Regular Sets of Higher-Order Pushdown Stacks

Abstract. It is a well-known result that the set of reachable stack contents in a pushdown automaton is a regular set of words. We consider the more general case of higher-order pushdown automata and investigate, with a particular stress on effectiveness and complexity, the natural notion of regularity for higher-order stacks: a set of level k stacks is regular if it is obtained by a regular sequence of level k operations. We prove that any regular set of level k stacks admits a normalized representation and we use it to show that the regular sets of a given level form an effective Boolean algebra. In fact, this notion of regularity coincides with the notion of monadic second order definability over the canonical structure associated to level k stacks. Finally, we consider the link between regular sets of stacks and families of infinite graphs defined by higher-order pushdown systems.

• Type: Conference
• Year: 2005
• Where: MFCS
• Authors: Arnaud Carayol
• Keywords: MFCS 2005, Pushdown Automaton, Reachable Stack Contents, Regular Sets