A TIME AND SPACE EFFICIENT ALGORITHM FOR MINIMIZING COVER AUTOMATA FOR FINITE LANGUAGES

2003 ◽  
Vol 14 (06) ◽  
pp. 1071-1086 ◽  
Author(s):  
HEIKO KÖRNER
Keyword(s):  
Data Structure ◽  
Programming Language ◽  
Finite Automaton ◽  
Efficient Algorithm ◽  
Previous Method ◽  
Deterministic Finite Automaton ◽  
Time And Space ◽  
Language L ◽  
Finite Language ◽  
The Common

A deterministic finite automaton (DFA) [Formula: see text] is called a cover automaton (DFCA) for a finite language L over some alphabet Σ if [Formula: see text], with l being the length of some longest word in L. Thus a word w ∈ Σ* is in L if and only if |w| ≤ l and [Formula: see text]. The DFCA [Formula: see text] is minimal if no DFCA for L has fewer states. In this paper, we present an algorithm which converts an n–state DFA for some finite language L into a corresponding minimal DFCA, using only O(n log n) time and O(n) space. The best previously known algorithm requires O(n2) time and space. Furthermore, the new algorithm can also be used to minimize any DFCA, where the best previous method takes O(n4) time and space. Since the required data structure is rather complex, an implementation in the common programming language C/C++ is also provided.

Model reformulation for conflict-free routing problems using Petri Net and Deterministic Finite Automaton

2015 ◽  
Vol 20 (3) ◽  
pp. 262-269 ◽  
Author(s):  
Ryosuke Nakamura ◽  
Kenji Sawada ◽  
Seiichi Shin ◽  
Kenji Kumagai ◽  
Hisato Yoneda
Keyword(s):  
Petri Net ◽  
Finite Automaton ◽  
Deterministic Finite Automaton ◽  
Routing Problems ◽  
Model Reformulation

FINDING THE LARGEST EMPTY DISK CONTAINING A QUERY POINT

2013 ◽  
Vol 23 (04n05) ◽  
pp. 335-355 ◽  
Author(s):  
HAIM KAPLAN ◽  
MICHA SHARIR
Keyword(s):  
Data Structure ◽  
Efficient Algorithm ◽  
Alternative Solution ◽  
Query Point

Let P be a set of n points in the plane. We present an efficient algorithm for preprocessing P, so that, for a given query point q, we can quickly report the largest disk that contains q but its interior is disjoint from P. The storage required by the data structure is O(n log n), the preprocessing cost is O(n log 2 n), and a query takes O( log 2 n) time. We also present an alternative solution with an improved query cost and with slightly worse storage and preprocessing requirements.

IMIDB: An Algorithm for Indexed Mining of Incremental Databases

2017 ◽  
Vol 26 (1) ◽  
pp. 69-85
Author(s):  
Mohammed M. Fouad ◽  
Mostafa G.M. Mostafa ◽  
Abdulfattah S. Mashat ◽  
Tarek F. Gharib
Keyword(s):  
Data Structure ◽  
Association Rules ◽  
Efficient Algorithm ◽  
Performance Comparison ◽  
Incremental Mining ◽  
Itemset Mining ◽  
Large Databases ◽  
Transactional Databases ◽  
Dynamic Databases ◽  
Database Size

AbstractAssociation rules provide important knowledge that can be extracted from transactional databases. Owing to the massive exchange of information nowadays, databases become dynamic and change rapidly and periodically: new transactions are added to the database and/or old transactions are updated or removed from the database. Incremental mining was introduced to overcome the problem of maintaining previously generated association rules in dynamic databases. In this paper, we propose an efficient algorithm (IMIDB) for incremental itemset mining in large databases. The algorithm utilizes the trie data structure for indexing dynamic database transactions. Performance comparison of the proposed algorithm to recently cited algorithms shows that a significant improvement of about two orders of magnitude is achieved by our algorithm. Also, the proposed algorithm exhibits linear scalability with respect to database size.

scholarly journals Algoritmo eficiente en la generación de una tabla de primalidad de números usando Programación Funcional [An application of a simple and efficient algorithm to generate a prime number table using Functional Programming]

2014 ◽  
Author(s):  
Omar Iván TREJOS BURITICÁ
Keyword(s):  
Programming Language ◽  
Efficient Algorithm ◽  
Functional Programming ◽  
Logical Structure ◽  
Prime Numbers ◽  
Algorithm Efficiency ◽  
Palabras Clave ◽  
Simple Logic ◽  
Math Problems ◽  
Modern Technologies

