The descriptive complexity approach to LOGCFL

Building upon the known generalized-quantifier-based first-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC1 and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the context-free languages, and we obtain the surprising result that a variant of Greibach’s “hardest context-free language” is LOGCFL-complete under quantifier-free BIT-free projections. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that first-order logic with majority of pairs is strictly more expressive than first-order with ma...

• Type: Journal
• Year: 1998
• Where: CORR
• Authors: Clemens Lautemann, Pierre McKenzie, Thomas Schwentick, Heribert Vollmer
• Keywords: CORR 1998, Education, Generalized-quantifier-based first-order Characterization, Groupoidal Quantifier, Unary Groupoidal Quantifiers