Related papers: Philosophical Solution to P=?NP: P is Equal to NP
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
Traditional Von Neumann computing is falling apart in the era of exploding data volumes as the overhead of data transfer becomes forbidding. Instead, it is more energy-efficient to fuse compute capability with memory where the data reside.…
We prove that P = NP implies #P = FP by exploiting the topological structure of 3SAT solution spaces. The argument proceeds via a dichotomy: any polynomial-time algorithm for 3SAT either operates without global knowledge of the…
In this paper, we inquire the key concept P-reduction in Cook's theorem and reveal that there exists the fallacy of definition in P-reduction caused by the disguised displacement of NDTM from Oracle machine to Turing machine. The definition…
We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location.…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
We study algorithmic problems that belong to the complexity class of the existential theory of the reals (ER). A problem is ER-complete if it is as hard as the problem ETR and if it can be written as an ETR formula. Traditionally, these…
We consider the thesis that an arithmetical relation, which holds for any, given, assignment of natural numbers to its free variables, is Turing-decidable if, and only if, it is the standard representation of a PA-provable formula. We show…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
We study the canonical quantity-based network revenue management (NRM) problem where the decision-maker must irrevocably accept or reject each arriving customer request with the goal of maximizing the total revenue given limited resources.…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…
We distinguish finitarily between algorithmic verifiability, and algorithmic computability, to show that Goedel's 'formally' unprovable, but 'numeral-wise' provable, arithmetical proposition [(Ax)R(x)] can be finitarily evidenced as:…
Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…
Data-intensive workloads and applications, such as machine learning (ML), are fundamentally limited by traditional computing systems based on the von-Neumann architecture. As data movement operations and energy consumption become key…
I shall argue that a resolution of the PvNP problem requires building an iff bridge between the domain of provability and that of computability. The former concerns how a human intelligence decides the truth of number-theoretic relations,…
We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…
The vast majority of scientific community believes that P!=NP, with countless supporting arguments. The number of people who believe otherwise probably amounts to as few as those opposing the 2nd Law of Thermodynamics. But isn't nature…
There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as…