Search results for "BIT predicate"

The Descriptive Complexity Approach to LOGCFL

1999

Building upon the known generalized-quantifier-based firstorder 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 contextfree language" is LOGCFL-complete under quantifier-free BIT-free interpre…