A Molecular Solution to the Three-Partition Problem

2012 ◽  
Vol 5 (4) ◽  
pp. 14-29
Author(s):  
Maryam S. Nuser
Keyword(s):  
Molecular Computing ◽  
Partition Problem ◽  
Biomolecular Computing ◽  
Hard Problems ◽  
Np Complete ◽  
Computing Approach

Given a set of numbers, the three-partition problem is to divide them into disjoint triplets that all have the same sum. The problem is NP-complete. This paper presents an algorithm to solve this problem using the biomolecular computing approach. The algorithm uses a distinctive encoding technique that depends on the numbers values which omits the need to an adder to find the sum. The algorithm is explained and an analysis of its complexity in terms of time, the number of strands, number of tubes, and the longest library strand used is presented. A simulation of the algorithm is implemented and tested. This algorithm further proves the ability of molecular computing in solving hard problems.

NP vs QMA_\log(2)

2010 ◽  
Vol 10 (1&2) ◽  
pp. 141-151
Author(s):  
S. Beigi
Keyword(s):  
Quantum Algorithms ◽  
Np Hard ◽  
Complete Problems ◽  
Hard Problems ◽  
Np Complete ◽  
Np Hard Problems

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve NP-complete problems given a "short" quantum proof; more precisely, NP\subseteq QMA_{\log}(2) where QMA_{\log}(2) denotes the class of quantum Merlin-Arthur games in which there are two unentangled provers who send two logarithmic size quantum witnesses to the verifier. The inclusion NP\subseteq QMA_{\log}(2) has been proved by Blier and Tapp by stating a quantum Merlin-Arthur protocol for 3-coloring with perfect completeness and gap 1/24n^6. Moreover, Aaronson et al. have shown the above inclusion with a constant gap by considering $\widetilde{O}(\sqrt{n})$ witnesses of logarithmic size. However, we still do not know if QMA_{\log}(2) with a constant gap contains NP. In this paper, we show that 3-SAT admits a QMA_{\log}(2) protocol with the gap 1/n^{3+\epsilon}} for every constant \epsilon>0.

Dealing with Hardness

2017 ◽  
Author(s):  
Lance Fortnow
Keyword(s):  
Brute Force ◽  
Complete Problem ◽  
Hard Problems ◽  
Np Complete ◽  
Np Problems ◽  
Single Technique

This chapter demonstrates several approaches for dealing with hard problems. These approaches include brute force, heuristics, and approximation. Typically, no single technique will suffice to handle the difficult NP problems one needs to solve. For moderate-sized problems one can search over all possible solutions with the very fast computers available today. One can use algorithms that might not work for every problem but do work for many of the problems one cares about. Other algorithms may not find the best possible solution but still a solution that's good enough. Other times one just cannot get a solution for an NP-complete problem. One has to try to solve a different problem or just give up.

A O(m) Self-Stabilizing Algorithm for Maximal Triangle Partition of General Graphs

2017 ◽  
Vol 27 (02) ◽  
pp. 1750004
Author(s):  
Brahim Neggazi ◽  
Volker Turau ◽  
Mohammed Haddad ◽  
Hamamache Kheddouci
Keyword(s):  
Graph Matching ◽  
Partition Problem ◽  
Matching Problem ◽  
Np Complete ◽  
General Graphs

The triangle partition problem is a generalization of the well-known graph matching problem consisting of finding the maximum number of independent edges in a given graph, i.e., edges with no common node. Triangle partition instead aims to find the maximum number of disjoint triangles. The triangle partition problem is known to be NP-complete. Thus, in this paper, the focus is on the local maximization variant, called maximal triangle partition (MTP). Thus, paper presents a new self-stabilizing algorithm for MTP that converges in O(m) moves under the unfair distributed daemon.

Membrane Computing

2011 ◽  
pp. 1-31 ◽  
Author(s):  
Gheorghe Paun
Keyword(s):  
Membrane Computing ◽  
Living Cells ◽  
Point Of View ◽  
Natural Computing ◽  
Historical Evolution ◽  
Biological Phenomena ◽  
Complete Problems ◽  
Hard Problems ◽  
Np Complete ◽  
And Mathematics

Membrane computing is a branch of natural computing whose initial goal was to abstract computing models from the structure and the functioning of living cells. The research was initiated about five years ago (at the end of 1998), and since that time the area has been developed significantly from a mathematical point of view. The basic types of results of this research concern the computability power (in comparison with the standard Turing machines and their restrictions) and the efficiency (the possibility to solve computationally hard problems, typically NP-complete problems, in a feasible time and typically polynomial). However, membrane computing has recently become attractive also as a framework for devising models of biological phenomena, with the tendency to provide tools for modelling the cell itself, not only the local processes. This chapter surveys the basic elements of membrane computing, somewhat in its “historical” evolution: from biology to computer science and mathematics and back to biology. The presentation is informal, without any technical detail, and an invitation to membrane computing intended to acquaint the nonmathematician reader with the main directions of research of the domain, the type of central results, and the possible lines of future development, including the possible interest of the biologist looking for discrete algorithmic tools for modelling cell phenomena.

