## Towards Automated Integration of Guess and Check Programs in Answer Set Programming (2004)

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Venue: | LPNMR, volume 2923 of LNCS |

Citations: | 14 - 3 self |

### BibTeX

@INPROCEEDINGS{Eiter04towardsautomated,

author = {Thomas Eiter and Axel Polleres},

title = {Towards Automated Integration of Guess and Check Programs in Answer Set Programming},

booktitle = {LPNMR, volume 2923 of LNCS},

year = {2004},

pages = {100--113},

publisher = {Springer}

}

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### Abstract

Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise way, where the encoding reflects the typical "guess and check" nature of NP problems: The property is encoded in a way such that polynomial size certificates for it correspond to stable models of a program. However, the problem-solving capacity of full disjunctive logic programs (DLPs) is beyond NP at the second level of the polynomial hierarchy.

### Citations

2408 | Computational Complexity
- Papadimitriou
- 1995
(Show Context)
Citation Context ... if and only if the property p holds. Properties that are co-NP-complete often occur within the context of problems that reside in the class Σ P 2 , which is above NP in the polynomial time hierarchy =-=[33]-=-. In particular, the solutions of a ΣP 2 -complete problem can be typically singled out from given candidate solutions by testing a co-NP-complete property. Some well-known examples of such ΣP 2 -comp... |

877 | Classical negation in logic programs and disjunctive databases. New Generation Computing 9:365–385
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...rogram for Strategic Companies 28 C Ad Hoc Encoding for Quantified Boolean Formulas 30 D Ad Hoc Encodings for Strategic Companies 31INFSYS RR 1843-04-01 1 1 Introduction Answer set programming (ASP) =-=[35, 15, 26, 29, 31]-=-, also called A-Prolog [1, 2, 16], is widely proposed as a useful tool for solving problems in a declarative manner, by encoding the solutions to a problem in the answer sets of a normal logic program... |

541 |
Knowledge Representation, Reasoning, and Declarative Problem Solving
- Baral
- 2003
(Show Context)
Citation Context ...Encoding for Quantified Boolean Formulas 30 D Ad Hoc Encodings for Strategic Companies 31INFSYS RR 1843-04-01 1 1 Introduction Answer set programming (ASP) [35, 15, 26, 29, 31], also called A-Prolog =-=[1, 2, 16]-=-, is widely proposed as a useful tool for solving problems in a declarative manner, by encoding the solutions to a problem in the answer sets of a normal logic program. By well-known complexity result... |

342 | The DLV System for Knowledge Representation and Reasoning - Leone, Pfeifer, et al. - 2004 |

334 | Logic programs with stable model semantics as a constraint programming paradigm
- Niemelä
- 1999
(Show Context)
Citation Context ...rogram for Strategic Companies 28 C Ad Hoc Encoding for Quantified Boolean Formulas 30 D Ad Hoc Encodings for Strategic Companies 31INFSYS RR 1843-04-01 1 1 Introduction Answer set programming (ASP) =-=[35, 15, 26, 29, 31]-=-, also called A-Prolog [1, 2, 16], is widely proposed as a useful tool for solving problems in a declarative manner, by encoding the solutions to a problem in the answer sets of a normal logic program... |

293 | Complexity and expressive power of logic programming
- Dantsin, Eiter, et al.
- 1997
(Show Context)
Citation Context ...he solutions to a problem in the answer sets of a normal logic program. By well-known complexity results, in this way all problems with complexity in NP can be expressed and solved [39, 28]; see also =-=[6]-=-. A frequently considered example of an NP-complete problem which can be elegantly solved in ASP is Graph-3-Colorability, i.e., deciding whether some given graph G is 3-colorable. It is an easy exerci... |

268 | Foundations of logic programming
- Lifschitz
- 1996
(Show Context)
Citation Context ...wing, we show how our transformation tr resp. tr Opt from above can be used to automatically combine guess and check into a single program. We assume that the set Lit( guess ) is a Splitting Set [13] of guess [ check , i.e. no head literal from check occurs in guess . This can be easily achieved by introducing new predicate names, e.g., p 0 for a predicate p, and adding a rule p 0 (t): p(t... |

