Program schemes, arrays, Lindström quantifiers and zero-one laws

Program Schemes, Arrays, Lindström Quantifiers and Zero-One Laws

We characterize the class of problems accepted by a class of program schemes with arrays, NPSA, as the class of problems deened by the sentences of a logic formed by extending rst-order logic with a particular uniform (or vectorized) sequence of Lindstrr om quantiiers. A simple extension of a known result thus enables us to prove that our logic, and consequently our class of program schemes, ha...

A Perspective on Lindström Quantifiers and Oracles

Lindström Quantifiers and Leaf Language Definability

We show that examinations of the expressive power of logical formulae enriched by Lindström quantifiers over ordered finite structures have a well-studied complexity-theoretic counterpart: the leaf language approach to define complexity classes. Model classes of formulae with Lindström quantifiers are nothing else than leaf language definable sets. Along the way we tighten the best up to now kn...

Zero-One Law and Rational Quantifiers

We study extensions of finite variable logic Lω ∞ω by generalized quantifiers. We use strong version of so-called extension axioms and pebble games to show the zero-one law for the obtained logic. In some cases we show that the zero-one law does not hold by constructing a sentence with no limit probability. We construct these sentences with as few variables as possible and thus find the exact n...

Regular languages definable by Lindström quantifiers

In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.