Upper semilattice of binary strings with the relation "x is simple conditional to y"

2003 ◽  
Author(s):  
A. Muchnik ◽  
A. Romashchenko ◽  
A. Shen ◽  
N. Vereshchagin
Keyword(s):  
Upper Semilattice ◽  
Binary Strings

Artificial Chemistry and Molecular Darwinian Evolution in silico

2003 ◽  
Vol 68 (1) ◽  
pp. 139-177 ◽  
Author(s):  
Vladimír Kvasnička ◽  
Jiří Pospíchal
Keyword(s):  
Graph Theory ◽  
Molecular Level ◽  
Stable State ◽  
Chemical Reactor ◽  
Darwinian Evolution ◽  
Simplified Model ◽  
Asymptotically Stable ◽  
Artificial Chemistry ◽  
Neutral Mutations ◽  
Binary Strings

A simplified model of Darwinian evolution at the molecular level is studied by applying the methods of artificial chemistry. A chemical reactor (chemostat) contains molecules that are represented by binary strings, the strings being capable of replication with a probability proportional to their fitness. Moreover, the process of replication is not fully precise, sporadic mutations may produce new offspring strings, which are slightly different from their parent templates. The dynamics of such an autoreplicating system is described by Eigen's differential equations. These equations have a unique asymptotically stable state, which corresponds to those strings that have the highest rate constants (fitness). Fitness of binary string is calculated as a graph-theory similarity between a folding (phenotype) of respective string and the so-called required folding. The presented method offers a detailed view of mechanisms of the molecular Darwinian evolution, in particular of the meaning and importance of neutral mutations.

scholarly journals AN ASYMPTOTIC LOWER BOUND FOR THE MAXIMAL NUMBER OF RUNS IN A STRING

2008 ◽  
Vol 19 (01) ◽  
pp. 195-203 ◽  
Author(s):  
FRANTISEK FRANEK ◽  
QIAN YANG
Keyword(s):  
Lower Bound ◽  
Binary Strings

An asymptotic lower bound for the maxrun function ρ(n) = max {number of runs in string x | all strings x of length n} is presented. More precisely, it is shown that for any ε > 0, (α−ε)n is an asymptotic lower bound, where [Formula: see text]. A recent construction of an increasing sequence of binary strings “rich in runs” is modified and extended to prove the result.

An α-finite injury method of the unbounded type

1976 ◽  
Vol 41 (1) ◽  
pp. 1-17
Author(s):  
C. T. Chong
Keyword(s):  
Fine Structure ◽  
Initial Segment ◽  
Fundamental Importance ◽  
Upper Semilattice ◽  
The Past ◽  
Recursively Enumerable ◽  
Background Material ◽  
A Priority ◽  
Admissible Ordinals ◽  
Priority Argument

Let α be an admissible ordinal. In this paper we study the structure of the upper semilattice of α-recursively enumerable degrees. Various results about the structure which are of fundamental importance had been obtained during the past two years (Sacks-Simpson [7], Lerman [4], Shore [9]). In particular, the method of finite priority argument of Friedberg and Muchnik was successfully generalized in [7] to an α-finite priority argument to give a solution of Post's problem for all admissible ordinals. We refer the reader to [7] for background material, and we also follow closely the notations used there.Whereas [7] and [4] study priority arguments in which the number of injuries inflicted on a proper initial segment of requirements can be effectively bounded (Lemma 2.3 of [7]), we tackle here priority arguments in which no such bounds exist. To this end, we focus our attention on the fine structure of Lα, much in the fashion of Jensen [2], and show that we can still use a priority argument on an indexing set of requirements just short enough to give us the necessary bounds we seek.

scholarly journals Natural Language Processing by Enhanced Honey Encryption Technique

2019 ◽  
Vol 8 (12S) ◽  
pp. 159-163
Keyword(s):  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Cyber Attacks ◽  
Binary Form ◽  
Brute Force ◽  
Natural Languages ◽  
Cipher Text ◽  
The Right ◽  
Binary Strings

