Decomposability Property Research Articles

ABSTRACT RELATIONS BETWEEN RESTRICTED TERMINATION AND CONFLUENCE PROPERTIES OF REWRITE SYSTEMS

We investigate restricted termination and confluence properties of term rewriting systems, in particular weak termination, weak innermost termination, (strong) innermost termination, (strong) termination, and their interrelations. New criteria are provided which are sufficient for the equivalence of these properties. These criteria provide interesting possibilities to infer completeness, i.e. termination plus confluence, from restricted termination and confluence properties. Our main result states that any (strongly) innermost terminating, locally confluent overlay system is terminating, and hence confluent and complete. Using these basic results we are also able to prove some new results about modular termination of rewriting. In particular, we show that termination is modular for some classes of innermost terminating and locally confluent term rewriting systems, namely for non-overlapping and even for overlay systems. As an easy consequence this latter result also entails a simplified proof of the fact that completeness is a decomposable property of constructor systems. Similarly, a combined overlay system with shared constructors is complete if and only if its component sytems are complete overlay systems. Interestingly, these modularity results are obtained by means of a proof technique which itself constitutes a modular approach.

Suboptimum decoding of decomposable block codes

To decode a long block code with a large minimum distance by maximum likelihood decoding is practically impossible because the decoding complexity is simply enormous. However, if a code can be decomposed into constituent codes with smaller dimensions and simpler structure, it is possible to devise a practical and yet efficient scheme to decode the code. This paper investigates a class of decomposable codes, their distance and structural properties. It is shown that this class includes several classes of well-known and efficient codes as subclasses. Several methods for constructing decomposable codes or decomposing codes are presented. A two-stage (soft-decision or hard-decision) decoding scheme for decomposable codes, their translates or unions of translates is devised, and its error performance is analyzed for an AWGN channel. The two-stage soft-decision decoding is suboptimum. Error performances of some specific decomposable codes based on the proposed two-stage soft-decision decoding are evaluated. It is shown that the proposed two-stage suboptimum decoding scheme provides an excellent trade-off between the error performance and decoding complexity for codes of moderate and long block length. >

Completeness of Combinations of Conditional Constructor Systems

In this paper we extend the divide and conquer technique of Middeldorp and Toyama for establishing (semi-)completeness of constructor systems to conditional constructor systems. We show that both completeness (i.e. the combination of confluence and strong normalisation) and semi-completeness (confluence plus weak normalisation) are decomposable properties of conditional constructor systems without extra variables in the conditions of the rewrite rules.

Decomposable three-way layouts

In this paper we introduce an apparently new, and we believe important, subclass of three-way layouts or two-way elimination of heterogeneity designs specified by the full information matrix S 3.12 being decomposable in the following way, S 3.12=ξ 1 S 3.2+ξ 2 S 3.2−ξ 0 S 3.0 , ξ 1, ξ 2 and ξ 0 〉0; the information matrices S 3.1, S 3.2 and S 3.0 correspond, respectively, to the treatment-row subdesign, the treatment-column subdesign, and the model in which both rows and columns are ignored. The special case whenξ 1=ξ 2=ξ 0=1 was introduced in Baksalary and Shah (1990). Our subclass comprises designs for which the study of relationships between properties of the three-way design itself, and corresponding properties of its treatment-row and treatment-column subdesigns, is simplified. As the study of block designs is more straightforward than that of three-way designs, we see that the level of difficulty is here reduced from one three-way level to two-way level designs. We believe that our decomposability property identifies the most general subclass of three-way layouts or two-way elimination of heterogeneity designs for which certain results on connectedness, orthogonality and balance hold.

Operator-semistable operator Lévy's measures on finite dimensional vector spaces

In the paper various characterizations of full operator-semistable operator Levy's measures on finite dimensional vector spaces are presented. They are given in terms of: 1. some decomposability properties; 2. the characteristic functions; 3. stochastic integrals. Also a number of decomposability properities, especially for a full operator Levy's measure, are obtained.

