Related papers: Conflict complexity is lower bounded by block sens…
What factors contribute to the relative success and corresponding difficulties of in-context learning for Large Language Models (LLMs)? Drawing on insights from the literature on human concept learning, we test LLMs on carefully designed…
This paper proposes a model of decision-making under uncertainty in which an agent is constrained in her cognitive ability to consider complex acts. We identify the complexity of an act according to the corresponding partition of state…
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…
Modern shared memory multiprocessors permit reordering of memory operations for performance reasons. These reorderings are often a source of subtle bugs in programs written for such architectures. Traditional approaches to verify weak…
Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory. We construct a sequence of Boolean functions with bs(f) = 1/2 s(f)^2 + 1/2 s(f). The best…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…
Boolean matching is significant to digital integrated circuits design. An exhaustive method for Boolean matching is computationally expensive even for functions with only a few variables, because the time complexity of such an algorithm for…
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
In this work, we unify several quantum algorithmic frameworks for boolean functions that are based on the quantum adversary bound. First, we show that the $st$-connectivity framework subsumes the (adaptive/extended) learning graph…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
We study the problem of {\sl certification}: given queries to a function $f : \{0,1\}^n \to \{0,1\}$ with certificate complexity $\le k$ and an input $x^\star$, output a size-$k$ certificate for $f$'s value on $x^\star$. This abstractly…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Quantifying the complexity of quantum states that possess intrinsic structure, such as symmetry or encoding, in a fair manner constitutes a core challenge in the benchmarking of quantum technologies. This paper introduces the…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
Coalitional games are mathematical models suited to analyze scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental problem for coalitional games is to single…
Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NP-complete, but its complexity depends on a template, usually a set of relations, upon which they are…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…