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- W2949188445 abstract "(We apologize for pidgin LaTeX) Schlipf cite{sch91} proved that Stable Logic Programming (SLP) solves all $mathit{NP}$ decision problems. We extend Schlipf's result to prove that SLP solves all search problems in the class $mathit{NP}$. Moreover, we do this in a uniform way as defined in cite{mt99}. Specifically, we show that there is a single $mathrm{DATALOG}^{neg}$ program $P_{mathit{Trg}}$ such that given any Turing machine $M$, any polynomial $p$ with non-negative integer coefficients and any input $sigma$ of size $n$ over a fixed alphabet $Sigma$, there is an extensional database $mathit{edb}_{M,p,sigma}$ such that there is a one-to-one correspondence between the stable models of $mathit{edb}_{M,p,sigma} cup P_{mathit{Trg}}$ and the accepting computations of the machine $M$ that reach the final state in at most $p(n)$ steps. Moreover, $mathit{edb}_{M,p,sigma}$ can be computed in polynomial time from $p$, $sigma$ and the description of $M$ and the decoding of such accepting computations from its corresponding stable model of $mathit{edb}_{M,p,sigma} cup P_{mathit{Trg}}$ can be computed in linear time. A similar statement holds for Default Logic with respect to $Sigma_2^mathrm{P}$-search problemsfootnote{The proof of this result involves additional technical complications and will be a subject of another publication.}." @default.
- W2949188445 created "2019-06-27" @default.
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- W2949188445 date "2003-12-22" @default.
- W2949188445 modified "2023-09-27" @default.
- W2949188445 title "On the Expressibility of Stable Logic Programming" @default.
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