Position Automaton Construction for Regular Expressions with Intersection ⋆ Sabine Broda, Ant´onio Machiavelo, Nelma Moreira, and Rog´ erio Reis CMUP, Faculdade de Ciˆ encias da Universidade do Porto, Portugal sbb@dcc.fc.up.pt,ajmachia@fc.up.pt,{nam,rvr}@dcc.fc.up.pt Abstract. Positions and derivatives are two essential notions in the con- version methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regu- lar expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction gener- alizes the notion of position making it compatible with intersection. The resulting automaton is homogeneous and has the partial derivative au- tomaton as its quotient. 1 Introduction The position automaton, introduced by Glushkov [12], permits the conversion of a simple regular expression (involving only the sum, concatenation and star operations) into an equivalent nondeterministic finite automaton (NFA) without ε-transitions. The states in the position automaton (A pos ) correspond to the positions of letters in the corresponding regular expression plus an additional initial state. McNaughton and Yamada [15] also used the positions of a regular expression to define an automaton, however they directly computed a determin- istic version of the position automaton. The position automaton has been well studied [8,3] and is considered the standard automaton simulation of a regular expression [16]. Some of its interesting properties are: homogeneity, i.e. for each state, all in-transitions have the same label (letter); whenever deterministic, these automata characterize certain families of unambiguous regular expressions, and can be computed in quadratic time [4]; other automata simulations of regular expressions are quotients of the A pos , e.g. partial derivative automata (A pd ) [9] and follow automata [14]. Many authors observed that the position automaton construction could not directly be extended to regular expressions with intersection [3,6], as intersection (and also complementation) is not compatible with the notion of position. In fact, considering positions of letters in the expression (ab ⋆ ) ∩ a, whose language is {a}, we obtain the regular expression (a 1 b ⋆ 2 ) ∩ a 3 . Interpreting a 1 and a 3 as distinct alphabet symbols, the language described by this expression is empty and there is ⋆ This work was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.