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

Samuel R. Buss, Ryan Williams
2012 2012 IEEE 27th Conference on Computational Complexity  
This paper characterizes alternation trading based proofs that the satisfiability problem is not in the time and space bounded class DTISP(n c , n ), for various values c < 2 and < 1. We characterize exactly what can be proved for ∈ o(1) with currently known methods, and prove the conjecture of Williams that the best known lower bound exponent c = 2 cos(π/7) is optimal for alternation trading proofs. For general time-space tradeoff lower bounds on satisfiability, we give a theoretical and
more » ... eoretical and computational analysis of the alternation trading proofs for 0 < < 1, again proving time lower bounds for various values of which are optimal for the alternation trading proof paradigm.
doi:10.1109/ccc.2012.30 dblp:conf/coco/BussW12 fatcat:dvquddstuvgg5ifyxrv4zf3c2u