Paper: There is no recursive axiomatization for feasible functionals of type 2 (at LICS 1992)

Authors: Anil Seth

Abstract

The author shows a class of type-two feasible functionals, C ₂, that satisfies Cook's conditions, (1990) and cannot be expressed as the lambda closure of type-one poly-time functions and any recursively enumerable set of type-two feasible functionals. Further, no class of total type-two functionals containing this class is representable as the lambda closure of a recursively enumerable set of type-two total computable functionals and type-one poly-time functions. The definition of C₂ provides a clear computational procedure for functionals of C₂. Using functionals of class C₂ a more general notion of polynomial-time reducibility between two arbitrary type-one functions can be introduced

BibTeX

  @InProceedings{Seth-Thereisnorecursivea,
    author = 	 {Anil Seth},
    title = 	 {There is no recursive axiomatization for feasible functionals of type 2 },
    booktitle =  {Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science (LICS 1992)},
    year =	 {1992},
    month =	 {June}, 
    pages =      {286--295},
    location =   {Santa Cruz, CA, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }