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## ASSAT: Computing Answer Sets of a Logic Program by SAT Solvers (2002)

Venue: | Artificial Intelligence |

Citations: | 260 - 7 self |

### Citations

1847 | The stable model semantics for logic programming.
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...e answer set of a normal logic program, our system has a clear edge over the state-of-art answer set programming systems Smodels and DLV. 1s1 Introduction Logic programming with answer sets semantics =-=[7]-=- and propositional logic are closely related. It is well-known that there is a local and modular translation from clauses to logic program rules such that the models of a set of clauses and the answer... |

1406 | Depth-first search and linear graph algorithms
- TARJAN
- 1972
(Show Context)
Citation Context ...g loop under M is a strongly connected component in the subgraph of GP induced by M − , and that the strongly connected components of a graph and their dependency chains can be computed in O(n+e) time=-=[22]-=-, where n is the number of nodes and e the number of arcs in the graph. So a terminating loop under M can be found in O(m + k) time, where m is the size of M − ,andk the number of arcs in the subgraph... |

1350 | Chaff: Engineering an Efficient SAT Solver. In:
- Moskewicz, Madigan, et al.
- 2001
(Show Context)
Citation Context ...lanning, our results confirmed the findings of [8], but we did it with many more and much larger instances. For our system, ASSAT 2.0,we tried the following SAT solvers: Chaff2 (Mar 23, 2001 version) =-=[17]-=-, Walksat 41 [19], GRASP (Feb, 2000 version) [20], Satz 215.2 [13], and SATO 4.1 (Zhang) [25]. In our experiments, we compare the performance of our system with Smodels version 2.27 [21] and DLV (May ... |

1069 |
Negation as failure.
- Clark
- 1978
(Show Context)
Citation Context ...gic program P ,wedenotebyatom(P )the set of atoms appearing in the program P . Given a logic program P ,its completion, written Comp(P ), is the union of the constraints in P and the Clark completion =-=[5]-=- of the set of rules in P , that is, it consists of following sentences: • For each p ∈ atom(P ), let p ← G1, ···,p← Gn be all the rules about p in P ,thenp ≡ G1 ∨···∨Gn is in Comp(P ). In particular,... |

683 | Where the Really Hard Problems Are;
- Cheeseman, Kanefsky, et al.
- 1991
(Show Context)
Citation Context ...n-Hamiltonian graphs which are hard. Most of them were really easy for all the systems and occurred when the number of edges is relatively small compared to that of vertices. There were reports (e.g. =-=[4]-=-) that randomly generated graphs with m close to (logn+loglogn)n/2, where n is the number of vertices and m the edges, have a 50% chance of being Hamiltonian, and was believed to be the “phase-transit... |

682 |
Towards a theory of declarative knowledge. In
- Apt, Blair, et al.
- 1988
(Show Context)
Citation Context ...ress this problem, we define a loop in a program to be a set of atoms such that for any pair of atoms in the set, there is a positive path from one to the other in the dependency graph of the program =-=[1]-=-. The basic idea of our translation is then to associate a formula with each loop in a program. The formula captures the logical conditions under which the atoms in the loop can be in an answer set. F... |

449 | GRASP: A New Search Algorithm for Satisfiability”,
- Silva, Sakallah
- 1999
(Show Context)
Citation Context ...], but we did it with many more and much larger instances. For our system, ASSAT 2.0,we tried the following SAT solvers: Chaff2 (Mar 23, 2001 version) [17], Walksat 41 [19], GRASP (Feb, 2000 version) =-=[20]-=-, Satz 215.2 [13], and SATO 4.1 (Zhang) [25]. In our experiments, we compare the performance of our system with Smodels version 2.27 [21] and DLV (May 16, 2003 version) [12] on the problem of computin... |

400 | Noise strategies for improving local search. - Selman, Kautz, et al. - 1994 |