Traditional encryption systems and techniques have always been vulnerable to brute force cyber-attacks. This is due to bytes encoding of characters utf8 also known as ASCII characters. Therefore, an opponent who intercepts a cipher text and attempts to decrypt the signal by applying brute force with a faulty pass key can detect some of the decrypted signals by employing a mixture of symbols that are not uniformly dispersed and contain no meaningful significance. Honey encoding technique is suggested to curb this classical authentication weakness by developing cipher-texts that provide correct and evenly dispersed but untrue plaintexts after decryption with a false key. This technique is only suitable for passkeys and PINs. Its adjustment in order to promote the encoding of the texts of natural languages such as electronic mails, records generated by man, still remained an open-end drawback. Prevailing proposed schemes to expand the encryption of natural language messages schedule exposes fragments of the plaintext embedded with coded data, thus they are more prone to cipher text attacks. In this paper, amending honey encoded system is proposed to promote natural language message encryption. The main aim was to create a framework that would encrypt a signal fully in binary form. As an end result, most binary strings semantically generate the right texts to trick an opponent who tries to decipher an error key in the cipher text. The security of the suggested system is assessed..

scholarly journals The Number of Moves of the Largest Disc in Shortest Paths on Hanoi Graphs

10.37236/4252 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Simon Aumann ◽  
Katharina A.M. Götz ◽  
Andreas M. Hinz ◽  
Ciril Petr
Keyword(s):  
Shortest Paths ◽  
General Setting ◽  
Optimal Number ◽  
Numerical Results ◽  
Breadth First Search ◽  
Tower Of Hanoi ◽  
Optimal Paths ◽  
Widespread Interest ◽  
Binary Strings

In contrast to the widespread interest in the Frame-Stewart conjecture (FSC) about the optimal number of moves in the classical Tower of Hanoi task with more than three pegs, this is the first study of the question of investigating shortest paths in Hanoi graphs $H_p^n$ in a more general setting. Here $p$ stands for the number of pegs and $n$ for the number of discs in the Tower of Hanoi interpretation of these graphs. The analysis depends crucially on the number of largest disc moves (LDMs). The patterns of these LDMs will be coded as binary strings of length $p-1$ assigned to each pair of starting and goal states individually. This will be approached both analytically and numerically. The main theoretical achievement is the existence, at least for all $n\geqslant p(p-2)$, of optimal paths where $p-1$ LDMs are necessary. Numerical results, obtained by an algorithm based on a modified breadth-first search making use of symmetries of the graphs, lead to a couple of conjectures about some cases not covered by our ascertained results. These, in turn, may shed some light on the notoriously open FSC.

Finding Active Membership Functions for Genetic-Fuzzy Data Mining

2015 ◽  
Vol 14 (06) ◽  
pp. 1215-1242 ◽  
Author(s):  
Chun-Hao Chen ◽  
Tzung-Pei Hong ◽  
Yeong-Chyi Lee ◽  
Vincent S. Tseng
Keyword(s):  
Data Mining ◽  
Association Rules ◽  
Fuzzy Data ◽  
Membership Functions ◽  
Linguistic Terms ◽  
Fuzzy Association Rules ◽  
Fitness Functions ◽  
The Given ◽  
Binary Strings ◽  
Active Membership

Since transactions may contain quantitative values, many approaches have been proposed to derive membership functions for mining fuzzy association rules using genetic algorithms (GAs), a process known as genetic-fuzzy data mining. However, existing approaches assume that the number of linguistic terms is predefined. Thus, this study proposes a genetic-fuzzy mining approach for extracting an appropriate number of linguistic terms and their membership functions used in fuzzy data mining for the given items. The proposed algorithm adjusts membership functions using GAs and then uses them to fuzzify the quantitative transactions. Each individual in the population represents a possible set of membership functions for the items and is divided into two parts, control genes (CGs) and parametric genes (PGs). CGs are encoded into binary strings and used to determine whether membership functions are active. Each set of membership functions for an item is encoded as PGs with real-number schema. In addition, seven fitness functions are proposed, each of which is used to evaluate the goodness of the obtained membership functions and used as the evolutionary criteria in GA. After the GA process terminates, a better set of association rules with a suitable set of membership functions is obtained. Experiments are made to show the effectiveness of the proposed approach.

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