Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis in the so-called Gelfond–Lifschitz transformation. The primary goal of this work is to present an alternative and epistemic-based characterization of stable model semantics, to the Gelfond-Lifschitz transformation. In particular, we show that stable model semantics can be defined entirely as an extension of the Kripke-Kleene semantics. Indeed, we show that the closed world assumption can be seen as an additional source of ‘falsehood’ to be added cumulatively to the Kripke-Kleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.

We propose and study algorithms to compute minimal models, stable models and answer sets of $t$-CNF theories, and normal and disjunctive $t$-programs. We are especially interested in algorithms with non-trivial worst-case performance bounds. The bulk of the paper is concerned with the classes of 2- and 3-CNF theories, and normal and disjunctive 2- and 3-programs, for which we obtain significantly stronger results than those implied by our general considerations. We show that one can find all minimal models of 2-CNF theories and all answer sets of disjunctive 2-programs in time $O(m1\mbox{.}4422\mbox{..}^n)$. Our main results concern computing stable models of normal 3-programs, minimal models of 3-CNF theories and answer sets of disjunctive 3-programs. We design algorithms that run in time $O(m1\mbox{.}6701\mbox{..}^n)$, in the case of the first problem, and in time $O(mn^2 2\mbox{.}2782\mbox{..}^n)$, in the case of the latter two. All these bounds improve by exponential factors the best algorithms known previously. We also obtain closely related upper bounds on the number of minimal models, stable models and answer sets a $t$-CNF theory, a normal $t$-program or a disjunctive $t$-program may have.

The software approach to developing Digital Signal Processing (DSP) applications brings some great features such as flexibility, re-usability of resources and easy upgrading of applications. However, it requires long and tedious tests and verification phases because of the increasing complexity of the software applications. This implies the need of a software programming environment capable of putting together DSP modules and providing facilities to debug, verify and validate the code. The objective of the work is to provide such facilities as simulation and verification for developing DSP software applications. This led us to developing an extension toolkit, EPSPECTRA, built upon PSPECTRA, one of the first toolkits available to design basic software radio applications on standard PC workstations. In this paper, we first present EPSPECTRA, an ESTEREL-based extension of PSPECTRA that makes the design and implementation of portable DSP applications easier. It allows the drastic reduction of testing and verification time while requiring relatively little expertise in formal verification methods. Second, we demonstrate the use of EPSPECTRA, taking as an example the radio interface part of a GSM base station. We also present the verification procedures for the three safety properties of the implementation programs which have complex control-paths. These have to obey strict scheduling rules. In addition, EPSPECTRA achieves the verification of the targeted application since the same model is used for the executable code generation and for the formal verification.