389 | Logic programs with stable model semantics as a constraint programming paradigm.
- Niemela
- 1999
(Show Context)
Citation Context ...is a local and modular translation from clauses to logic program rules such that the models of a set of clauses and the answer sets of its corresponding logic program are in one-to-one correspondence =-=[24, 18]-=-. The other direction is more difficult and interesting. Niemelä [18] showed that there cannot be a modular translation from normal logic programs to sets of clauses, in the sense that for any program... |

192 | Causal theories of action and change.
- McCain, Turner
- 1997
(Show Context)
Citation Context ...e and Lifschitz [10] extended our Theorem 1 and the notion of loops and loop formulas to disjunctive logic programs, Lee [9] showed that a similar result 26sholds for McCain and Turner’s causal logic =-=[16]-=-, and finally Lee and Lin [11] showed that the idea works for propositional circumscription as well. Finally, ASSAT as well as the experimental results reported in this paper can be found at http://ww... |

161 | Propositional semantics for disjunctive logic programs’,
- Ben-Eliyahu-Zohary, Dechter
- 1992
(Show Context)
Citation Context ...ally 2-literal ones. For these programs, their experiments showed the advantage of computing answer sets using SAT solvers such as SATO over Smodels [21]. In the general case, Ben-Eliyahu and Dechter =-=[3]-=- gave a translation for a class of disjunctive logic programs, which includes all normal logic programs. However, one problem with their translation is that it may need to use a quadratic number of ex... |

90 | Cmodels-2: Sat-based answer set solver enhanced to non-tight programs, in:
- Lierler, Maratea
- 2004
(Show Context)
Citation Context ...lization between SAT solvers and specialized answer set solvers that will benefit both areas. Since this work was first published [15], it has been extended in several directions. Lierler and Maratea =-=[14]-=- extended it to handle so-called cardinality constraints and choice rules in their second version of CMODELS. Lee and Lifschitz [10] extended our Theorem 1 and the notion of loops and loop formulas to... |

59 | Loop formulas for disjunctive logic programs.
- Lee, Lifschitz
- 2003
(Show Context)
Citation Context ...5], it has been extended in several directions. Lierler and Maratea [14] extended it to handle so-called cardinality constraints and choice rules in their second version of CMODELS. Lee and Lifschitz =-=[10]-=- extended our Theorem 1 and the notion of loops and loop formulas to disjunctive logic programs, Lee [9] showed that a similar result 26sholds for McCain and Turner’s causal logic [16], and finally Le... |

57 | Implementing the Davis-Putnam method
- ZHANG, STICKEL
- 2000
(Show Context)
Citation Context ...ger instances. For our system, ASSAT 2.0,we tried the following SAT solvers: Chaff2 (Mar 23, 2001 version) [17], Walksat 41 [19], GRASP (Feb, 2000 version) [20], Satz 215.2 [13], and SATO 4.1 (Zhang) =-=[25]-=-. In our experiments, we compare the performance of our system with Smodels version 2.27 [21] and DLV (May 16, 2003 version) [12] on the problem of computing one answer set of a normal logic program. ... |

31 | Fages’ theorem and answer set programming
- Babovich, Erdem, et al.
(Show Context)
Citation Context ...ut the converse is not true in general. Fages [6] essentially showed that if a logic program has no positive loops, then every model of its completion is also an answer set. Recently, Babovich et al. =-=[2]-=- extended Fages’ result and showed that this continues to be true if the logic program is what they called “tight” on every model of its completion. Intuitively, the completion semantics is too weak b... |

25 | Loop formulas for circumscription.
- Lee, Lin
- 2006
(Show Context)
Citation Context ...our Theorem 1 and the notion of loops and loop formulas to disjunctive logic programs, Lee [9] showed that a similar result 26sholds for McCain and Turner’s causal logic [16], and finally Lee and Lin =-=[11]-=- showed that the idea works for propositional circumscription as well. Finally, ASSAT as well as the experimental results reported in this paper can be found at http://www.cs.ust.hk/assat/ . Acknowled... |

