Related papers: A Lower Bound of $2^n$ Conditional Branches for Bo…
Circuit polynomials are polynomials satisfying a number of conditions that make it easy to compute sharp and certifiable global lower bounds for them. Consequently, one may use them to find certifiable lower bounds for any polynomial by…
One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them…
We investigate explainability via short Boolean formulas in the data model based on unary relations. As an explanation of length k, we take a Boolean formula of length k that minimizes the error with respect to the target attribute to be…
Thread pooling is a common programming idiom in which a fixed set of worker threads are maintained to execute tasks concurrently. The workers repeatedly pick tasks and execute them to completion. Each task is sequential, with possibly…
We study the satisfiability of string constraints where context-free membership constraints may be imposed on variables. Additionally a variable may be constrained to be a subword of a word obtained by shuffling variables and their…
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
It is known that correlation-immune (CI) Boolean functions used in the framework of side-channel attacks need to have low Hamming weights. The supports of CI functions are (equivalently) simple orthogonal arrays when their elements are…
We prove a lower bound of $\tilde{\Omega}(n^{1/3})$ for the query complexity of any two-sided and adaptive algorithm that tests whether an unknown Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is monotone or far from monotone. This…
A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on…
The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…
We reduce the problem of proving deterministic and nondeterministic Boolean circuit size lower bounds to the analysis of certain two-dimensional combinatorial cover problems. This is obtained by combining results of Razborov (1989),…
Let $P$ be a partially ordered set. If the Boolean lattice $(2^{[n]},\subset)$ can be partitioned into copies of $P$ for some positive integer $n$, then $P$ must satisfy the following two trivial conditions: (1) the size of $P$ is a power…
Recently, several mathematicians have investigated various partition functions with the goal of discovering Ramanujan-type congruences. One such function is $\overline{B}_{2^\alpha}(n)$, which represents the number of $2^\alpha-$regular…
In this paper, we investigate an approach to circuit lower bounds via bounded width circuits. The approach consists of two steps: (i) We convert circuits to (deterministic or nondeterministic) bounded width circuits. (ii) We prove lower…
Arithmetic complexity is considered simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic…
A formulation of "Ne\v{c}iporuk's lower bound method" slightly more inclusive than the usual complexity-measure-specific formulation is presented. Using this general formulation, limitations to lower bounds achievable by the method are…
It is already shown that a Boolean function for a NP-complete problem can be computed by a polynomial-sized circuit if its variables have enough number of automorphisms. Looking at this previous study from the different perspective gives us…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
Recent work has unveiled a theory for reasoning about the decisions made by binary classifiers: a classifier describes a Boolean function, and the reasons behind an instance being classified as positive are the prime-implicants of the…