3. Towards SCSPs Solutions

Abstract

Local consistency algorithms, as usually used for classical CSPs, can be exploited in the SCSP framework as well, provided that certain conditions on the semiring operations are satisfied. We show how the SCSP framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can also be used in newly defined schemes. We generalize to soft constraints the approximation techniques usually used for local consistency in classical constraint satisfaction and programming. The theoretical results show that this is indeed possible without losing the fundamental properties of such techniques (and the experimental results (on partial arc-consistency) [111] show that this work can help develop more efficient implementations for logic-based languages working with soft constraints). Then, we consider dynamic programming-like algorithms, and we prove that these algorithms can always be applied to SCSPs, and have a linear time complexity when the given SCSPs can be provided with a parsing tree of bounded size. Finally, we provide several instances of SCSPs which show the generality and also the expressive power of the framework.