Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Computing with first-order logic
Selected papers of the 23rd annual ACM symposium on Theory of computing
Evolving algebras 1993: Lipari guide
Specification and validation methods
Fixpoint logics, relational machines, and computational complexity
Journal of the ACM (JACM)
A restricted second order logic for finite structures
Information and Computation
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We prove that a very basic class of program schemes augmented with access to a queue and an additional numeric universe within which counting is permitted accepts exactly the class of recursively solvable problems. The class of problems accepted when access to the numeric universe is removed is exactly the class of recursively solvable problems that are closed under extensions. We build upon NSPQ(1) an infinite hierarchy of classes of program schemes and show that the class of problems accepted by these program schemes has a zero-one law and consists of those problems defined in any vectorized Lindström logic formed using operators whose corresponding problems are recursively solvable and closed under extensions. We apply our results to yield logical characterizations of complexity classes and provide logical analogs to inequalities and hypotheses from complexity theory involving the classes NP through to ELEMENTARY.