Related papers: New Bounds for Energy Complexity of Boolean Functi…
Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through…
The approximate degree of a Boolean function f is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly…
A Boolean function is a function that produces a Boolean value output by logical calculation of Boolean inputs. It plays key roles in programing algorithms and design of circuits. Minimization of Boolean function is able to optimize the…
One of the major open problems in complexity theory is to demonstrate an explicit function which requires super logarithmic depth, a.k.a, the $\mathbf{P}$ versus $\mathbf{NC^1}$ problem. The current best depth lower bound is $(3-o(1))\cdot…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to…
A nearest neighbor representation of a Boolean function is a set of positive and negative prototypes in $R^n$ such that the function has value 1 on an input iff the closest prototype is positive. For $k$-nearest neighbor representation the…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met. In this paper, we first show that…
A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…
An extremal point of a positive threshold Boolean function $f$ is either a maximal zero or a minimal one. It is known that if $f$ depends on all its variables, then the set of its extremal points completely specifies $f$ within the universe…
We show that for any Boolean function f on {0,1}^n, the bounded-error quantum communication complexity of XOR functions $f\circ \oplus$ satisfies that $Q_\epsilon(f\circ \oplus) = O(2^d (\log\|\hat f\|_{1,\epsilon} + \log…
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…
Reversible logic circuit is a necessary construction for achieving ultra low power dissipation as well as for prominent post-CMOS computing technologies such as Quantum computing. Consequently automatic synthesis of a Boolean function using…
We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints.…
We show that for any constant $c>0$, any (two-sided error) adaptive algorithm for testing monotonicity of Boolean functions must have query complexity $\Omega(n^{1/2-c})$. This improves the $\tilde\Omega(n^{1/3})$ lower bound of [CWX17] and…
A number of complexity measures for Boolean functions have previously been introduced. These include (1) sensitivity, (2) block sensitivity, (3) witness complexity, (4) subcube partition complexity and (5) algorithmic complexity. Each of…
The Coulomb exchange and correlation energy density functionals for electron systems are applied to nuclear systems. It is found that the exchange functionals in the generalized gradient approximation provide agreements with the exact-Fock…
In this paper, I consider a fine-grained dichotomy of Boolean counting constraint satisfaction problem (#CSP), under the exponential time hypothesis of counting version (#ETH). Suppose $\mathscr{F}$ is a finite set of algebraic…
The Boolean circuit simplification problem involves finding a smaller circuit that computes the same function as a given Boolean circuit. This problem is closely related to several key areas with both theoretical and practical applications,…