Computing large and small stable models
<|reference_start|>Computing large and small stable models: In this paper, we focus on the problem of existence and computing of small and large stable models. We show that for every fixed integer k, there is a linear-time algorithm to decide the problem LSM (large stable models problem): does a logic program P have a stable model of size at least |P|-k. In contrast, we show that the problem SSM (small stable models problem) to decide whether a logic program P has a stable model of size at most k is much harder. We present two algorithms for this problem but their running time is given by polynomials of order depending on k. We show that the problem SSM is fixed-parameter intractable by demonstrating that it is W[2]-hard. This result implies that it is unlikely, an algorithm exists to compute stable models of size at most k that would run in time O(n^c), where c is a constant independent of k. We also provide an upper bound on the fixed-parameter complexity of the problem SSM by showing that it belongs to the class W[3].<|reference_end|>
@article{truszczynski2000computing,
    title={Computing large and small stable models},
    author={Miroslaw Truszczynski},
    journal={Theory and Practice of Logic Programming, 2(1), pp. 2002},
    year={2000},
    archivePrefix={arXiv},
    eprint={cs/0002001},
    primaryClass={cs.LO cs.AI}
}