An Optical Polynomial Time Solution for the Satisfiability Problem

2013 ◽  
pp. 15-24 ◽  
Author(s):  
Sama Goliaei ◽  
Saeed Jalili
Keyword(s):  
Polynomial Time ◽  
Satisfiability Problem ◽  
Time Solution

scholarly journals FAST ALGORITHMIC NIELSEN–THURSTON CLASSIFICATION OF FOUR-STRAND BRAIDS

2012 ◽  
Vol 21 (05) ◽  
pp. 1250043 ◽  
Author(s):  
MATTHIEU CALVEZ ◽  
BERT WIEST
Keyword(s):  
Conjugacy Class ◽  
Polynomial Time ◽  
Word Length ◽  
Conjugacy Problem ◽  
Time Solution

We give an algorithm which decides the Nielsen–Thurston type of a given four-strand braid. The complexity of our algorithm is quadratic with respect to word length. The proof of its validity is based on a result which states that for a reducible 4-braid which is as short as possible within its conjugacy class (short in the sense of Garside), reducing curves surrounding three punctures must be round or almost round. As an application, we give a polynomial time solution to the conjugacy problem for non-pseudo-Anosov four-strand braids.

A polynomial time solution for labeling a rectilinear map

1998 ◽  
Vol 65 (4) ◽  
pp. 201-207 ◽  
Author(s):  
Chung Keung Poon ◽  
Zhu Binhai ◽  
Chin Francis
Keyword(s):  
Polynomial Time ◽  
Time Solution

TYPE INFERENCE FOR FIRST-CLASS MESSAGES WITH FEATURE CONSTRAINTS

2000 ◽  
Vol 11 (01) ◽  
pp. 29-63
Author(s):  
MARTIN MÜLLER ◽  
SUSUMU NISHIMURA
Keyword(s):  
Polynomial Time ◽  
Type System ◽  
Type Inference ◽  
Satisfiability Problem ◽  
Recent Proposal ◽  
Inference Problem ◽  
Np Complete ◽  
Feature Constraints ◽  
Feature Trees ◽  
Selection Constraint

We present a constraint system, OF, of feature trees that is appropriate to specify and implement type inference for first-class messages. OF extends traditional systems of feature constraints by a selection constraint x <y> z, "by first-class feature tree" y, which is in contrast to the standard selection constraint x[f]y, "by fixed feature" f. We investigate the satisfiability problem of OF and show that it can be solved in polynomial time, and even in quadratic time if the number of features is bounded. We compare OF with Treinen's system EF of feature constraints with first-class features, which has an NP-complete satisfiability problem. This comparison yields that the satisfiability problem for OF with negation is NP-hard. Further we obtain NP-completeness, for a specific subclass of OF with negation that is useful for a related type inference problem. Based on OF we give a simple account of type inference for first-class messages in the spirit of Nishimura's recent proposal, and we show that it has polynomial time complexity: We also highlight an immediate extension of this type system that appears to be desirable but makes type inference NP-complete.

scholarly journals On A Quantum Proof Of The Equivalence of P And NP

2019 ◽  
Author(s):  
Adewale Oluwasanmi
Keyword(s):  
Polynomial Time ◽  
Solution Space ◽  
Quantum Systems ◽  
Satisfiability Problem ◽  
Quantum Mechanical ◽  
Correctness Proof ◽  
Classical Systems ◽  
Classical Architecture ◽  
General Quantum

We present an algorithm, along with a correctness proof, for solving the 3 Satisfiability problem that is inspired by quantum mechanical principles and that runs in polynomial time with respect to the size of the input problem. Even though we term both our algorithm and its associated proof as quantum (for reasons which we will demonstrate), it is intended to be run on standard classical architecture. In the article, we posit that the 3 Satisfiability problem has an intrinsic complex quantum form that can be programmed in order to build a model of the solution space for satisfiable instances or show that such a model cannot be constructed. This yields surprising results on the ability for classical systems to abstractly simulate general quantum systems.

scholarly journals Polynomial time solution to NP-complete problem Hamiltonian cycle (P=NP Proof)

2021 ◽  
Author(s):  
Yasaman KalantarMotamedi
Keyword(s):  
Computer Science ◽  
Polynomial Time ◽  
Hamiltonian Cycle ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Rigorous Proof ◽  
Complete Problem ◽  
Time Solution ◽  
Np Complete

P vs NP is one of the open and most important mathematics/computer science questions that has not been answered since it was raised in 1971 despite its importance and a quest for a solution since 2000. P vs NP is a class of problems that no polynomial time algorithm exists for any. If any of the problems in the class gets solved in polynomial time, all can be solved as the problems are translatable to each other. One of the famous problems of this kind is Hamiltonian cycle. Here we propose a polynomial time algorithm with rigorous proof that it always finds a solution if there exists one. It is expected that this solution would address all problems in the class and have a major impact in diverse fields including computer science, engineering, biology, and cryptography.

scholarly journals On the Largest Dynamic Monopolies of Graphs with a Given Average Threshold

2015 ◽  
Vol 58 (2) ◽  
pp. 306-316 ◽  
Author(s):  
Kaveh Khoshkhah ◽  
Manouchehr Zaker
Keyword(s):  
Polynomial Time ◽  
Upper Bound ◽  
Nonnegative Integer ◽  
Planar Graphs ◽  
Worst Case ◽  
Time Solution

AbstractLet G be a graph and let τ be an assignment of nonnegative integer thresholds to the vertices of G. A subset of vertices, D, is said to be a τ-dynamicmonopoly if V(G) can be partitioned into subsets D0 , D1, …, Dk such that D0 = D and for any i ∊ {0, . . . , k−1}, each vertex v in Di+1 has at least τ(v) neighbors in D0∪··· ∪Di. Denote the size of smallest τ-dynamicmonopoly by dynτ(G) and the average of thresholds in τ by τ. We show that the values of dynτ(G) over all assignments τ with the same average threshold is a continuous set of integers. For any positive number t, denote the maximum dynτ(G) taken over all threshold assignments τ with τ ≤ t, by Ldynt(G). In fact, Ldynt(G) shows the worst-case value of a dynamicmonopoly when the average threshold is a given number t. We investigate under what conditions on t, there exists an upper bound for Ldynt(G) of the form c|G|, where c < 1. Next, we show that Ldynt(G) is coNP-hard for planar graphs but has polynomial-time solution for forests.

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