### Time-space lower bounds for satisfiabilityTime-space lower bounds for satisfiability

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 Author Fortnow, Lance ♦ Lipton, Richard ♦ van Melkebeek, Dieter ♦ Viglas, Anastasios Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2005 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Complexity of satisfiability ♦ Time-space lower bounds Abstract We establish the first polynomial time-space lower bounds for satisfiability on general models of computation. We show that for any constant $\textit{c}$ less than the golden ratio there exists a positive constant $\textit{d}$ such that no deterministic random-access Turing machine can solve satisfiability in time $n^{c}$ and space $n^{d},$ where $\textit{d}$ approaches 1 when $\textit{c}$ does. On conondeterministic instead of deterministic machines, we prove the same for any constant $\textit{c}$ less than &2radic;.Our lower bounds apply to nondeterministic linear time and almost all natural NP-complete problems known. In fact, they even apply to the class of languages that can be solved on a nondeterministic machine in linear time and space $n^{1/c}.Our$ proofs follow the paradigm of indirect diagonalization. We also use that paradigm to prove time-space lower bounds for languages higher up in the polynomial-time hierarchy. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2005-11-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 52 Issue Number 6 Page Count 31 Starting Page 835 Ending Page 865

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Source: ACM Digital Library