Subgroup Consistent Poverty Indices

It seems desirable that the overall level of poverty should fall whenever poverty decreases within some of the population and is unchanged outside that group. Yet this simple and attractive property, which we call subgroup consistency, is violated by many of the poverty indices suggested in recent years. This paper characterizes the class of consistent poverty iindices, and identifies the special features associated with this property. ONE OF THE MOST APPEALING PROPERTIES of poverty indices suggested in recent years is a simple consistency axiom which requires the overall level of poverty to fall if a of the population experiences a reduction in poverty, while poverty in the rest of the population remains unchanged.2 This property-which we term subgroup consistency-is desirable for a number of reasons. From a practical point of view, it is needed- to coordinate the effects of a decentralized strategy towards poverty alleviation. For a decentralized strategy typically in- volves a collection of activities targeted at specific subgroups or regions of the country. If the poverty indicator is not consistent, we may be faced with a situation in which each local effort achieves its objective of reducing poverty within its targeted group, and yet the level of poverty in the population as a whole increases. Subgroup consistency may therefore be viewed as an essential counterpart to a coherent poverty program. Subgroup consistency may also be regarded as a natural analogue of the monotonicity condition of Sen (1976), since monotonicity requires that aggre- gate poverty fall (or, at least, does not increase) if one person's poverty is reduced, ceteris paribus, while consistency demands that aggregate poverty fall if one subgroup's poverty is reduced, ceteris paribus. Furthermore, consistency is closely related to the property of decomposability, which allows aggregate poverty to be expressed as a population-share weighted average of poverty levels, and hence facilitates the disaggregated- analysis of poverty by region or ethnic group of the type undertaken by Anand (1983). As it happens, the traditional poverty indices used by Anand and others -the headcount ratio (the fraction of the population that is poor) and the 1 Earlier versions of this paper were presented at a conference on Measurement and Modelling

Decomposition of properties and definition of fuzzy set

A mathematical model of fuzzy set is suggested in this paper. It is based on the understanding of a fuzzy set as a collection of objects showing some common property. This property itself is defined as decomposable into elementary properties. The degree to which an object shows a decomposable property, depends on the size, or more generally, importance of the collection of its elementary properties, that is evaluated by means of a set function that we refer to as pseudomeasure. With each pseudomeasure on a class of collections of elementary properties we associate a pseudomeasure that is complementary to it, and with each decomposable property, a complementary decomposable property interpreted as not showing the original property. We consider products of decomposable properties corresponding to the traditional operations of intersection and union of fuzzy sets. The model of a fuzzy set introduced leads to formulating compositions of decomposable properties (and associated fuzzy sets) that are not confined only to those based on operations of intersection and union, although they include them.

On the extension of classical propositional logic by means of a triangular norm

In this article, we introduce a generalized extension principle by substituting a more general triangular norm T for the min intersection operator in Zadeh's extension principle. We also introduce a family of propositional logics, sup- T extension logics, obtained by the extension of classical-logical functions. A few general properties of these sup-T extension logics are derived. It is also shown that classical binary logic and the Kleene ternary logic are special cases of these logics for any choice of T, obtained by a convenient restriction of the truth domain. the very practical decomposability property of classical logic is furthermore shown to hold for the sup-min extension logic, albeit in a somewhat more limited form.

Decomposable solutions for N — person bargaining games

Two solutions for n-person bargaining games are defined and axiomatized, which exhibit the so called “decomposability property”. One of the solutions extends the two-person Kalai-Smorodinsky solution to n-person games. The other is the Raiffa solution.

Supplements to operator-stable and operator-semistable laws on Euclidean spaces

Operator-stable laws and operator-semistable laws (introduced as limit distributions by M. Sharpe and R. Jajte, respectively) are characterized by decomposability properties. Disintegration of their corresponding Lévy measures requires appropriate cross sections. Furthermore in both situations the Lévy measures constitute a Bauer simplex whose extreme boundary can be explicitly given. Finally the infinitely differentiable Lebesgue density of an operator-semistable law is shown to be even analytic in some cases.

