### From Almost Optimal Algorithms to Logics for Complexity Classes via Listings and a Halting ProblemFrom Almost Optimal Algorithms to Logics for Complexity Classes via Listings and a Halting Problem

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 Author Chen, Yijia ♦ Flum, Jrg Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2012 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Optimal algorithms ♦ Listings ♦ Logics for complexity classes ♦ Parameterized complexity Abstract Let C denote one of the complexity classes “polynomial time,” “logspace,” or “nondeterministic logspace.” We introduce a logic $L(C)_{inv}$ and show generalizations and variants of the equivalence $(L(C)_{inv}$ captures C if and only if there is an almost C-optimal algorithm in C for the set Taut of tautologies of propositional logic). These statements are also equivalent to the existence of a listing of subsets in C of Taut by corresponding Turing machines and equivalent to the fact that a certain parameterized halting problem is in the parameterized complexity class $XC_{uni}.$ 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 2012-08-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 59 Issue Number 4 Page Count 34 Starting Page 1 Ending Page 34

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Source: ACM Digital Library