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Advanced Search Results For "POLYNOMIALS"

1 - 10 of 112,907 results for
 "POLYNOMIALS"
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SPARKs: Succinct Parallelizable Arguments of Knowledge.

Publication Type: Academic Journal

Source(s): Journal of the ACM. Sep2022, Vol. 69 Issue 5, p1-88. 88p.

Abstract: We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument of knowledge with the following three efficiency properties for computing and proving a (non-deterministic, polynomial time) parallel RAMcomputation...

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Incorporating Lindblad decay dynamics into mixed quantum-classical simulations.

Publication Type: Academic Journal

Source(s): Journal of Chemical Physics. 8/14/2022, Vol. 157 Issue 6, p1-24. 24p.

Abstract: We derive the L -mean-field Ehrenfest (MFE) method to incorporate Lindblad jump operator dynamics into the MFE approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assu...

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Permutation invariant polynomial neural network based diabatic ansatz for the (E + A) × (e + a) Jahn–Teller and Pseudo-Jahn–Teller systems.

Publication Type: Academic Journal

Source(s): Journal of Chemical Physics. 7/7/2022, Vol. 157 Issue 1, p1-10. 10p.

Abstract: In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the relat...

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Atomic Embeddability, Clustered Planarity, and Thickenability.

Publication Type: Academic Journal

Source(s): Journal of the ACM. Mar2022, Vol. 69 Issue 2, p1-34. 34p.

Abstract: We study the atomic embeddability testing problem, which is a common generalization of clustered planarity (c-planarity, for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomia...

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Twin-width I: Tractable FO Model Checking.

Publication Type: Academic Journal

Source(s): Journal of the ACM. Jan2022, Vol. 69 Issue 1, p3-46. 46p.

Abstract: Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA'14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, Kt -free unit d-dimensional ball...

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Fifty Years of P vs. NP and the Possibility of the Impossible.

Publication Type: Periodical

Source(s): Communications of the ACM. Jan2022, Vol. 65 Issue 1, p76-85. 10p. 1 Color Photograph, 1 Map.

Authors:

Abstract: The article discusses the computer science (CS) and mathematical theorem difficulty known as the polynomial (P) vs. nondeterministic polynomial problem (NP) problem, which was first introduced by computer scientists and mathematician Steve Cook in 1971...

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Inverse interval scheduling via reduction on a single machine.

Publication Type: Academic Journal

Source(s): European Journal of Operational Research. Dec2022, Vol. 303 Issue 2, p541-549. 9p.

Abstract: • Inverse counterpart of the interval scheduling problem is considered. • We reduce the non-preemptive job intervals with a least cost. • We focus on a single machine. • We prove the problem is strongly NP-hard. • We devise a polynomial time approximat...

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Vibrational levels of a generalized Morse potential.

Publication Type: Academic Journal

Source(s): Journal of Chemical Physics; 10/14/2022, Vol. 157 Issue 14, p1-13, 13p

Abstract: Copyright of Journal of Chemical Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users m...

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NFA Admits an FPRAS: Efficient Enumeration, Counting, and Uniform Generation for Logspace Classes.

Publication Type: Academic Journal

Source(s): Journal of the ACM. Dec2021, Vol. 68 Issue 6, p1-34. 34p.

Abstract: In this work, we study two simple yet general complexity classes, based on logspace Turing machines, that provide a unifying framework for efficient query evaluation in areas such as information extraction and graph databases, among others. We investig...

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Hypergraph k-Cut for Fixed k in Deterministic Polynomial Time.

Publication Type: Academic Journal

Source(s): Mathematics of Operations Research. Nov2022, Vol. 47 Issue 4, p3380-3399. 20p.

Abstract: We consider the Hypergraph-k-Cut problem. The input consists of a hypergraph G = (V , E) with nonnegative hyperedge-costs c : E → R + and a positive integer k. The objective is to find a minimum cost subset F ⊆ E such that the number of connected compo...

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