We show a connection between the deMorgan formula size of a Boolean function and the noise stability of the function. Using this connection, we show that the Fourier spectrum of any balanced Boolean function computed by a deMorgan formula of size s is concentrated on coefficients of degree up to O( √ s). These results have several applications that apply to any function f that can be computed b...

This paper proposes to use two information retrieval system models (Boolean information retrieval model and extended Boolean (fuzzy) information retrieval model). These models differ by using Boolean queries or fuzzy weighted queries. It also proposes a way for optimizing user query for the two models by using genetic programming and fuzzy logic. And proposes to use more number of Boolean opera...

Two boolean functions f, g : {0, 1} → {0, 1} are isomorphic if they are identical up to relabeling of the input variables. We consider the problem of testing whether two functions are isomorphic or far from being isomorphic with as few queries as possible. In the setting where one of the functions is known in advance, we show that the non-adaptive query complexity of the isomorphism testing pro...

This paper deals with a power-conscious ANDEXOR-Inverter type logic implementation for a complex class of Boolean functions, namely Achilles’ heel functions. Different variants of the above function class have been considered viz. positive, negative and pure horn for analysis and simulation purposes. The proposed realization is compared with the decomposed implementation corresponding to an exi...

Searching for relevant documents is a laborious task involved in preparing systematic reviews of biomedical literature. Currently, complex Boolean queries are iteratively developed, and then each document of the final query result is assessed for relevance. However, the result set sizes of these queries are hard to control, and in practice it is difficult to balance the competing desires to kee...

Combinatorial properties of zeons have been applied to graph enumeration problems, colorings, routing problems in communication networks, partition-dependent stochastic integrals, and Boolean satisfiability. Power series elementary zeon functions are naturally reduced finite sums by virtue the nilpotent zeons. Further, extension any analytic complex function has polynomial representations on as...

In this paper, we consider further applications of (n,m)-functions for the construction 2-designs. For instance, provide a new application extended Assmus-Mattson theorem, by showing that linear codes certain APN functions with classical Walsh spectrum support With result, give several sufficient conditions an function to be CCZ-inequivalent quadratic one. On other hand, use and combinatorial d...