213 | Disjunctive Datalog
- Eiter, Gottlob, et al.
- 1997
(Show Context)
Citation Context ...strategic (cf. [11]). Conformant Planning: Checking whether a given plan is conformant [8], provided executability of actions is polynomially decidable (cf. [4, 22]). Further examples can be found in =-=[6, 5-=-]. In general, the corresponding logic program p for this check can be easily formulated and the overall problem (evaluating the QBF, finding a strategic companies set resp. a conformant plan) solved... |

210 | ASSAT: Computing answer sets of a logic program by SAT solvers
- Lin, Yuting
- 2004
(Show Context)
Citation Context ... which we build, aimed at transforming head-cycle free disjunctive logic programs into SAT problems. It might be interesting to investigate whether related methods such as the one developed for ASSAT =-=[27]-=-, which was recently generalized by Lee and Lifschitz [22] to disjunctive programs, can be adapted for our approach.INFSYS RR 1843-04-01 27 Acknowledgments We thank Gerald Pfeifer for his help on exp... |

159 | Stable Semantics for Disjunctive Programs
- Przymusinski
- 1991
(Show Context)
Citation Context ... meta , where F () is a factual representation of and meta is a fixed meta-interpreter. T4 tr() is modular (at the syntactic level), i.e., tr() = S r2 tr(r). Moreover, it is a stratified DLP [20, 21=-=] and uses -=-negation only in its "deterministic" part. We also describe optimizations and a transformation to positive DLPs, and show that in a precise sense, modular transformations to such programs do... |

147 | Propositional semantics for disjunctive logic programs
- Ben-Eliyahu, Dechter
- 1994
(Show Context)
Citation Context ... problem is, e.g., the property that a graph is not 3-colorable. Such properties p can analogously be expressed by a normal logic program (equivalently, by a head-cycle free disjunctive logic program =-=[-=-1]) p , where the property holds iff p has no answer set at all. Checks in co-NP typically occur as subproblems within more complex problems which have complexity higher than NP, for instance: Quant... |

144 | Answer set programming and plan generation
- Lifschitz
(Show Context)
Citation Context ...bout meta-interpretation in ASP [16, 2, 3]. We fruitfully exploit 2 the construction of tr() to further elucidate the natural guess and check programming paradigm for ASP, as discussed in [11] or in [=-=14] (named &q-=-uot;Generate/Define/Test" there), and we fill a gap by providing an automated construction for integrating guess and check programs. It is worth noticing that such an integration is non-trivial e... |

127 | Conformant Planning via Symbolic Model Checking and Heuristic Search - Cimatti, Roveri, et al. - 2004 |

126 |
A critique of pure reason
- McDermott
- 1987
(Show Context)
Citation Context ...ns, cf. [4, 22]. Hence, the problem can be solved with a guess and (co-NP) check strategy. As an example, we consider a simplified version of the well-known "Bomb in the Toilet" planning pro=-=blem (cf. [4, 17]-=-): We have been alarmed that a possibly armed bomb is in a lavatory which has a toilet bowl. Possible actions are dunking the bomb into the bowl and flushing the toilet. After just dunking, the bomb m... |

85 | A logic programming approach to knowledge-state planning: Semantics and complexity
- Eiter, Faber, et al.
- 2004
(Show Context)
Citation Context ...es: Checking whether a set of companies is strategic (cf. [11]). Conformant Planning: Checking whether a given plan is conformant [8], provided executability of actions is polynomially decidable (cf. =-=[4, 22-=-]). Further examples can be found in [6, 5]. In general, the corresponding logic program p for this check can be easily formulated and the overall problem (evaluating the QBF, finding a strategic com... |