Photosensitive amorphous silicon films deposited from hexafluorodisilane

Hexafluorodisilane has an electronic state which suggests its more easily decomposable property than not only SiF 4 but also Si 2H 6. The structure analysis by IR and ESCA revealed that photosensitive wide gap films can be obtained by low power plasma CVD of Si 2F 6 under the conditions of paying sufficient care to avoid oxygen contamination and/or of mixing Si 2Fe 6 with hydrogen. Some fundamental properties of the films were elucidated.

Optimum inventory policies with discrete time proportional demand, discrete replenishment opportunities and different optimizing criteria

This paper extends the deterministic, single product, dynamic E0Q model to the case where demand increases linearly with time but at discrete time points and where the number of replenishments is also discrete. The problem is to find the number of orders and the replenishment schedule that will either maximize the return on the investment on inventory or minimize inventory costs. The proposed solution to either problem requires to first find the replenishment schedule that will minimize the total inventory throughout the planning horizon, for a given number of orders and then find the optimal number of replenishment points. The solution algorithms exploit the discrete nature of the demand and do not require the decomposability property of dynamic programming. This is particularly important in the return on investment case, where decomposability cannot be achieved.

An axiomatic characterization of the Theil measure of income inequality

This paper provides a characterization of a frequently used measure of income inequality. It has been known for some time that the Theil measure of income inequality (1) is consistent with the Lorenz criterion, when it applies, and (2) exhibits a simple and empricically useful decomposition by population subgroup into within-group and between-group terms. The major theorem establishes the converse: the decomposability property defines the Theil measure uniquely (up to a positive multiple) among all Lorenz-consistent measures.

Geometric decomposability properties of probability measures

Geometric decomposability properties of probability measures

General theorems on rates of convergence in distribution of random variables I. General limit theorems

Let (X n) nϵ N be a sequence of real, independent, not necessarily identically distributed random variables (r.v.) with distribution functions F X n , and S n = Σ i=1 n X i . The authors present limit theorems together with convergence rates for the normalized sums ϕ( n) S n , where ϕ: N → R +, ϕ( n) → 0, n → ∞, towards appropriate limiting r.v. X, the convergence being taken in the weak (star) sense. Thus higher order estimates are given for the expression ∝ R f(x) d[F ϕ(n)S n (x) − F X(x)] which depend upon the normalizing function ϕ, decomposability properties of X and smoothness properties of the function f under consideration. The general theorems of this unified approach subsume O- and o-higher order error estimates based upon assumptions on associated moments. These results are also extended to multi-dimensional random vectors.

Geometric decomposability properties of probability measures

Geometric decomposability properties of probability measures

Geometric decomposability properties of probability measures

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Analytic Completion and Decomposability Properties In Tubold Domains

Analytic Completion and Decomposability Properties In Tubold Domains

The algebra generated by physical filters

This paper investigates mathematical properties of a finite-dimensional real algebra of linear operators which are generated by an orthomodular lattice of filters in the sense of Mielnik [4]. Properties of filter decomposability and a representation theorem for the vector space underlying the algebra mentioned are derived.

The Factorisation of the rectangular distribution

Questions of the decomposability of distribution functions into real-valued components of bounded variation were discussed by P. Lévy (1964) in relation to the nature of the components, whether non-decreasing (distribution functions in particular) or absolutely continuous (a.c.) or both. Hanson (1965), in a review of Lévy's paper, raised the question of whether or not a rectangular distribution could be decomposed into two a.c. distributions. In fact, D. G. Kendall had conjectured earlier (Kendall (1960)) that no such decomposition is possible. The object of this paper is to state and prove the truth of Kendall's conjecture. “Decomposition” or “factorisation” will be understood throughout the paper to mean decomposition into distributions. Decompositions of the rectangular distribution into one a.c. and one discrete factor are well known (see, e.g., Lukacs (1960) pp. 128–9), and decompositions in which both factors are singular continuous (s.c.) have been discovered by Kendall and by P. M. Lee; it is shown here that no other combinations of factor-type can exist. References to other work on related decomposability properties are given in the papers by Lévy and Kendall cited above.