On the expressibility of stable logic programming

Abstract

Schlipf (1995) proved that Stable Logic Programming (SLP) solves all decision problems. We extend Schlipf's result to prove that SLP solves all search problems in the class . Moreover, we do this in a uniform way as defined in Marek and Truszczyński (1991). Specifically, we show that there is a single program such that given any Turing machine with non-negative integer coefficients and any input , there is an extensional database 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 that reach the final state in at most steps. Moreover, can be computed in polynomial time from and the description of 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 -search problems.The proof of this result involves additional technical complications and will be a subject of another publication.