85 | The expressive powers of the logic programming semantics
- Schlipf
- 1995
(Show Context)
Citation Context ...nner, by encoding the solutions to a problem in the answer sets of a normal logic program. By well-known complexity results, in this way all problems with complexity in NP can be expressed and solved =-=[39, 28]-=-; see also [6]. A frequently considered example of an NP-complete problem which can be elegantly solved in ASP is Graph-3-Colorability, i.e., deciding whether some given graph G is 3-colorable. It is ... |

80 | Unfolding partiality and disjunctions in stable model semantics
- Janhunen, Niemelä, et al.
- 2000
(Show Context)
Citation Context ...allows one to formulate problems in ΣP 2 in a single (disjunctive) program, since this formalism captures the complexity class ΣP 2 , cf. [6, 13]. Hence, efficient ASP engines such as DLV [23] or GNT =-=[21]-=- can be used to solve such programs directly in a one-step approach. A difficulty here is that sometimes, an encoding of a problem in a single logic program (e.g., for the conformant planning problem ... |

65 | On properties of update sequences based on causal rejection. Theory and Practice of Logic Programming
- Eiter, Fink, et al.
- 2002
(Show Context)
Citation Context ... separate guess and check programs, which are often easy to formalize, while a manual integrated encoding may be difficult to find (as in the case of conformant planning or minimal update answer sets =-=[-=-5]). 7 Conclusion We presented a method for rewriting a head-cycle free (extended) disjunctive logic program (HDLP) into a stratified disjunctive logic program without constraints tr(), such that the... |

64 | On the declarative and procedural semantics of logic programs
- Przymusinski
- 1995
(Show Context)
Citation Context ... meta , where F () is a factual representation of and meta is a fixed meta-interpreter. T4 tr() is modular (at the syntactic level), i.e., tr() = S r2 tr(r). Moreover, it is a stratified DLP [20, 21=-=] and uses -=-negation only in its "deterministic" part. We also describe optimizations and a transformation to positive DLPs, and show that in a precise sense, modular transformations to such programs do... |

64 | Declarative problem-solving using the DLV system
- Eiter, Faber, et al.
- 2000
(Show Context)
Citation Context ...hether some given graph G is 3-colorable. It is an easy exercise in ASP to write a program which determines whether a graph is 3-colorable. A straightforward encoding, following the “Guess and Check” =-=[8, 23]-=- respectively “Generate/Define/Test” approach [26], consists of two parts: • A “guessing” part, which assigns nondeterministically each node of the graph one of three colors: col(red,X) vcol(green,X) ... |

60 | Representing knowledge in A-prolog
- Gelfond
- 2002
(Show Context)
Citation Context ...Encoding for Quantified Boolean Formulas 30 D Ad Hoc Encodings for Strategic Companies 31INFSYS RR 1843-04-01 1 1 Introduction Answer set programming (ASP) [35, 15, 26, 29, 31], also called A-Prolog =-=[1, 2, 16]-=-, is widely proposed as a useful tool for solving problems in a declarative manner, by encoding the solutions to a problem in the answer sets of a normal logic program. By well-known complexity result... |

59 | Expressive Planning and Explicit Knowledge
- Goldman, Boddy
- 1996
(Show Context)
Citation Context ...0 INFOMIX. whether 8Y ((X); Y ) evaluates to true. Strategic Companies: Checking whether a set of companies is strategic (cf. [11]). Conformant Planning: Checking whether a given plan is conformant [8=-=-=-], provided executability of actions is polynomially decidable (cf. [4, 22]). Further examples can be found in [6, 5]. In general, the corresponding logic program p for this check can be easily formu... |

52 |
A logic programming approach to the integration, repairing and querying of inconsistent databases
- Greco, Greco, et al.
- 2001
(Show Context)
Citation Context ...conformant [17]. The latter problem is in co-NP, provided that executability of actions is polynomially decidable, cf. [10, 40]. This list can be extended, and further examples can be found, e.g., in =-=[13, 12, 18, 38]-=-. The problems described above can be solved using ASP in a two-step approach as follows: 1. Generate a candidate solution S by means of a logic program Πguess. 2. Check the solution S by “running” an... |

