Related papers: A Circuit Complexity Formulation of Algorithmic In…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
This paper proposes a new logic optimization paradigm based on circuit simulation, which reduces the need for Boolean computations such as SAT-solving or constructing BDDs. The paper develops a Boolean resubstitution framework to…
In this paper, we study the computational complexity of the commutative determinant polynomial computed by a class of set-multilinear circuits which we call regular set-multilinear circuits. Regular set-multilinear circuits are commutative…
The rapid development of artificial intelligence (AI) systems has created an urgent need for their scientific quantification. While their fluency across a variety of domains is impressive, AI systems fall short on tests requiring…
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…
We survey lower-bound results in complexity theory that have been obtained via newfound interconnections between propositional proof complexity, boolean circuit complexity, and query/communication complexity. We advocate for the theory of…
Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…
Quantum circuit complexity has played a central role in recent advances in holography and many-body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real-time) framework. In a departure from standard…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
Many learning tasks can be viewed as sequence prediction problems. For example, online classification can be converted to sequence prediction with the sequence being pairs of input/target data and where the goal is to correctly predict the…
We investigate the expressive power of neural networks from the point of view of descriptive complexity. We study neural networks that use floating-point numbers and piecewise polynomial activation functions from two perspectives: 1) the…
We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. We focus on the class of structured d-DNNF circuits originally introduced in…
We introduce an information-theoretic framework that views learning as universal prediction under log loss, characterized through regret bounds. Central to the framework is an effective notion of architecture-based model complexity, defined…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
We study the query complexity on slices of Boolean functions. Among other results we show that there exists a Boolean function for which we need to query all but 7 input bits to compute its value, even if we know beforehand that the number…
We investigate the complexity of uniform OR circuits and AND circuits of polynomial-size and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant (0/1) gates.…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension,…
In sequential circuits, the current output may depend on both past and current inputs. However, certain kinds of sequential circuits do not refer to all of the past inputs to generate the current output; they only refer to a subset of past…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…