Constructing NFAs by Optimal Use of Positions in Regular Expressions

Abstract

We give two new algorithms for constructing small nondeterministic finite automata (NFA) from regular expressions. The first constructs NFAs with ?-moves (?NFA) which are smaller than all the other ?NFAs obtained by similar constructions. Their size is at most 3/2 |?|+ 5/2, where ? is the regular expression. The second constructs NFAs. It uses ?-elimination in the ?NFAs we just introduced and builds a quotient of the well-known position automaton. Our NFA is always smaller and faster to compute than the position automaton. It uses optimally the information from the positions of a regular expression.