46 | Loop formulas for disjunctive logic programs
- Lee, Lifschitz
- 2003
(Show Context)
Citation Context ...junctive logic programs into SAT problems. It might be interesting to investigate whether related methods such as the one developed for ASSAT [27], which was recently generalized by Lee and Lifschitz =-=[22]-=- to disjunctive programs, can be adapted for our approach.INFSYS RR 1843-04-01 27 Acknowledgments We thank Gerald Pfeifer for his help on experimental evaluation and fruitful discussions. We are also... |

43 | Default logic as a query language
- Cadoli, Eiter, et al.
- 1997
(Show Context)
Citation Context ...hod can be automatically integrated into a single logic program. Such an encoding was previously unkown. 6.3 Strategic Companies Another ΣP 2 -complete problem is the strategic companies problem from =-=[4]-=-. Briefly, a holding owns companies, each of which produces some goods. Moreover, several companies may jointly have control over another company. Now, some companies should be sold, under the constra... |

32 |
A note on the expressive power of prolog
- Papadimitriou
- 1985
(Show Context)
Citation Context ...-input predicates accessed through not can be computed by a positive normal program, since such programs capture polynomial time computability by well-known results on the expressive power of Datalog =-=[1-=-8]; thus, negation of input predicates in F () is sufficient in this case. 7 3.2 Optimizations meta can be modified in several respects. We discuss here some modifications which, though not necessari... |

25 | Diagnostic reasoning with a-prolog
- Balduccini, Gelfond
(Show Context)
Citation Context ...Encoding for Quantified Boolean Formulas 30 D Ad Hoc Encodings for Strategic Companies 31INFSYS RR 1843-04-01 1 1 Introduction Answer set programming (ASP) [35, 15, 26, 29, 31], also called A-Prolog =-=[1, 2, 16]-=-, is widely proposed as a useful tool for solving problems in a declarative manner, by encoding the solutions to a problem in the answer sets of a normal logic program. By well-known complexity result... |

24 |
An abductive framework for computing knowledge base updates. Theory and Practice of Logic Programming
- Sakama, Inoue
(Show Context)
Citation Context ...conformant [17]. The latter problem is in co-NP, provided that executability of actions is polynomially decidable, cf. [10, 40]. This list can be extended, and further examples can be found, e.g., in =-=[13, 12, 18, 38]-=-. The problems described above can be solved using ASP in a two-step approach as follows: 1. Generate a candidate solution S by means of a logic program Πguess. 2. Check the solution S by “running” an... |

23 |
DLV homepage, since
- Faber, Pfeifer
- 1996
(Show Context)
Citation Context ...nvironment and General Setting All tests were performed on an AMD Athlon 1200MHz machine with 256MB of main memory running SuSE Linux 8.1. All our experiments have been conducted using the DLV system =-=[23, 14]-=-, which is a state-of-the-art Answer Set Programming engine capable of solving DLPs. Another available system, GNT [21] 4 which is not reported here showed worse performance/higher memory consumption ... |

22 | Polynomial-length planning spans the polynomial hierarchy
- Turner
- 2002
(Show Context)
Citation Context ...es: Checking whether a set of companies is strategic (cf. [11]). Conformant Planning: Checking whether a given plan is conformant [8], provided executability of actions is polynomially decidable (cf. =-=[4, 22-=-]). Further examples can be found in [6, 5]. In general, the corresponding logic program p for this check can be easily formulated and the overall problem (evaluating the QBF, finding a strategic com... |

18 |
Computing preferred answer sets by meta-interpretation in answer set programming. Theory and Practice of Logic Programming
- Eiter, Faber, et al.
(Show Context)
Citation Context ... tr() for integrating separate guess and check programs guess and check , respectively, into a single DLP solve such that the answer sets of solve yield the solutions of the overall problem. (3) We demonstrate the method on the examples of QBFs and conformant planning [8] under fixed polynomial plan length (cf. [4, 22]), where our method proves to loosen some restrictions of previous encodin... |

