Boolean function

This paper describes a mathematical model for all path length parameters (APL: Average Path Length, LPL: Longest Path Length, and SPL: Shortest Path Length) of Binary Decision Diagrams (BDDs). The proposed model is based on an empirical analysis of randomly generated Boolean functions. The formal core of the developed model is a unique equation for the path-related objective functions over

Data structures for Boolean functions build an essential component of design automation tools, especially in the area of logic synthesis. The state of the art data structure is the ordered binary decision diagram (OBDD), which results from general binary decision diagrams (BDDs), also called branching programs, by ordering restrictions. In the context of EXOR-based logic synthesis another type of decision diagram (DD), called (ordered) functional decision diagram ((O)FDD) becomes increasingly important. We study the relation between (ordered, free) BDDs and FDDs. Both, BDDs and FDDs, result from DDs by defining the represented function in different ways. If the underlying DD is complete, the relation between both types of interpretation can be described by a Boolean transformation τ. This allows us to relate the FDD-size of f and the BDD-size of τ(f) also in the case that the corresponding DDs are free or ordered, but not (necessarily) complete. We use this property to derive several results on the computational power of OFDDs and OBDDs. Symmetric functions are shown to have efficient representations as OBDDs and OFDDs as well. Classes of functions are given that have exponentially more concise OFDDs than OBDDs, and vice versa. Finally, we determine the complexity of some standard operations if OFDDs are used for the representation of Boolean functions.

In this paper we will explain the meaning of non-linearity in boolean functions, and how to calculate it using Walsh Transform. We will start by providing a brief background on Boolean Functions. We will explain the process by which we calculate nonlinearity and also provide an explanation of the Fast Walsh-Hadamard Transform, which will allow for quicker implentation of this calculation. To conclude, we will provide some motivation behind the importance of nonlinear-ity and give an overview of Bent Functions.

Fruit peel coloring is one of the most important measures of commercial values in various citrus fruits. It is well documented that a gaseous plant hormone, ethylene, regulates the peel color changes associated with fruit ripening. To handle the peel color quality, it is necessary to develop a universal measure of ethylene-directed color changes. Here, we proposed a novel colorimetric formula: y* = [ (L* n • max-L* t) 2 + (a* n • max-a* t) 2 + (b* n • max-b* t) 2 ] 1/2 (y* > 0), based the CIE 1976 L*a*b* colour space units, which reflect the wholistic changes in fruit color. Since all known colorimetric values are specialized for estimation of the changes in certain single pigment, our formula may be useful for assessing the total fruit color development in a controlled atmosphere.

We consider the thesis that an arithmetical relation, which holds for any, given, assignment of natural numbers to its free variables, is Turing-decidable if, and only if, it is the standard representation of a PA-provable formula. We show that, classically, such a thesis is, both, unverifiable and irrefutable, and, that it implies the Turing Thesis is false; that Goedel's arithmetical predicate R(x), treated as a Boolean function, is in the complexity class NP, but not in P; and that the Halting problem is effectively solvable, albeit not algorithmically.

In this paper, a C++ class for analising Vector Boolean Functions from a cryptographic perspective is presented. This implementation uses the NTL library from Victor Shoup, replacing some of the general purpose modules of this library by some more specialized and better suited to cryptography, and adding new modules that complement the existing ones. With this class, we can obtain

We are proposing a cost-efficient realization scheme for completely-specified logic functions characterized by a huge disproportion. The functions described contain millions of input words but only few of them can give us information. An appropriate method of logic synthesis for identifying mentioned vectors (registered vectors) has been developed. In this method logic functions are implemented using both embedded memory blocks

Studies handling the lights and the colors as key components of computation attracted the scientists and engineers since these studies are potentially applicable to the signal processing through optical interconnections between electronic devices. Here, a novel optical computing model is proposed by modifying the known optical parallel logic gates, after employing the printed colors as the input/output data, instead of shadowgram images projected on a screen. The proposed approach allows spontaneous and parallel Boolean operations by simply overlaying the colors printed on films or duplicating the prints on papers. By setting a limited number of color prototypes with known CIELAB color coordinates, prediction of color changes due to duplicated color printing and/or film-on-paper overlaying of the printed colors was performed through Boolean “AND” operation and their experimental confirmation after actual color reading was also performed. Furthermore, possible applications of this CIELAB-coded printable logic gate system in natural computing and development of novel color barcodes were discussed.

In this paper, a C++ class for analising Vector Boolean Functions from a cryptographic perspective is presented. This implementation uses the NTL library from Victor Shoup, replacing some of the general purpose modules of this library by some more specialized and better suited to cryptography, and adding new modules that complement the existing ones. With this class, we can obtain the classical representation of Vector Boolean Function such as its Truth Table and Algebraic Normal Form (ANF). It is possible to calculate mathematical structures such as the Walsh Spectrum, Linear Profile, Differential Profile and Autocorrelation Spectrum. Cryptographic criteria such as nonlinearity, linearity distance, order of correlation immunity, bal-ancedness, algebraic degree and propagation criterion can be obtained with this class. It permits to find out some interesting cryptologic parameters such as linear structures, linear potential, differential potential and the maximum possible nonlineari...

In recent years, reversible logic has emerged as a promising computing paradigm having application in low-power CMOS, quantum computing, nanotechnology and optical computing. Optical logic gates have the potential to work at macroscopic (light pulses carry information), or quantum (single photons carry information) levels with great efficiency. However, relatively little has been published on designing reversible logic circuits in all-optical domain. In this paper, we propose and design a novel scheme of Toffoli and Feynman gates in all-optical domain. We have described their principle of operations and used a theoretical model to assist this task, finally confirming through numerical simulations. Semiconductor optical amplifier (SOA)-based Mach–Zehnder interferometer (MZI) can play a significant role in this field of ultra-fast all-optical signal processing. The all-optical reversible circuits presented in this paper will be useful to perform different arithmetic (full adder, BCD adder) and logical (realization of Boolean function) operations in the domain of reversible logic-based information processing.

We show that Gödel has defined an arithmetical relation R(n) which— when treated as a Boolean function—is constructively computable as true for any given natural number n, but which is not Turing-computable as true for any given natural number n. This implies ...