Related papers: A Lower Bound for Boolean Satisfiability on Turing…

For $S \subseteq \{0,1\}^n$ a Boolean function $f \colon S \to \{-1,1\}$ is a polynomial threshold function (PTF) of degree $d$ and weight $W$ if there is a polynomial $p$ with integer coefficients of degree $d$ and with sum of absolute…

We consider the problem of jointly minimizing forms of two Boolean functions $f, g \colon \{0,1\}^J \to \{0,1\}$ such that $f + g \leq 1$ and so as to separate disjoint sets $A \cup B \subseteq \{0,1\}^J$ such that $f(A) = \{1\}$ and $g(B)…

We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree (number of occurrences) of variables in various forms of redundancy-free boolean conjunctive normal forms…

We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…

Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., "yes" and "no", every voting system can be described by a (monotone) Boolean function…

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 construct simple, explicit matrices with columns having unit $\ell^2$ norm and discrepancy approaching $1 + \sqrt{2} \approx 2.414$. This number gives a lower bound, the strongest known as far as we are aware, on the constant appearing…

Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…

It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…

This paper explores the Boolean Satisfiability Problem (SAT) in the context of Kolmogorov complexity theory. We present three versions of the distinguishability problem-Boolean formulas, Turing machines, and quantum systems-each focused on…

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…

Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve…

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…

We study the query complexity of testing for properties defined by read once formulas, as instances of {\em massively parametrized properties}, and prove several testability and non-testability results. First we prove the testability of any…

Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…

We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in $\text{Quasi-NP} = \text{NTIME}[n^{(\log n)^{O(1)}}]$ and…

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…

We prove that, to compute a Boolean function $f$ on $N$ variables with error probability $\epsilon$, any quantum black-box algorithm has to query at least $\frac{1 - 2\sqrt{\epsilon}}{2} \rho_f N = \frac{1 - 2\sqrt{\epsilon}}{2} \bar{S}_f$…

Given the family $P$ of all nonempty subsets of a set $U$ of alternatives, a choice over $U$ is a function $c \colon \Omega \to P$ such that $\Omega \subseteq P$ and $c(B) \subseteq B$ for all menus $B \in \Omega$. A choice is total if…

Using methods and ideas from statistical mechanics, we propose a simple method for obtaining rigorous upper bounds for satisfiability transition in random boolean expressions composed of N variables and M clauses with K variables per…