15 | On the effect of default negation on the expressiveness of disjunctive rules
- Janhunen
(Show Context)
Citation Context ..., the transformation tr(), as well as the ground instantiation of tr(), is computable in LOGSPACE (thus in polynomial time). Note that tr() is not polynomial faithful modular (PFM) in the sense of [9]: (i) T1 does not claim a strict one-to-one correspondence between the answer sets of and tr(). Indeed, tr() might have several answer sets corresponding to a particular answer set S of , reflec... |

15 |
Enhancing answer set planning
- Leone, Rosati, et al.
- 2001
(Show Context)
Citation Context ..., corresponding to the single conformant plan P= dunk, flush as desired. Note that our rewriting method is more generally applicable than the encoding for conformant planning proposed by Leone et al. =-=[12]-=- who require that state transitions are specified by a positive constraint-free LP. Our method can still safely be used in presence of negation and constraints, provided action execution always leads ... |

13 |
and MirosÃlaw Truszczyński. Stable models and an alternative logic programming paradigm
- Marek
- 1999
(Show Context)
Citation Context ...rogram for Strategic Companies 28 C Ad Hoc Encoding for Quantified Boolean Formulas 30 D Ad Hoc Encodings for Strategic Companies 31INFSYS RR 1843-04-01 1 1 Introduction Answer set programming (ASP) =-=[35, 15, 26, 29, 31]-=-, also called A-Prolog [1, 2, 16], is widely proposed as a useful tool for solving problems in a declarative manner, by encoding the solutions to a problem in the answer sets of a normal logic program... |

12 | plp: A Generic Compiler for Ordered Logic Programs
- Delgrande, Schaub, et al.
(Show Context)
Citation Context ...gation only in its "deterministic" part. We also describe optimizations and a transformation to positive DLPs, and show that in a precise sense, modular transformations to such programs do n=-=ot exist-=-. (2) We show how to use tr() for integrating separate guess and check programs guess and check , respectively, into a single DLP solve such that the answer sets of solve yield the solutions of th... |

9 | On the expressibility of stable logic programming
- Marek, Remmel
- 2003
(Show Context)
Citation Context ...rges the range of techniques for expressing problems using ASP, in a direction which to our knowledge has not been explored so far. It also complements recent results about meta-interpretation in ASP =-=[16, 2, 3]. We frui-=-tfully exploit 2 the construction of tr() to further elucidate the natural guess and check programming paradigm for ASP, as discussed in [11] or in [14] (named "Generate/Define/Test" there),... |

9 | Comparing the expressive powers of some syntactically restricted classes of logic porgrams
- Janhunen
- 2000
(Show Context)
Citation Context ...code the answer sets of Π, if Π has some answer set, and that tr(Π) has a canonical answer set otherwise which is easy to recognize. The transformation tr(Π) is polynomial and modular in the sense of =-=[19]-=-, and employs meta-interpretation of Π.INFSYS RR 1843-04-01 3 Furthermore, we describe variants and modifications of tr(Π) aiming at optimization of the transformation. In particular, we present a tr... |

8 |
et al.: The DLV system for knowledge representation and reasoning
- Leone
- 2006
(Show Context)
Citation Context ...-N04 and European Commission grants FET-200137004 WASP and IST-2001-33570 INFOMIX. whether 8Y ((X); Y ) evaluates to true. Strategic Companies: Checking whether a set of companies is strategic (cf. [1=-=1]-=-). Conformant Planning: Checking whether a given plan is conformant [8], provided executability of actions is polynomially decidable (cf. [4, 22]). Further examples can be found in [6, 5]. In general,... |

2 |
Advances in Answer Set Planning
- Polleres
- 2003
(Show Context)
Citation Context ...f. A generalization of the method demonstrated here on a small planning problem expressed in Answer Set Programming to conformant planning in the DLV K planning system [10], is discussed in detail in =-=[34]-=-. In this system, planning problems are encoded in a logical action language, and the encodings are mapped to logic programs. For conformant planning problems, separate guess and check programs have b... |