Limits on Alternation-Trading Proofs for Time-Space Lower Bounds

This paper characterizes alternation trading based proofs that the satisfiability problem is not in the time and space bounded class DTISP(n(c), n(epsilon)), for various values c < 2 and epsilon < 1. We characterize exactly what can be proved for epsilon is an element of o(1) with currently known methods, and prove the conjecture of Williams that the best known lower bound exponent c = 2cos(pi/7) is optimal for alternation trading proofs. For general time-space tradeoff lower bounds on satisfiability, we give a theoretical and computational analysis of the alternation trading proofs for 0 < epsilon < 1, again proving time lower bounds for various values of epsilon which are optimal for the alternation trading proof paradigm.