Regular Expressions into Finite Automata

It is a well-established fact that each regular expression can be transformed into a nondeterministic finite automaton (NFA) with or without ∈-transitions, and all authors seem to provide their own variant of the construction. Of these, Berry and Sethi [BS86] have shown that the construction of an ∈-free NFA due to Glushkov [Glu61] is a natural representation of the regular expression, because it can be described in terms of the Brzozowski derivatives [Brz64] of the expression. Moreover, the Glushkov construction also plays a significant role in the document processing area: The SGML standard [ISO86], now widely adopted by publishing houses and government agencies for the syntactic specification of textual markup systems, uses deterministic regular expressions, i.e. expressions whose Glushkov automaton is deterministic, as a description language for document types.