Related papers: Model-Theoretic Characterizations of Boolean and A…
Boolean and quantum circuits have commonalities and differences. To formalize the syntactical commonality we introduce syntactic circuits where the gates are black boxes. Syntactic circuits support various semantics. One semantics is…
Rossman [In $\textit{Proc. $34$th Comput. Complexity Conf.}$, 2019] introduced the notion of $\textit{criticality}$. The criticality of a Boolean function $f : \{0,1\}^n \to \{0,1\}$ is the minimum $\lambda \geq 1$ such that for all…
We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting. We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log…
Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence. We consider a natural way to relativize the notion of depth…
We present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade off in terms of depth and space complexity. As a result we…
The approximate degree of a Boolean function $f \colon \{-1, 1\}^n \rightarrow \{-1, 1\}$ is the least degree of a real polynomial that approximates $f$ pointwise to error at most $1/3$. We introduce a generic method for increasing the…
In this paper we show derivations among logarithmic space bounded counting classes based on closure properties of $\#L$ that leads us to the result that $NL=C_=L\subseteq PL$.
The description complexity of a model is the length of the shortest formula that defines the model. We study the description complexity of unary structures in first-order logic FO, also drawing links to semantic complexity in the form of…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
We introduce a new algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent…
We consider efficiency in the implementation of deep neural networks. Hardware accelerators are gaining interest as machine learning becomes one of the drivers of high-performance computing. In these accelerators, the directed graph…
We propose a new algorithm for compiling Bayesian network classifier (BNC) into class formulas. Class formulas are logical formulas that represent a classifier's input-output behavior, and are crucial in the recent line of work that uses…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…
We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of…
We investigate machine models similar to Turing machines that are augmented by the operations of a first-order structure $\mathcal{R}$, and we show that under weak conditions on $\mathcal{R}$, the complexity class $\text{NP}(\mathcal{R})$…
A caveat to many applications of the current Deep Learning approach is the need for large-scale data. One improvement suggested by Kolmogorov Complexity results is to apply the minimum description length principle with computationally…
We present a framework for studying circuit complexity that is inspired by techniques that are used for analyzing the complexity of CSPs. We prove that the circuit complexity of a Boolean function $f$ is characterized by the partial…
Input-output maps are prevalent throughout science and technology. They are empirically observed to be biased towards simple outputs, but we don't understand why. To address this puzzle, we study the archetypal input-output map: a…
The best known size lower bounds against unrestricted circuits have remained around $3n$ for several decades. Moreover, the only known technique for proving lower bounds in this model, gate elimination, is inherently limited to proving…