We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

This paper presents a new approach to an on-chip asynchronous transmission system suitable for next generation asynchronous on-chip networks. It implements multivalued logic to reduce the number of wires and a low-voltage swing for lower dynamic power dissipation. Furthermore, the transmission system described here enjoys fully static design and has zero static power consumption. Two versions o...

In this paper we discuss Gabbay’s idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner’s suggestion of replacing the intuitionistic base system by Kleene’s three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson’s constructive logic N instead of intui...

The advantages and disadvantages of using multiple-valued logic in integrated circuits are discussed. The benefits of applying CCD's in the implementation of multiple-valued circuits are explained. The combination of a few basic multiple-valued logic (MVL) functions makes it possible to implement any MVL function. Three basic functions in four-valued, logic ho.ve been designed^ fabricated and t...

This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. This paper is devoted to co...

Let p be a prime, and let f(x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum ∑ k≡r (mod pβ) (n k ) (−1)f (⌊ k − r pα ⌋) , where α > β > 0, n > pα−1 and r ∈ Z. This polynomial extension of Fleck’s congruence has various backgrounds and several consequences such as ∑ k≡r (mod pα) (n k ) a ≡ 0 ( mod p ⌊ n−pα−1 φ(pα) ...

Let p be a prime, and let f (x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum k≡r (mod p β) n k (−1) k f k − r p α , where α β 0, n p α−1 and r ∈ Z. This polynomial extension of Fleck's congruence has various backgrounds and several consequences such as k≡r (mod p α) n k a k ≡ 0 mod p n−p α−1 ϕ(p α) provided that ...

We give a classification of dual functions, they are m -al functions. We call a function m-al with respect to an operator if the operator lives any function unchanged after m times of using the operator. And 2 ≤ m ≤ k. Functions with different m have very different properties. We give theoretical results for clones of self-dual (m = 2) and selfk -al (m = k) functions in k -valued logic at k ≤ 3...

Computing certain answers is the preferred way of answering queries in scenarios involving incomplete data. This, however, is computationally expensive, so practical systems use efficient techniques based on a particular three-valued logic, although this often leads to

A new optical computing experimental system is presented. Designed based on tri-valued logic, the system is built as a photoelectric hybrid computer system which is much advantageous over its electronic counterparts. Say, the tri-valued logic of the system guarantees that it is more powerful in information processing than that of systems with binary logic. And the optical characteristic of the ...