scholarly journals Hardness of Approximation for Langton’s Ant on a Twisted Torus

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 344
Author(s):  
Takeo Hagiwara ◽  
Tatsuie Tsukiji
Keyword(s):  
Computational Complexity ◽  
Cellular Automaton ◽  
Artificial Life ◽  
Lattice Gas ◽  
Hardness Of Approximation ◽  
Macroscopic Behavior ◽  
Almost All ◽  
Emergent Dynamics

Langton’s ant is a deterministic cellular automaton studied in many fields, artificial life, computational complexity, cryptography, emergent dynamics, Lorents lattice gas, and so forth, motivated by the hardness of predicting the ant’s macroscopic behavior from an initial microscopic configuration. Gajardo, Moreira, and Goles (2002) proved that Langton’s ant is PTIME -hard for reachability. On a twisted torus, we demonstrate that it is PSPACE hard to determine whether the ant will ever visit almost all vertices or nearly none of them.

Diffusion in tight confinement: A lattice-gas cellular automaton approach. II. Transport properties

2007 ◽  
Vol 126 (19) ◽  
pp. 194710 ◽  
Author(s):  
Pierfranco Demontis ◽  
Federico G. Pazzona ◽  
Giuseppe B. Suffritti
Keyword(s):  
Cellular Automaton ◽  
Transport Properties ◽  
Lattice Gas

A Lattice-Gas Cellular Automaton to Model Diffusion in Restricted Geometries

2006 ◽  
Vol 110 (27) ◽  
pp. 13554-13559 ◽  
Author(s):  
P. Demontis ◽  
F. G. Pazzona ◽  
G. B. Suffritti
Keyword(s):  
Cellular Automaton ◽  
Lattice Gas ◽  
Model Diffusion

MEMRISTOR CELLULAR AUTOMATA AND MEMRISTOR DISCRETE-TIME CELLULAR NEURAL NETWORKS

2009 ◽  
Vol 19 (11) ◽  
pp. 3605-3656 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Cellular Automaton ◽  
Discrete Time ◽  
Cellular Neural Network ◽  
Brain Functions ◽  
Rsa Algorithm ◽  
Logical Operations ◽  
Almost All ◽  
Higher Brain Functions

In this paper, we design a cellular automaton and a discrete-time cellular neural network (DTCNN) using nonlinear passive memristors. They can perform a number of applications, such as logical operations, image processing operations, complex behaviors, higher brain functions, RSA algorithm, etc. By modifying the characteristics of nonlinear memristors, the memristor DTCNN can perform almost all functions of memristor cellular automaton. Furthermore, it can perform more than one function at the same time, that is, it allows multitasking.

scholarly journals How to Approximate Ontology-Mediated Queries

2021 ◽  
Author(s):  
Anneke Haga ◽  
Carsten Lutz ◽  
Leif Sabellek ◽  
Frank Wolter
Keyword(s):  
Computational Complexity ◽  
Linear Time ◽  
Description Logics ◽  
Data Complexity ◽  
Fixed Parameter Tractable ◽  
Ontology Language ◽  
Fixed Parameter ◽  
Almost All

We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as the class of databases whose treewidth is bounded by a constant. We determine the computational complexity and the relative completeness of the resulting approximations. (Almost) all of them reduce the data complexity from coNP-complete to PTime, in some cases even to fixed-parameter tractable and to linear time. While approximations of kind (1) also reduce the combined complexity, this tends to not be the case for approximations of kind (2). In some cases, the combined complexity even increases.

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

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