The Separation of Relativized Versions of P and DNP for the Ring of the Reals

: We consider the uniform BSS model of computation where the machines can perform additions, multiplications, and tests of the form x 0. The oracle machines can also check whether a tuple of real numbers belongs to a given oracle set or not. We present oracle sets containing positive integers and pairs of numbers, respectively, such that the classes P and DNP relative to these oracles are not equal. The first set is constructed by diagonalization techniques and the second one is derived from the Knapsack Problem. Key Words: BSS model, oracle machine, relativizations, binary non-determinism, digital non-determinism

• Type: Journal
• Year: 2010
• Where: JUCS
• Authors: Christine Gaßner
• Keywords: BSS Model, JUCS 2010, Oracle, Oracle Machine