In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity. For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially. This, together with our empirical study for random instances generated below and in the phase transition region, suggests that the phase transition of the fixed ratio model is also easy.

In this paper, a Gaifman-Shapiro-style module architecture is tailored to the case of Smodels programs under the stable model semantics. The composition of Smodels program modules is suitably limited by module conditions which ensure the compatibility of the module system with stable models. Hence the semantics of an entire Smodels program depends directly on stable models assigned to its modules. This result is formalized as a module theorem which truly strengthens Lifschitz and Turner's splitting-set theorem for the class of Smodels programs. To streamline generalizations in the future, the module theorem is first proved for normal programs and then extended to cover Smodels programs using a translation from the latter class of programs to the former class. Moreover, the respective notion of module-level equivalence, namely modular equivalence, is shown to be a proper congruence relation: it is preserved under substitutions of modules that are modularly equivalent. Principles for program decomposition are also addressed. The strongly connected components of the respective dependency graph can be exploited in order to extract a module structure when there is no explicit a priori knowledge about the modules of a program. The paper includes a practical demonstration of tools that have been developed for automated (de)composition of Smodels programs. To appear in Theory and Practice of Logic Programming.