The eXtended Least Number Heuristic

Audemard, Gilles; Henocque, Laurent

doi:10.1007/3-540-45744-5_35

Cited by 8 publications

(8 citation statements)

References 6 publications

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“…In the same spirit, the heuristic xlnh [4] (eXtended lnh) improves the range of predicted symmetries further, yet still allowing to account for these symmetries with a constant space/time algorithm (that relies on high water mark comparisons as does lnh). Unlike lnh, which focuses on function cells, xlnh first focuses the search by generating the canonical interpretations of a unary function (bijective if one exits), then pursues by instantiating functions one after another relying on a function ordering heuristic.…”

Section: Predictive Symmetry Eliminationmentioning

confidence: 95%

“…A term is recursively built on function symbols, variable names, and elements from a finite domain D n . 4 A literal is an equation t 1 = t 2 or its negation t 1 = t 2 , where t 1 and t 2 are terms or any predicate 5 p. The formulas (or axioms) in L are first-order clauses (disjunction of literals) in which all the variables are universally quantified. When a clause is a disjunct of n literals, it is said to be of length n. True and False are formulas.…”

Section: Syntaxmentioning

confidence: 99%

“…We call here predictive the methods that can exploit known interchangeabilities between domain elements using polytime (here constant) algorithms. Two such methods have been used so far: the least number heuristic (lnh) introduced by [33] and the extended least number heuristic (xlnh) by [4]. In the latter case, interchangeabilities are detected after a canonical interpretation has been constructed for a unary function.…”

Section: Predictive Symmetry Eliminationmentioning

confidence: 99%

“…This section presents the full version of the xlnh heuristic, which generalizes its first presentation in [4]. xlnh is a symmetry-preserving and cut-generating heuristic, in the spirit of the well-known lnh heuristic, first introduced in [33].…”

Section: Eliminating Global Symmetry Using the Xlnh Heuristicmentioning

confidence: 99%

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Predicting and Detecting Symmetries in FOL Finite Model Search

Audemard¹,

Benhamou²,

Henocque³

2006

J Autom Reasoning

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Symmetries abound in logically formulated problems where many axioms are universally quantified, as this is the case in equational theories. Two complementary approaches have been used so far to dynamically tackle those symmetries: prediction and detection. The best-known predictive symmetry elimination method is the least number heuristic (lnh). A more recent predictive method, the extended least number heuristic (xlnh), focuses first on the enumeration of a bijection in the problem and easily exploits in the sequel the remaining isomorphisms. On the other hand, dynamic symmetry detection is costly in the general case (the problem is Graph Iso complete) but allows one to exploit more symmetries, and efficient (polytime) yet incomplete detection algorithms can be used on each node. This paper presents a generalization of xlnh that focuses on the enumeration of a unary function that does not require the function to be bijective, a general notion of symmetry for finite-model search in first-order logic together with an efficient symmetry detection algorithm, and a function-ordering heuristic that exploits the inherent structure of first-order logic theories to improve the search when using function-centric methods. A comprehensive study of the compared efficiency of all methods, in isolation and in combination, demonstrates the acceleration that can be expected in all cases.G. Audemard (B) CRIL, Université d'Artois, rue de l'université SP 16, These ideas are implemented by using the known system SEM as an experimentation framework, to allow for accurate comparisons.

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Section: Predictive Symmetry Eliminationmentioning

confidence: 95%

Section: Syntaxmentioning

confidence: 99%

Section: Predictive Symmetry Eliminationmentioning

confidence: 99%

Section: Eliminating Global Symmetry Using the Xlnh Heuristicmentioning

confidence: 99%

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Predicting and Detecting Symmetries in FOL Finite Model Search

Audemard¹,

Benhamou²,

Henocque³

2006

J Autom Reasoning

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“…In the spirit of usual finite model semantics, T C members are interpreted by elements of P(O) 2 , and R C members by elements of P(O × O) (relations).…”

Section: Definition 1 (Syntax)mentioning

confidence: 99%