Languages that capture complexity classes
SIAM Journal on Computing
Some relationships between logics of programs and complexity theory
Theoretical Computer Science
Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Recursive applicative program schemes
Handbook of theoretical computer science (vol. B)
Handbook of theoretical computer science (vol. B)
On the power of built-in relations in certain classes of program schemes
Information Processing Letters
Even Simple Programs Are Hard To Analyze
Journal of the ACM (JACM)
Programming primitives for database languages
POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Universality of data retrieval languages
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Adding For-Loops to First-Order Logic
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Generalized Quantifiers and 0-1 Laws
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Record of the Project MAC conference on concurrent systems and parallel computation
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We characterize the class of problems accepted by a class of program schemes with arrays, NPSA, as the class of problems defined by the sentences of a logic formed by extending first-order logic with a particular uniform sequence of Lindström quantifiers. We prove that our logic, and consequently our class of program schemes, has a zero-one law. However, we show that there are problems definable in a basic fragment of our logic, and so also accepted by basic program schemes, which are not definable in bounded-variable infinitary logic. Hence, the class of problems NPSA is not contained in the class of problems defined by the sentences of partial fixed-point logic even though in the presence of a built-in successor relation, both NPSA and partial fixed-point logic capture the complexity class PSPACE.