Related papers: Multiplicative Complexity of Vector Valued Boolean…
The algebraic degree of Boolean functions (or vectorial Boolean functions) is an important cryptographic parameter that should be computed by fast algorithms. They work in two main ways: (1) by computing the algebraic normal form and then…
The vectorial Boolean functions are employed in cryptography to build block coding algorithms. An important criterion on these functions is their resistance to the differential cryptanalysis. Nyberg defined the notion of almost perfect…
Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
We show that any $n$-variate polynomial computable by a syntactically multilinear circuit of size $\operatorname{poly}(n)$ can be computed by a depth-$4$ syntactically multilinear ($\Sigma\Pi\Sigma\Pi$) circuit of size at most…
In order to formally understand the power of neural computing, we first need to crack the frontier of threshold circuits with two and three layers, a regime that has been surprisingly intractable to analyze. We prove the first super-linear…
Circuit lower bounds are important since it is believed that a super-polynomial circuit lower bound for a problem in NP implies that P!=NP. Razborov has proved superpolynomial lower bounds for monotone circuits by using method of…
A monotone Boolean (OR,AND) circuit computing a monotone Boolean function f is a read-k circuit if the polynomial produced (purely syntactically) by the arithmetic (+,x) version of the circuit has the property that for every prime implicant…
Recent improvements in adder optimization could be achieved by optimizing the AND-trees occurring within the constructed circuits. The overlap of such trees and its potential for pure size optimization has not been taken into account…
Boolean circuits of McCulloch-Pitts threshold gates are a classic model of neural computation studied heavily in the late 20th century as a model of general computation. Recent advances in large-scale neural computing hardware has made…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
For a Boolean function $\Phi\colon\{0,1\}^d\to\{0,1\}$ and an assignment to its variables $\mathbf{x}=(x_1, x_2, \dots, x_d)$ we consider the problem of finding the subsets of the variables that are sufficient to determine the function…
We consider the problem of computing the second elementary symmetric polynomial S^2_n(X) using depth-three arithmetic circuits of the form "sum of products of linear forms". We consider this problem over several fields and determine EXACTLY…
We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions…
The problem of finding a minimal circuit to implement a given function is one of the oldest in electronics. It is known to be NP-hard. Still, many tools exist to find sub-optimal circuits to implement a function. In electronics, such tools…
Reversible computation is gaining increasing relevance in the context of several post-CMOS technologies, the most prominent of those being Quantum computing. One of the key theoretical problem pertaining to reversible logic synthesis is the…
We show that sharp thresholds for Boolean functions directly imply average-case circuit lower bounds. More formally we show that any Boolean function exhibiting a sharp enough threshold at \emph{arbitrary} critical density cannot be…
We consider probabilistic circuits working over the real numbers, and using arbitrary semialgebraic functions of bounded description complexity as gates. In particular, such circuits can use all arithmetic operations +, -, x, /,…
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…
We provide accurate upper bounds on the Boolean circuit complexity of the standard and the Karatsuba methods of integer multiplication