Forest Expressions

We define regular expressions for unranked trees (actually, ordered sequences of unranked trees, called forests). These are compared to existing regular expressions for trees. On the negative side, our expressions have complementation, and do not define all regular languages. On the positive side, our expressions do not use variables, and have a syntax very similar to that of regular expressions for word languages. We examine the expressive power of these expressions, especially from a logical point of view. The class of languages defined corresponds to a form of chain logic [5, 6]. Furthermore, the star-free expressions coincide with first-order logic. Finally, we show that a concatenation hierarchy inside the expressions corresponds to the quantifier prefix hierarchy for first-order logic, generalizing a result of Wolfgang Thomas [4].

• Type: Conference
• Year: 2007
• Where: CSL
• Authors: Mikolaj Bojanczyk
• Keywords: CSL 2007, Regular Expressions, Unranked Trees, first-order Logic