We present a formulae-as-types interpretation of Subtractive Logic (i.e. bi-intuitionistic logic). This presentation is two-fold: we first define a very natural restriction of the λμ-calculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a comp...

A simple method for maintaining balance in ternary search tries is presented. The new kind of self-balancing ternary search trie, called an r-trie, generalizes the balancing strategy of Aragon and Seidel’s randomized binary search trees (treaps). This means that an r-trie is shaped like a ternary search trie built by inserting the strings in random order. As a result, the time cost of searching...

In the year 1971, W. G. Lister [14] introduced the notion of ternary ring. Later in the year 2014, J. R. Castillo and Jocelyn S. ParaderoVilela [2] introduced the notion of krasner ternary hyperring. In [6] we introduce the notion of multiplicative ternary hyperring. In this paper we study prime hyperideals in a multiplicative ternary hyperring. We obtain some Characterizations of prime hyperid...

density, viscosity and refractive index of pure, binary and ternary mixtures of diethanolamine (dea) and methyl diethanolamine (mdea) with water have been measured at different temperatures from 288.15 k to 323.15 k at atmospheric pressure. also, this study presents the effects of mixture composition and temperature upon these thermo- physical properties. to measure the density and refractive i...

the effect of magnetic field on the liquid-liquid equilibrium of two ternary systems (water + acetic acid + butyl acetate and water + acetic acid + dimethyl succinate) at 298.15 k under atmospheric pressure was investigated. the results obtained show that the strength of the magnetic field (0.02 t) affects the solubility of acetic acid in the used organic solvents. distribution coefficients and...

Balanced ternary number representation and arithmetic, based on the symmetric radix-3 digit set {−1, 0, +1}, has been studied at various times in the history of computing. Among established advantages of balanced ternary arithmetic are representational symmetry, favourable error characteristics and rounding by truncation. In this study, we show an additional advantage: that of lower-error trunc...

Alteration in gene transcripts is related to a wide spectrum of physiological and pathological changes in cells. Therefore, the identification of differential gene expression can be used to understand biological processes at a molecular level [1-4]. Various techniques such as Expressed Sequence Tags (EST), differential display, Serial Analysis of Gene Expression (SAGE), cDNA microarray, and sub...

We introduce and investigate a new type of reductions between counting problems, which we call subtractive reductions. We show that the main counting complexity classes #P, #NP, as well as all higher counting complexity classes # · kP, k 2, are closed under subtractive reductions. We then pursue problems that are complete for these classes via subtractive reductions. We focus on the class #NP (...

and prove that the study of such structures is equivalent to the study of generalized Boolean algebras. We call such structures Boolean subtractive algebras since they are subtractive algebras in the sense of Crapo and Rota ([1], 3.7). Alternatively, such structures might be called generalized colonies since, as we later prove, every colony is a Boolean subtractive algebra. As an example of a B...