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Regular expressions are used in many practical applications. Practical regular expressions are commonly called "regex". It is known that regex are different from regular expressions. In this paper, we give regex a formal treatment. We make a distinction between regex and extended regex; while regex represent regular languages, extended regex represent a family of languages larger than regular languages. We prove a pumping lemma for the languages expressed by extended regex. We show that the languages represented by extended regex are incomparable with context-free languages and a proper subset of context-sensitive languages. Other properties of the languages represented by extended regex are also studied. [ABSTRACT FROM AUTHOR]

One of the new approaches to data classification uses prefix codes and finite state automata as representations of prefix codes. A prefix code is a (possibly infinite) set of strings such that no string is a prefix of another one. An important task driven by the need for the efficient storage of such automata in memory is the decomposition (in the sense of formal languages concatenation) of prefix codes into prime factors. We investigate properties of such prefix code decompositions. A prime decomposition is a decomposition of a prefix code into a concatenation of nontrivial prime prefix codes. A prefix code is prime if it cannot be decomposed into at least two nontrivial prefix codes. In the paper a linear time algorithm is designed which finds the prime decomposition F[sub 1]F[sub 2]…F[sub k] of a regular prefix code F given by its minimal deterministic automaton. Our results are especially interesting for infinite regular prefix codes. [ABSTRACT FROM AUTHOR]

A deterministic finite automaton (DFA) [formula] is called a cover automaton (DFCA) for a finite language L over some alphabet Σ if [formula], 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]. The DFCA [formula] 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(n[sup 2]) time and space. Furthermore, the new algorithm can also be used to minimize any DFCA, where the best previous method takes O(n[sup 4]) time and space. Since the required data structure is rather complex, an implementation in the common programming language C/C++ is also provided. [ABSTRACT FROM AUTHOR]