Abstract
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(mc), where m is the size of the program and 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].
Original language | English |
---|---|
Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Theory and Practice of Logic Programming |
Volume | 2 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2002 |
Keywords
- Fixed-parameter complexity
- Stable models
ASJC Scopus subject areas
- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics
- Artificial Intelligence