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Inductive TimeSpace Lower Bounds for SAT and Related Problems
 Computational Complexity
, 2005
"... Abstract. We improve upon indirect diagonalization arguments for lower bounds on explicit problems within the polynomial hierarchy. Our contributions are summarized as follows. 1. We present a technique that uniformly improves upon most known nonlinear time lower bounds for nondeterminism andalterna ..."
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Cited by 14 (5 self)
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Abstract. We improve upon indirect diagonalization arguments for lower bounds on explicit problems within the polynomial hierarchy. Our contributions are summarized as follows. 1. We present a technique that uniformly improves upon most known nonlinear time lower bounds for nondeterminism andalternating computation, on both subpolynomial (n o(1) ) space RAMs and sequential onetape machines with random access to the input. We obtain improved lower bounds for Boolean satisfiability (SAT), as well as all NPcomplete problems that have efficient reductions from SAT, and ΣkSAT, for constant k ≥ 2. For example, SAT cannot be solved by random access machines using n √ 3 time and subpolynomial space. 2. We show how indirect diagonalization leads to timespace lower bounds for computation with bounded nondeterminism. For both the random access and multitape Turing machine models, we prove that for all k ≥ 1, there is a constant ck> 1 such that linear time with n 1/k nondeterministic bits is not contained in deterministic n ck time with subpolynomial space. This is used to prove that satisfiability of Boolean circuits with n inputs and n k size cannot be solved by deterministic multitape Turing machines running in n k·ck time and subpolynomial space.
Algorithms and Resource Requirements for Fundamental Problems
, 2007
"... no. DGE0234630. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. ..."
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Cited by 10 (7 self)
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no. DGE0234630. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.
Relationships among Time and Space Complexity Classes
, 2001
"... Multitape Turing machines are the canonical mathematical model for studying the time and space requirements of problems. Most computational problems that are ecient in practice have ecient algorithms on multitape Turing machines, and vice versa. ..."
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Cited by 1 (0 self)
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Multitape Turing machines are the canonical mathematical model for studying the time and space requirements of problems. Most computational problems that are ecient in practice have ecient algorithms on multitape Turing machines, and vice versa.