Related papers: Complexity and mission computability of adaptive c…
We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).
We consider the class of counting problems,i.e. functions in $\#$P, which are self reducible, and have easy decision version, i.e. for every input it is easy to decide if the value of the function $f(x)$ is zero. For example,…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
We consider the communication complexity of a number of distributed optimization problems. We start with the problem of solving a linear system. Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of…
Large language models (LLMs) have shown remarkable performance in various tasks but often fail to handle queries that exceed their knowledge and capabilities, leading to incorrect or fabricated responses. This paper addresses the need for…
We address lower bounds on the time complexity of algorithms solving the propositional satisfiability problem. Namely, we consider two DPLL-type algorithms, enhanced with the unit clause and pure literal heuristics. Exponential lower bounds…
Adaptable computing is an increasingly important paradigm that specializes system resources to variable application requirements, environmental conditions, or user requirements. Adapting computing resources to variable application…
Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of functions which are "fractionally computable" by a partial…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
An affine model of computation is defined as a subset of iterated immediate-snapshot runs, capturing a wide variety of shared-memory systems, such as wait-freedom, t-resilience, k-concurrency, and fair shared-memory adversaries. The…
The optimization of dynamic problems is both widespread and difficult. When conducting dynamic optimization, a balance between reinitialization and computational expense has to be found. There are multiple approaches to this. In parallel…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We are given a set of $n$ jobs and a single processor that can vary its speed dynamically. Each job $J_j$ is characterized by its processing requirement (work) $p_j$, its release date $r_j$ and its deadline $d_j$. We are also given a budget…
Resource-constrained classification tasks are common in real-world applications such as allocating tests for disease diagnosis, hiring decisions when filling a limited number of positions, and defect detection in manufacturing settings…
Resource-constrained systems are prevalent in communications. Such a system is composed of many components but only some of them can be allocated with resources such as time slots. According to the amount of information about the system,…
Efforts to apply transformer-based language models (TLMs) to the problem of reasoning in natural language have enjoyed ever-increasing success in recent years. The most fundamental task in this area to which nearly all others can be reduced…
This paper is concerned with linear parameter-dependent systems and considers the notion uniform ensemble reachability. The focus of this work is on constructive methods to compute suitable parameter-independent open-loop inputs for such…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…