17 |
Li and Anbulagan. Heuristics based on unit propagation for satisfiability problems
- M
- 1997
(Show Context)
Citation Context ...with many more and much larger instances. For our system, ASSAT 2.0,we tried the following SAT solvers: Chaff2 (Mar 23, 2001 version) [17], Walksat 41 [19], GRASP (Feb, 2000 version) [20], Satz 215.2 =-=[13]-=-, and SATO 4.1 (Zhang) [25]. In our experiments, we compare the performance of our system with Smodels version 2.27 [21] and DLV (May 16, 2003 version) [12] on the problem of computing one answer set ... |

16 |
Finding hamiltonian cycles: algorithms, graphs and performance
- Vandegriend
- 1998
(Show Context)
Citation Context ...m close to (logn+loglogn)n/2, where n is the number of vertices and m the edges, have a 50% chance of being Hamiltonian, and was believed to be the “phase-transition” area of HC. However, Vandegriend =-=[23]-=- observed that for his heuristic algorithms, these graphs were very easy. Our experiments seemed to confirm this. For instance, a randomly generated graph with 70 vertices and 230 edges would have rou... |

10 | Two-literal logic programs and satisfiability representation of stable models: A comparison
- HUANG, JIA, et al.
(Show Context)
Citation Context ...m becomes interesting when we drop the requirement of modularity. In the special case when all rules in a program have at most one literal in their bodies (so-called 2-literal programs), Huang et al. =-=[8]-=- showed that there is an efficient translation to sets of clauses that do not need to use any extra variables. They also observed that many of the logic programs in answer set programming applications... |

8 |
Nondefinite vs. definite causal theories
- Lee
(Show Context)
Citation Context ...cardinality constraints and choice rules in their second version of CMODELS. Lee and Lifschitz [10] extended our Theorem 1 and the notion of loops and loop formulas to disjunctive logic programs, Lee =-=[9]-=- showed that a similar result 26sholds for McCain and Turner’s causal logic [16], and finally Lee and Lin [11] showed that the idea works for propositional circumscription as well. Finally, ASSAT as w... |

7 | Iterative belief revision in extended logic programming, Theor
- You, Cartwright, et al.
- 1996
(Show Context)
Citation Context ...is a local and modular translation from clauses to logic program rules such that the models of a set of clauses and the answer sets of its corresponding logic program are in one-to-one correspondence =-=[24, 18]-=-. The other direction is more difficult and interesting. Niemelä [18] showed that there cannot be a modular translation from normal logic programs to sets of clauses, in the sense that for any program... |

4 |
et al. DLV: a disjunctive datalog system, release 2000-10-15
- Leone
- 2000
(Show Context)
Citation Context ...rcuit (HC) show that for the problem of generating one answer set of a logic program, our system has a clear advantage over the two popular specialized answer set generators, Smodels [18, 21] and DLV =-=[12]-=-. On the other hand, this work also benefits SAT in providing some hard instances: we have encountered some relatively small SAT problems (about 720 variables and 4500 clauses) that could not be solve... |

4 | engineering an efficient SAT solver - Chaff - 2001 |

3 |
The Psychology of Learning and Motivation
- Simons
- 2000
(Show Context)
Citation Context ... in answer set programming applications are essentially 2-literal ones. For these programs, their experiments showed the advantage of computing answer sets using SAT solvers such as SATO over Smodels =-=[21]-=-. In the general case, Ben-Eliyahu and Dechter [3] gave a translation for a class of disjunctive logic programs, which includes all normal logic programs. However, one problem with their translation i... |

2 |
Consistency of clark’s completion and existence of stable of stable models
- Fages
- 1994
(Show Context)
Citation Context ...onsider the completion of a a logic program. It is well-known that every answer set of a logic program is also a model of the completion of the program, but the converse is not true in general. Fages =-=[6]-=- essentially showed that if a logic program has no positive loops, then every model of its completion is also an answer set. Recently, Babovich et al. [2] extended Fages’ result and showed that this c... |

1 | DLV: a disjunctive datalog system, release 2001-6-11. At http://www.dbai.tuwien.ac.at/ proj/dlv - Leone - 2001 |