Resumen En el presente artículo se acude a la Programación Funcional para generar una tabla de análisis de primalidad de números en un rango dado a partir del uso de un algoritmo que, por las necesidades del mismo objetivo, tiene características de ser eficiente. Se plantea la fundamentación de dicho algoritmo y además se aprovecha su estructura lógica para resolver el problema propuesto. El propósito de este artículo es mostrar una arista útil de la eficiencia algorítmica teniendo en cuenta las características tecnológicas modernas y los problemas que la matemática provee. Se hace uso del lenguaje de programación Scheme y se aprovechan sus potencialidades para manejo, tamaño y cálculo de datos. Se demuestra que, acudiendo a algoritmos eficientes y a una lógica muy simple, la tecnología computacional moderna puede ser de una inmensa utilidad para resolver problemas matemáticos. Palabras Clave: Algoritmo, eficiencia, matemáticas, números primos, programación funcional   Abstract In this article, we use Functional Programming to generate an analytic table of prime numbers in a specific range using an efficient algorithm. You can find the foundation and we use its logical structure to solve the problem. The proposal of this article is to show the useful face of the applied efficient algorithmic knowing the modern technologies y the math problems. We use Scheme as a programming language and we use its potentialities to manage, to storage and calculate data. We demonstrate that, using efficient algorithms and a simple logic, the computational technologies are very useful solving math problems. Keywords: Algorithm, efficiency, maths, prime numbers, Functional programming

Finding Undercut-Free Parting Directions for Polygons with Curved Edges

2005 ◽  
Vol 6 (1) ◽  
pp. 60-68 ◽  
Author(s):  
Sara McMains ◽  
Xiaorui Chen
Keyword(s):  
Opposite Direction ◽  
Efficient Algorithm ◽  
Time And Space ◽  
Normal Graph

We consider the problem of whether a given geometry can be molded in a two-part, rigid, reusable mold with opposite removal directions. We describe an efficient algorithm for solving the opposite direction moldability problem for a 2D “polygon” bounded by edges that may be either straight or curved. We introduce a structure, the normal graph of the polygon, that represents the range of normals of the polygon’s edges, along with their connectivity. We prove that the normal graph captures the directions of all lines corresponding to feasible parting directions. Rather than building the full normal graph, which could take time O(nlogn) for a polygon bounded by n possibly curved edges, we build a summary structure in O(n) time and space, from which we can determine all feasible parting directions in time O(n).

The Research for Extension Software Data Structure

2010 ◽  
Vol 121-122 ◽  
pp. 849-853
Author(s):  
Xiao Mao Wu ◽  
Hui Ming Guo ◽  
Yong Quan Yu
Keyword(s):  
Data Structure ◽  
Software Design ◽  
Element Model ◽  
Structure Model ◽  
The Common ◽  
Matter Element Model

In this paper, we analyze the data structure of design of matter-element model from the level of software design, combined with the features of the common used data structure and matter-element model in Extenics, finally propose a new data structure model, which adapt to computation, reasoning and transformation using matter-element model.

LOGARITHMIC-TIME LINK PATH QUERIES IN A SIMPLE POLYGON

1995 ◽  
Vol 05 (04) ◽  
pp. 369-395 ◽  
Author(s):  
ESTHER M. ARKIN ◽  
JOSEPH S.B. MITCHELL ◽  
SUBHASH SURI
Keyword(s):  
Data Structure ◽  
Shortest Path ◽  
Simple Polygon ◽  
Additive Constant ◽  
Time And Space ◽  
Link Distance ◽  
Path Distance ◽  
Path Queries ◽  
Shortest Path Distance ◽  
Small Additive

We develop a data structure for answering link distance queries between two arbitrary points in a simple polygon. The data structure requires O(n3) time and space for its construction and answers link distance queries in O(log n) time, after which a minimum-link path can be reported in time proportional to the number of links. Here, n denotes the number of vertices of the polygon. Our result extends to link distance queries between pairs of segments or polygons. We also propose a simpler data structure for computing a link distance approximately, where the error is bounded by a small additive constant. Finally, we also present a scheme for approximating the link and the shortest path distance simultaneously.

MAGIC NUMBERS FOR SYMMETRIC DIFFERENCE NFAS

2005 ◽  
Vol 16 (05) ◽  
pp. 1027-1038 ◽  
Author(s):  
LYNETTE VAN ZIJL
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Symmetric Difference ◽  
Magic Numbers ◽  
Deterministic Finite Automaton ◽  
Nondeterministic Finite Automata ◽  
Binary Case ◽  
Nondeterministic Finite Automaton

Iwama et al. showed that there exists an n-state binary nondeterministic finite automaton such that its equivalent minimal deterministic finite automaton has exactly 2n - α states, for all n ≥ 7 and 5 ≤ α ≤ 2n-2, subject to certain coprimality conditions. We investigate the same question for both unary and binary symmetric difference nondeterministic finite automata. In the binary case, we show that for any n ≥ 4, there is an n-state symmetric difference nondeterministic finite automaton for which the equivalent minimal deterministic finite automaton has 2n - 1 + 2k - 1 - 1 states, for 2 < k ≤ n - 1. In the unary case, we consider a large practical subclass of unary symmetric difference nondeterministic finite automata: for all n ≥ 2, we argue that there are many values of α such that there is no n-state unary symmetric difference nondeterministic finite automaton with an equivalent minimal deterministic finite automaton with 2n - α states, where 0 < α < 2n - 1. For each n ≥ 2, we quantify such values of α precisely.

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