scholarly journals DERIVED TERMS WITHOUT DERIVATION A SHIFTED PERSPECTIVE ON THE DERIVED-TERM AUTOMATON

2021 ◽  
Vol 37 (3) ◽  
pp. 201-221
Author(s):  
Sylvain Lombardy ◽  
Jacques Sakarovitch
Keyword(s):  
Partial Derivative ◽  
Regular Expression ◽  
Rational Expressions

We present here a construction for the derived term automaton (aka partial derivative, or Antimirov, automaton) of a rational (or regular) expression based on a sole induction on the depth of the expression and without making reference to an operation of derivation of the expression. It is particularly well-suited to the case of weighted rational expressions.

ON THE AVERAGE SIZE OF GLUSHKOV AND PARTIAL DERIVATIVE AUTOMATA

2012 ◽  
Vol 23 (05) ◽  
pp. 969-984 ◽  
Author(s):  
SABINE BRODA ◽  
ANTÓNIO MACHIAVELO ◽  
NELMA MOREIRA ◽  
ROGÉRIO REIS
Keyword(s):  
Partial Derivative ◽  
Upper Bound ◽  
Regular Expression ◽  
Regular Expressions ◽  
Average Case ◽  
Alphabet Size ◽  
Large Alphabet ◽  
Exact Counting ◽  
Average Transition ◽  
Average Size

In this paper, the relation between the Glushkov automaton [Formula: see text] and the partial derivative automaton [Formula: see text] of a given regular expression, in terms of transition complexity, is studied. The average transition complexity of [Formula: see text] was proved by Nicaud to be linear in the size of the corresponding expression. This result was obtained using an upper bound of the number of transitions of [Formula: see text]. Here we present a new quadratic construction of [Formula: see text] that leads to a more elegant and straightforward implementation, and that allows the exact counting of the number of transitions. Based on that, a better estimation of the average size is presented. Asymptotically, and as the alphabet size grows, the number of transitions per state is on average 2. Broda et al. computed an upper bound for the ratio of the number of states of [Formula: see text] to the number of states of [Formula: see text] which is about ½ for large alphabet sizes. Here we show how to obtain an upper bound for the number of transitions in [Formula: see text], which we then use to get an average case approximation. In conclusion, assymptotically, and for large alphabets, the size of [Formula: see text] is half the size of the [Formula: see text]. This is corroborated by some experiments, even for small alphabets and small regular expressions.

ON THE AVERAGE STATE COMPLEXITY OF PARTIAL DERIVATIVE AUTOMATA: AN ANALYTIC COMBINATORICS APPROACH

2011 ◽  
Vol 22 (07) ◽  
pp. 1593-1606 ◽  
Author(s):  
SABINE BRODA ◽  
ANTÓNIO MACHIAVELO ◽  
NELMA MOREIRA ◽  
ROGÉRIO REIS
Keyword(s):  
Lower Bound ◽  
Asymptotic Behaviour ◽  
Partial Derivative ◽  
Regular Expression ◽  
Finite Automata ◽  
Regular Expressions ◽  
Alphabet Size ◽  
State Complexity ◽  
Analytic Combinatorics ◽  
Average State

The partial derivative automaton ([Formula: see text]) is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton ([Formula: see text]). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in [Formula: see text] and describe its asymptotic behaviour. This depends on the alphabet size, k, and for growing k's its limit approaches half the number of states in [Formula: see text]. The lower bound corresponds to consider the [Formula: see text] automaton for the marked version of the regular expression, i.e. where all its letters are made different. Experimental results suggest that the average number of states of this automaton, and of the [Formula: see text] automaton for the unmarked regular expression, are very close to each other.

NORMALIZED EXPRESSIONS AND FINITE AUTOMATA

2007 ◽  
Vol 17 (01) ◽  
pp. 141-154 ◽  
Author(s):  
J.-M. CHAMPARNAUD ◽  
F. OUARDI ◽  
D. ZIADI
Keyword(s):  
Partial Derivative ◽  
Regular Expression ◽  
Linear Time ◽  
Finite Automata ◽  
Experimental Studies ◽  
Regular Expressions ◽  
Theoretical Comparison ◽  
Theoretical Question

There exist two well-known quotients of the position automaton of a regular expression. The first one, called the equation automaton, was first introduced by Mirkin from the notion of prebase and has been redefined by Antimirov from the notion of partial derivative. The second one, due to Ilie and Yu and called the follow automaton, can be obtained by eliminating ε-transitions in an ε-NFA that is always smaller than the classical ε-NFAs (Thompson, Sippu and Soisalon–Soininen). Ilie and Yu discussed the difficulty of succeeding in a theoretical comparison between the size of the follow automaton and the size of the equation automaton and concluded that it is very likely necessary to realize experimental studies. In this paper we solve the theoretical question, by first defining a set of regular expressions, called normalized expressions, such that every regular expression can be normalized in linear time, and proving then that the equation automaton of a normalized expression is always smaller than its follow automaton.

Improvement in Look-ahead Matching Hardware for Regular Expression

2016 ◽  
Vol 136 (10) ◽  
pp. 692-697
Author(s):  
Shuto Higa ◽  
Chikatoshi Yamada ◽  
Kei Miyagi ◽  
Shuichi Ichikawa
Keyword(s):  
Regular Expression ◽  
Look Ahead

Rancang Bangun Aplikasi Chatbot Sebagai Media Pencarian Informasi Anime Menggunakan Regular Expression Pattern Matching

2017 ◽  
Vol 9 (1) ◽  
pp. 19-24 ◽  
Author(s):  
David Domarco ◽  
Ni Made Satvika Iswari
Keyword(s):  
Information Retrieval ◽  
Expression Pattern ◽  
Pattern Matching ◽  
Language Processing ◽  
Regular Expression ◽  
Technology Development ◽  
Data Retrieval ◽  
Index Terms ◽  
Retrieval Engine ◽  
Behavioral Intention To Use

Technology development has affected many areas of life, especially the entertainment field. One of the fastest growing entertainment industry is anime. Anime has evolved as a trend and a hobby, especially for the population in the regions of Asia. The number of anime fans grow every year and trying to dig up as much information about their favorite anime. Therefore, a chatbot application was developed in this study as anime information retrieval media using regular expression pattern matching method. This application is intended to facilitate the anime fans in searching for information about the anime they like. By using this application, user can gain a convenience and interactive anime data retrieval that can’t be found when searching for information via search engines. Chatbot application has successfully met the standards of information retrieval engine with a very good results, the value of 72% precision and 100% recall showing the harmonic mean of 83.7%. As the application of hedonic, chatbot already influencing Behavioral Intention to Use by 83% and Immersion by 82%. Index Terms—anime, chatbot, information retrieval, Natural Language Processing (NLP), Regular Expression Pattern Matching

1/(1-1/k)-Optimal Algorithm for Regular Expression Grouping

2012 ◽  
Vol 23 (9) ◽  
pp. 2261-2272 ◽  
Author(s):  
Ting-Wen LIU ◽  
Yong SUN ◽  
Dong-Bo BU ◽  
Li GUO ◽  
Bin-Xing FANG
Keyword(s):  
Regular Expression ◽  
Optimal Algorithm

Efficient Regular Expression Compression Algorithm for Deep Packet Inspection

2009 ◽  
Vol 20 (8) ◽  
pp. 2214-2226 ◽  
Author(s):  
Qian XU ◽  
Yue-Peng E ◽  
Jing-Guo GE ◽  
Hua-Lin QIAN
Keyword(s):  
Regular Expression ◽  
Compression Algorithm ◽  
Deep Packet Inspection ◽  
Packet Inspection
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