Multi-tilde-bar expressions and their automata

Extended to multi-tilde–bar regular expressions and efficient finite automata constructions

“…We now recall the syntactical definition of extended to multi-tilde-bar regular expressions (EmtbREs) [6]. Notice that these expressions will be proven to be regular later (see Corollary 1).…”

“…(See [6].) An Extended to multi-tilde-bar Regular Expression (EmtbRE) over an alphabet A is inductively defined by:…”

“…The original semantical definition of the language of an EmtbRE [6] is based on the description of how words are generated by overlapping tildes and bars. Our approach is different: we provide a recursive definition of the language of an EmtbRE.…”

“…Following [13,17], these algorithms are based on the computation of the Null, First, Last and Follow sets (called Glushkov functions) associated with a linearized version of the expression. Recently Mignot [18] considered a family of extended expressions called Extended to multi-tilde-bar Regular Expressions (EmtbREs) and he showed that, under some restrictions, the Glushkov functions can be defined for an EmtbRE (see also [6,7]). This class of regular expressions is superpolynomially more succinct than standard expressions [6].…”

“…Recently Mignot [18] considered a family of extended expressions called Extended to multi-tilde-bar Regular Expressions (EmtbREs) and he showed that, under some restrictions, the Glushkov functions can be defined for an EmtbRE (see also [6,7]). This class of regular expressions is superpolynomially more succinct than standard expressions [6]. In this paper we present an algorithm which efficiently computes the Glushkov functions of an unrestricted EmtbRE.…”