We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of stable set polytope. We apply it to majority functions and prove their formula size lower bounds improved from the classical result of Khrapchenko [13]. Moreover, we introduce a notion of unbalanced recursive ternary...

in [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.also, we exhibited the topic of limit summability of real functions in [2,3]. inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. finally, we pose an unsolved problem aboutthem.

Quantum-Dot Cellular Automata (QCAs) are becoming more and more one of the most promising candidates for the alternative processing platform of the future. Since their advent in the early 1990s the required technological processes, as well as the QCA structures that implement the basic and functionally complete set of binary logic functions, have been developed. This article, however, presents ...

A non-linear transform, called ‘‘sign Haar transform’’ has recently been introduced. The transform is unique and converts binary/ternary vectors into ternary spectral domain. Recursive definitions for the calculation of sign Haar transform are developed. Essential properties of logic functions and variables in the spectral domain of a quantized transform based on Haar functions are presented. S...

We enumerate all ternary length-` square-free words, which are words avoiding squares of words up to length `, for ` ≤ 24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary square-free words. We then consider ternary square-free words with fixed letter densities, thereby proving exponential growth for certain ensemble...

In this paper we analyze ternary bicooperative games, which are a refinement of the concept of a ternary voting game introduced by Felsenthal and Machover. Furthermore, majority voting rules based on the difference of votes are simple bicooperative games. First, we define the concepts of the defender and detractor swings for a player. Next, we introduce the Banzhaf power index and the normalize...

We describe a method for generating logic simulation code which correctly responds to any number of unde ned logic values at the code inputs. The method is based on our development of the Ordered Ternary Decision Diagram, itself based on Kleenean ternary logic, which explicitly and correctly manages the unknown logic value `U' in addition to the `1' and `0' of conventional OBDDs. We describe th...

A non-linear transform, called ‘Sign Hadamard-Haar transform’ is introduced. The transform is unique and converts ternary vectors into ternary spectral domain. Recursive definition and fast transform have been developed. Formulae to represent Sign Hadamard-Haar spectra for basic logic functions and their variables for two different codings are shown. New transform is extremely effective in term...

I characterize a finite additive utility representation for preferences over menus. The numbers of both positive and negative components in this representation are expressed explicitly in terms of preference. These expressions can be used to characterize models of temptation, perfectionism, context effects, and other phenomena. © 2008 Elsevier Inc. All rights reserved. JEL classification: D81

The paper suggests architecture of a reconfigurable processor, which can be customized for implementing different search algorithms over discrete matrices. Such algorithms might be used for solving various problems of combinatorial optimization, such as covering, Boolean satisfiability, etc. The proposed architecture contains memory blocks for binary or ternary matrix, general-purpose registers...