## Semantics vs. Syntax vs. Computations -- Machine Models For Type-2 . . . (1997)

Venue: | JOURNAL OF COMPUTER AND SYSTEM SCIENCE |

Citations: | 10 - 0 self |

### BibTeX

@ARTICLE{Royer97semanticsvs.,

author = {James Royer},

title = {Semantics vs. Syntax vs. Computations -- Machine Models For Type-2 . . . },

journal = {JOURNAL OF COMPUTER AND SYSTEM SCIENCE},

year = {1997},

volume = {54},

pages = {424--436}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper investigates analogs of the Kreisel-Lacombe-Shoenfield Theorem in the context of the type-2 basic feasible functionals. We develop a direct, polynomial-time analog of effective operation in which the time boundingon computations is modeled after Kapron and Cook's scheme for their basic polynomial-time functionals. We show that if P = NP, these polynomial-time effective operations are strictly more powerful on R (the class of recursive functions) than the basic feasible functions. We also consider a weaker notion of polynomial-time effective operation where the machines computing these functionals have access to the computations of their procedural parameter, but not to its program text. For this version of polynomial-time effective operations, the analog of the Kreisel-Lacombe-Shoenfield is shown to hold---their power matches that of the basic feasible functionals on R.