All Outputs (3)

Hierarchies in classes of program schemes (1999)
Journal Article
Arratia-Quesada, A., Chauhan, S., & Stewart, I. (1999). Hierarchies in classes of program schemes. Journal of Logic and Computation, 9(6), 915-957. https://doi.org/10.1093/logcom/9.6.915

We begin by proving that the class of problems accepted by the program schemes of NPS is exactly the class of problems defined by the sentences of transitive closure logic (program schemes of NPS are obtained by generalizing basic non-deterministic w... Read More about Hierarchies in classes of program schemes.

A perspective on Lindström quantifiers and oracles (1999)
Book Chapter
Stewart, I. (1999). A perspective on Lindström quantifiers and oracles. In J. Väänänen (Ed.), Generalized quantifiers and computation : 9th European Summer School in Logic, Language, and Information ESSLLI’97 Workshop, 11-22 August 1997, Aix-en-Provence, France ; revised lectures (51-71). Springer Verlag. https://doi.org/10.1007/3-540-46583-9_3

This paper presents a perspective on the relationship between Lindström quantifiers in model theory and oracle computations in complexity theory. We do not study this relationship here in full generality (indeed, there is much more work to do in orde... Read More about A perspective on Lindström quantifiers and oracles.

On the power of built-in relations in certain classes of program schemes (1999)
Journal Article
Chauhan, S., & Stewart, I. (1999). On the power of built-in relations in certain classes of program schemes. Information Processing Letters, 69(2), 77-82. https://doi.org/10.1016/s0020-0190%2898%2900196-3

We completely classify the relative expressibilities of the program schemes of NPS augmented with the built-in relations: linear order; addition; multiplication; and BIT. We employ pebble games allied with some number theory.