Related papers: On the Relationship between Energy Complexity and …
Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number…
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…
$\newcommand{\F}{\mathbb{F}}$We study the Boolean function parameters sensitivity ($s$), block sensitivity ($bs$), and alternation ($alt$) under specially designed affine transforms. For a function $f:\F_2^n\to \{0,1\}$, and $A=Mx+b$ for $M…
We establish an explicit link between depth-3 formulas and one-sided approximation by depth-2 formulas, which were previously studied independently. Specifically, we show that the minimum size of depth-3 formulas is (up to a factor of n)…
The embedded DRAM (eDRAM) is more and more used in System On Chip (SOC). The integration of the DRAM capacitor process into a logic process is challenging to get satisfactory yields. The specific process of DRAM capacitor and the low…
Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in $\mathcal{Z}_2$ Even Effective Field Theories ($\mathcal{Z}_2$ EEFTs). We consider a massive…
The energy-energy correlator (EEC) and multiplicity are two fundamental observables probing complementary aspects of QCD jets: the former characterizes the angular structure of energy flows in a scale-dependent manner, while the latter is…
The FCC integrated programme comprises an $\rm e^+e^-$ high-luminosity circular collider that will produce very large samples of data in an energy range $88 \le \sqrt{s} \le 365$ GeV, followed by a high-energy $\rm pp$ machine that, with…
We describe a $\tilde{O}(d^{5/6})$-query monotonicity tester for Boolean functions $f:[n]^d \to \{0,1\}$ on the $n$-hypergrid. This is the first $o(d)$ monotonicity tester with query complexity independent of $n$. Motivated by this…
We prove a lower bound $\Omega\left(\frac{k+l}{k^2l^2}N^{2-\frac{k+l+2}{kl}}\right)$ on the maximal possible weight of a $(k,l)$-free (that is, free of all-ones $k\times l$ submatrices) Boolean circulant $N \times N$ matrix. The bound is…
We present an energy-specific Bethe-Salpeter equation (BSE) implementation for efficient core and valence optical spectrum calculations. In energy-specific BSE, high-lying excitation energies are obtained by constructing trial vectors and…
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…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
To study the question under which circumstances small solutions can be found faster than by exhaustive search (and by how much), we study the fine-grained complexity of Boolean constraint satisfaction with size constraint exactly $k$. More…
The $\epsilon$-approximate degree of a Boolean function $f: \{-1, 1\}^n \to \{-1, 1\}$ is the minimum degree of a real polynomial that approximates $f$ to within $\epsilon$ in the $\ell_\infty$ norm. We prove several lower bounds on this…
Correlation functions of energy flow operators (energy-energy correlators) are one of the simplest observables in quantum field theory and gravity, with diverse applications ranging from real world collider physics to constraining the space…
Neural gates compute functions based on weighted sums of the input variables. The expressive power of neural gates (number of distinct functions it can compute) depends on the weight sizes and, in general, large weights (exponential in the…
An evaluation of the gate capacitance of a field-effect transitor (FET) whose channel length and width are several ten nanometer, is a key point for sensors applications. However, experimental and precise evaluation of capacitance in the aF…
In previous work carried out in the setting of program algebra, including work in the area of instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only instructions of a few of the possible…
We analyze the energy barriers that allow escapes from a given local minimum in a mean-field model of glasses. We perform this study by using the Kac-Rice method and computing the typical number of critical points of the energy function at…