Location automata for regular expressions with shuffle and intersection

Abstract

We define the notion of location for regular expressions with shuffle by extending the notion of position in standard regular expressions. Locations allow for the definition of the sets Follow, First, and Last with their usual semantics. From these, we construct an automaton for regular expressions with shuffle (APOS), which generalises the standard position/Glushkov automaton. The sets mentioned above are also the foundation for other constructions, such as the Follow automaton, and automata based on pointed expressions. As a consequence, all these constructions can be generalised to the shuffle operator. We show that the partial derivative automaton is a right-quotient of APOS. We relate APOS with another automaton construction based on positions that has been previously studied (A∂pos). The prefix automaton is extended to the shuffle operator and shown not to be a quotient of APOS. Locations are also used to define a position automaton for regular expressions with the intersection.