique for proving correctness of programs. Finally, necessary and sufficient conditions for simulation are given.
616 citations
TL;DR: The conditions whereby two different faults can produce the same alteration in the circuit behavior are investigated and this relationship between two faults is shown to be an equivalence relation, and three different types of equivalence relations are specified.
Abstract: This paper is a study of the effects of faults on the logical operation of combinational (acyclic) logic circuits. In particular, the conditions whereby two different faults can produce the same alteration in the circuit behavior are investigated. This relationship between two faults is shown to be an equivalence relation, and three different types of equivalence relations are specified. Necessary and sufficient conditions for the existence of these equivalence relations are proved. An algorithm for determining the equivalence classes for one of the types of equivalence is presented. Other types of algebraic properties of faults are discussed.
172 citations
01 Dec 1971
TL;DR: An algorithm is given for determining if two finite automata with start states are equivalent and the asymptotic running time of the algorithm is bounded by a constant times the product of the number of states of the larger automation with the size of the input alphabet.
Abstract: : An algorithm is given for determining if two finite automata with start states are equivalent. The asymptotic running time of the algorithm is bounded by a constant times the product of the number of states of the larger automation with the size of the input alphabet. (Author)
109 citations
66 citations
TL;DR: In this article, a simple and direct derivation for a multidimensional utility function whose lexicographically-ordered expected utility vectors preserve an individual's preference order on a set of probability measures is given.
Abstract: A relation
56 citations
01 Jun 1971
48 citations
TL;DR: In this paper, the connections between the regular differentials defined on a manifold and its zero-dimensional cycles equivalent under several relations of equivalence directly generalizing rational equivalence were investigated.
Abstract: In the paper we investigate the connections between the regular differentials defined on a manifold and its zero-dimensional cycles equivalent under several relations of equivalence directly generalizing rational equivalence. Bibliography: 3 items.
39 citations
32 citations
TL;DR: The developmental priority of identity conservation as contrasted with equivalence conservation theorized by Elkind (1967) was investigated using quantity and number conservation tasks using 60 four-, five-, and six-year-old children of middle socioeconomic class background.
31 citations
TL;DR: A theory of equivalent integer programs was developed in this article, where it was shown that every all-integer integer programming problem is equivalent to infinitely many other integer programming problems, such that the solution to any one problem in the equivalence class determines the solution of every other problem.
Abstract: A theory of equivalent integer programs is developed that shows that every all-integer integer programming problem is equivalent to infinitely many other integer programming problems The equivalence is such that the solution to any one problem in the equivalence class determines the solution to every other problem in the class Procedures to construct certain canonical problems in each equivalence class are described The relationship of this theory to computational algorithms is discussed
30 citations
TL;DR: Stability type results concerning continuous solutions of perturbed systems of Volterra equations as well as theorems concerning the asymptotic equivalence of such perturbed and unperturbed systems are established in this article.
Abstract: Stability type results concerning continuous solutions of perturbed systems of Volterra equations as well as theorems concerning the asymptotic equivalence of such perturbed and unperturbed systems are established.
TL;DR: An equivalence theorem is presented that provides a simple method of equivalent transformation of parabolic media that leads to flexibility in the design of distributed optical structures, such as gas lenses and inhomogeneous optical fibers.
Abstract: Equivalence properties of lenslike media with parabolic index profiles are analyzed on the basis of geometrical optics. By equivalent media we mean here those with the same ray-transfer matrix representation. An equivalence theorem is presented that provides a simple method of equivalent transformation of parabolic media. The practical importance of the equivalent transformation is that it leads to flexibility in the design of distributed optical structures, such as gas lenses and inhomogeneous optical fibers.
01 Jun 1971
TL;DR: In this article, the relation between dominance and equivalence is considered and some properties are pointed out, such as equivalence and dominance relations, for the same class of faults, for which it is shown that there exist machines for which this property of being strongly connected is destroyed by every possible single fault.
Abstract: : The paper is concerned with the relationships among faults as they affect sequential machine behavior. Of particular interest are equivalence and dominance relations. It is shown that for output faults (i.e., faults that do not affect state behavior), fault equivalence is related to the existence of an automorphism of the state table. For the same class of faults, the relation between dominance and equivalence is considered and some properties are pointed out. Another class of possible faults is also considered, namely, memory faults (i.e., faults in the logic feedback lines). These clearly affect the state behavior of the machine, and their influence on machine properties, such as being strongly connected, is discussed. It is proven that there exist classes of machines for which this property of being strongly connected is destroyed by every possible single fault. Further results on both memory and output faults are also presented. (Author)
TL;DR: A drug has a chemical name and generic name of the active therapeutic ingredient, and one or more dosage forms containing it, may be official in the National Formulary or United States Pharmacopeia.
Abstract: drugs. First, there are the chemical name and generic name of the active therapeutic ingredient. Secondly, the active therapeutic ingredient, and one or more dosage forms containing it, may be official in the National Formulary or United States Pharmacopeia. Third, there may be one or more trademarks or brand names of products made by one or more manufacturers. Much confusion has existed in the past, and still exists today, because many scientists and laymen unintentionally or intentionally use one name where another name should have been used.
TL;DR: A generalization of the coherent potential approximation that is exactly equivalent to self-consistent diagrammatic summation techniques is discussed in this paper, where explicit expressions for the pair case are given.
TL;DR: The equivalence theorem for S-matrix elements was proved in this article, where the dynamical and kinematical aspects of the equivalence result were distinguished, and the latter condition was shown to violate the free field condition.
Abstract: The authors attempt to prove the equivalence theorem for S-matrix elements. The dynamical aspect-which ensures that the dynamics is coordinate independent, and requires care in preservation of the order of non-commuting operators-and the kinematical aspect, which ensures that asymptotic fields are unchanged are distinguished. It is the latter condition which causes difficulty; whilst trivial for the free field the authors give non-trivial examples which violate it.
TL;DR: In this paper, the number and cardinality of the corresponding equivalence classes of Green's equivalence relations are determined, and the number of idempotent and generalized ǫ elements in ℱn is also determined.
Abstract: Letℱn be the set of all partial functions on ann-element setXn, i.e., the set of all functions whose domain and range are subsets ofXn. Green's equivalence relationsℛ, ℒ, ℋ andℋ are considered, and the number and cardinality of the corresponding equivalence classes are determined. The number of idempotent and generalized idempotent elements inℱn is also determined.