A New Code-Based Blind Signature Scheme

2021 ◽  
Author(s):  
Siyuan Chen ◽  
Peng Zeng ◽  
Kim-Kwang Raymond Choo
Keyword(s):  
Coding Theory ◽  
Blind Signature ◽  
Quantum Computers ◽  
Security Level ◽  
Zero Knowledge ◽  
Syndrome Decoding ◽  
Cryptographic Primitive ◽  
Hard Problems ◽  
Np Complete ◽  
Level 2

Abstract Blind signature is an important cryptographic primitive with widespread applications in secure e-commerce, for example to guarantee participants’ anonymity. Existing blind signature schemes are mostly based on number-theoretic hard problems, which have been shown to be solvable with quantum computers. The National Institute of Standards and Technology (NIST) began in 2017 to specify a new standard for digital signatures by selecting one or more additional signature algorithms, designed to be secure against attacks carried out using quantum computers. However, none of the third-round candidate algorithms are code-based, despite the potential of code-based signature algorithms in resisting quantum computing attacks. In this paper, we construct a new code-based blind signature (CBBS) scheme as an alternative to traditional number-theoretic based schemes. Specifically, we first extend Santoso and Yamaguchi’s three pass identification scheme to a concatenated version (abbreviated as the CSY scheme). Then, we construct our CBBS scheme from the CSY scheme. The security of our CBBS scheme relies on hardness of the syndrome decoding problem in coding theory, which has been shown to be NP-complete and secure against quantum attacks. Unlike Blazy et al.’s CBBS scheme which is based on a zero-knowledge protocol with cheating probability $2/3$, our CBBS scheme is based on a zero-knowledge protocol with cheating probability $1/2$. The lower cheating probability would reduce the interaction rounds under the same security level and thus leads to a higher efficiency. For example, to achieve security level $2^{-82}$, the signature size in our CBBS scheme is $1.63$ MB compared to $3.1$ MB in Blazy et al.’s scheme.

A reservoir computing approach for molecular computing

2018 ◽  
Author(s):  
Wataru Yahiro ◽  
Nathanael Aubert-Kato ◽  
Masami Hagiya
Keyword(s):  
Molecular Computing ◽  
Reservoir Computing ◽  
Computing Approach

scholarly journals A stochastic quantum program synthesis framework based on Bayesian optimization

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yao Xiao ◽  
Shahin Nazarian ◽  
Paul Bogdan
Keyword(s):  
Lower Cost ◽  
Program Synthesis ◽  
Bayesian Optimization ◽  
Quantum Computers ◽  
Optimal Program ◽  
Von Neumann ◽  
Np Complete ◽  
High Level ◽  
Fine Tune ◽  
Computing Approach

AbstractQuantum computers and algorithms can offer exponential performance improvement over some NP-complete programs which cannot be run efficiently through a Von Neumann computing approach. In this paper, we present BayeSyn, which utilizes an enhanced stochastic program synthesis and Bayesian optimization to automatically generate quantum programs from high-level languages subject to certain constraints. We find that stochastic synthesis can comparatively and efficiently generate a program with a lower cost from the high dimensional program space. We also realize that hyperparameters used in stochastic synthesis play a significant role in determining the optimal program. Therefore, BayeSyn utilizes Bayesian optimization to fine-tune such parameters to generate a suitable quantum program.

scholarly journals Solving the Graph Problem on the Maximal Clique Problem on the P-Systems with Mitochondria Enzymes Layer

2019 ◽  
Vol 10 (1) ◽  
pp. 275
Author(s):  
Ford Lumban Gaol ◽  
Tokuro Matsuo
Keyword(s):  
Undirected Graph ◽  
Maximal Clique ◽  
P Systems ◽  
Hard Problems ◽  
Np Complete ◽  
New Feature ◽  
Recent Version ◽  
Natural Cell ◽  
Np Hard Problems

P systems with mitochondria enzymes layer computing is a recent version of P systems; it integrates a new feature inspired from the enzymes gate of a natural cell to the cell-like P systems. The model of a computational layer is well known as a problem of Non-Deterministic (NP-complete) in polynomial time. In this paper, we propose a P systems with enzymes to solve one of the most NP-hard problems, which is the determination of the maximal clique in a given undirected graph. In this context, the evolution strategy proposed is based on using objects under the control of enzymes placed on layers.

scholarly journals Partitioning the vertex set of a bipartite graph into complete bipartite subgraphs

2014 ◽  
Vol Vol. 16 no. 3 (Graph Theory) ◽  
Author(s):  
Oleg Duginov
Keyword(s):  
Bipartite Graphs ◽  
Partition Problem ◽  
Induced Subgraphs ◽  
Permutation Graphs ◽  
Vertex Partition ◽  
Vertex Set ◽  
International Audience ◽  
Bipartite Permutation Graphs ◽  
Np Complete ◽  
Polynomially Solvable

Graph Theory International audience Given a graph and a positive integer k, the biclique vertex-partition problem asks whether the vertex set of the graph can be partitioned into at most k bicliques (connected complete bipartite subgraphs). It is known that this problem is NP-complete for bipartite graphs. In this paper we investigate the computational complexity of this problem in special subclasses of bipartite graphs. We prove that the biclique vertex-partition problem is polynomially solvable for bipartite permutation graphs, bipartite distance-hereditary graphs and remains NP-complete for perfect elimination bipartite graphs and bipartite graphs containing no 4-cycles as induced subgraphs.

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