Syracuse University SURFACE College of Engineering and Computer Science - Former Departments, Centers, Institutes and College of Engineering and Computer Science Projects 1997 Semantics vs. Syntax vs. Computations: Machine models for type-2 polynomial-time bounded functionals James S. Royer Syracuse University, School of Computer and Information Science,
[email protected] Follow this and additional works at: https://surface.syr.edu/lcsmith_other Part of the Computer Sciences Commons Recommended Citation Royer, James S., "Semantics vs. Syntax vs. Computations: Machine models for type-2 polynomial-time bounded functionals" (1997). College of Engineering and Computer Science - Former Departments, Centers, Institutes and Projects. 19. https://surface.syr.edu/lcsmith_other/19 This Article is brought to you for free and open access by the College of Engineering and Computer Science at SURFACE. It has been accepted for inclusion in College of Engineering and Computer Science - Former Departments, Centers, Institutes and Projects by an authorized administrator of SURFACE. For more information, please contact
[email protected]. Semantics vs. Syntax vs. Computations Machine Models for Type-2 Polynomial-Time Bounded Functionals Intermediate Draft, Revision 2 + ǫ James S. Royer School of Computer and Information Science Syracuse University Syracuse, NY 13244 USA Email:
[email protected] Abstract This paper investigates analogs of the Kreisel-Lacombe-Shoen®eld Theorem in the con- text of the type-2 basic feasible functionals. We develop a direct, polynomial-time analog of effective operation in which the time boundingon computationsismodeled after Kapronand Cook's scheme fortheirbasic poly- nomial-time functionals. We show that if P = NP, these polynomial-time effective op- erations are strictly more powerful on R (the class of recursive functions) than the basic feasible functions.