Finite automataComputation complexitySeveral algorithms have been designed to convert a regular expression into an equivalent finite automaton. One of the most popular constructions, due to Glushkov and to McNaughton and Yamada, is based on the computation of the Null, First, Last and Follow sets ...
We give a Kleene theorem for 1-unambiguous languages and characterize 1-unambiguous regular languages in terms of structural properties of the minimal deterministic automata that recognize them. As a result we are able to prove the decidability of whether a given regular expression denotes a 1-...
International Conference on Implementation and Application of Automata 347Accesses Abstract In this article we generalize the concepts of position automaton and ZPC structure to the regularK-expressions. We show that the ZPC structure can be built in linear time in the size of the expression and tha...
Regular expressions are used to specify regular languages and finite automata are used to recognize the regular languages. Many computer applications such as compilers, operating system utilities, text editors make use of regular languages. In these applications, the regular expressions and finite automat...
Decimal = (sign)?(digit)+ Identifier = (letter)(letter | digit)* The only problem left with the lexical analyzer is how to verify the validity of a regular expression used in specifying the patterns of keywords of a language. A well-accepted solution is to use finite automata for verifica...
If a string can be derived from the rules 1, 2 and 3 then it is also a regular expression. Note that a* means zero or more occurrence of a in the string while a+ means that one or more occurrence of a in the string. That means a* denotes language L = {є , a, aa, aaa,...
A consequence of this definition is the following property: E = { w in X*: E >= w } that is, every regular expression is equal to the set of words derived from it. (1.9) Infinite Automata and Recursive Systems of Equations Suppose you attempt to treat the following set as a regular...
dregex - Deterministic Regular Expression Engine dregex is a Java library that implements a regular expression engine using deterministic finite automata (DFA). It supports some Perl-style features and yet retains linear matching time. It can, additionally, do set operations (union, intersection, an...
In fact, this machine accepts the regular language (ab∪aba)* (Recall that I am being sloppy about parenthesizing. This isn't a "real" regular expression but you get the point that when I say that I mean L(((ab)∪((ab)a))*) I'm sure.) We've got lots of magic already, so...
A string is a regular expression if and only if it can be derived from the primitive regular expressions by a finite number of applications of the rules in step 2. The next definition describes the languages that can be represented by regular expressions. Definition 11 The language L(r) deno...