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- W1968653910 abstract "The concepts of $textbf{SAT}$-hardness and $textbf{SAT}$-completeness modulo npolylogn time and linear size reducibility, denoted by $textbf{SAT}$-hard (npolylogn, n) and $textbf{SAT}$-complete (npolylogn, n), respectively, are introduced. Regardless of whether $textbf{P} = textbf{NP}$ or $textbf{P} neq textbf{NP}$, it is shown that intuitively Each $textbf{SAT}$-hard (npolylogn, n) problem requires essentially at least as much deterministic time as, and Each $textbf{SAT}$-complete (npolylogn, n) problem requires essentially the same deterministic time as the satisfiability problem for 3CNF formulas. It is proved that the $leqq$, satisfiability, tautology, unique satisfiability, equivalence, and minimization problems are already $textbf{SAT}$-complete (npolylogn, n), for very simple Boolean formulas and for very simple systems of Boolean equations. These completeness results are used to characterize the deterministic time complexities of a number of problems for lattices, propositional calculi, combinatorial circuits, finite fields, rings ${bf Z}_{k}(k geqq 2)$, binary decision diagrams, and monadic single variable program schemes. A number of these hardness results are “best” possible." @default.
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- W1968653910 date "1990-02-01" @default.
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- W1968653910 title "The Complexity of Very Simple Boolean Formulas with Applications" @default.
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- W1968653910 doi "https://doi.org/10.1137/0219003" @default.
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