A Logic for PTIME and a Parameterized Halting Problem

In [7] Nash, Remmel, and Vianu have raised the question whether a logic L, already introduced by Gurevich in 1988, captures polynomial time, and they give a reformulation of this question in terms of a parameterized halting problem p-ACC for nondeterministic Turing machines. We analyze the precise relationship between L and p-ACC. We show that p-ACC is not fixed-parameter tractable if "P = NP holds for all time constructible and increasing functions." Moreover, a slightly stronger complexity theoretic hypothesis implies that L does not capture polynomial time. Furthermore, we analyze the complexity of various variants of p-ACC and address its construction problem.

• Type: Journal
• Year: 2010
• Where: BIRTHDAY
• Authors: Yijia Chen, Jörg Flum
• Keywords: Applied Computing, BIRTHDAY 2010, Nondeterministic Turing Machines, Parameterized Halting Problem, Polynomial Time