A Novel Approach For Detecting Symmetries in CSP Models

Mears, Christopher; Banda, Maria García de la; Wallace, Mark; Demoen, Bart

doi:10.1007/978-3-540-68155-7_14

Cited by 15 publications

(14 citation statements)

References 13 publications

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“…Part of future work is to extract other types of implicit knowledge, such as smaller types, definitional totality and more complex finite-domain constraints such as all-different. In the field of CP, Mears et al (2008) search for symmetries in a problem specification using a different approach, namely by generating multiple solutions for several instances, from which symmetry candidates are extracted, which can then be verified using e.g., theorem provers. Wittocx et al (2013) have studied unit propagation on a symbolic level by deriving formulas entailed by the theory by reasoning on unit propagation schemes .…”

Section: Discussionmentioning

confidence: 99%

Detection and exploitation of functional dependencies for model generation

Cat¹,

Bruynooghe²

2013

Theory and Practice of Logic Programming

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Recent work in Answer Set Programming has integrated ideas from Constraint Programming. This has led to a new field called ASP Modulo CSP (CASP), in which the ASP language is enriched with constraint atoms representing constraint satisfaction problems. These constraints have a more compact grounding and are handled by a new generation of search algorithms. However, the burden is on the modeler to exploit these new constructs in his declarative problem specifications. Here, we explore how to remove this burden by automatically generating constraint atoms. We do so in the context of FO(·)IDP, a knowledge representation language that extends first-order logic with, among others, inductive definitions, arithmetic and aggregates. We uncover functional dependencies in declarative problem specifications with a theorem prover and exploit them with a transformation that introduces functions. Experimental evaluation shows that we obtain more compact groundings and better search performance.

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Section: Discussionmentioning

confidence: 99%

Detection and exploitation of functional dependencies for model generation

Cat¹,

Bruynooghe²

2013

Theory and Practice of Logic Programming

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“…This paper extends and revises earlier work [23] by generalising the method to other properties, providing a more extensive experimental evaluation, and providing a much more detailed explanation and formalisation of the patterns and algorithms used for lifting symmetries from instances to models. The paper is organised as follows.…”

Section: Introductionmentioning

confidence: 86%

A method for detecting symmetries in constraint models and its generalisation

et al. 2014

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The symmetries that appear in many constraint problems can be used to significantly speed up the search for solutions to these problems. While the accurate detection of symmetries in instances of a given constraint problem is possible, current methods tend to be impractical for real-sized instances. On the other hand, methods capable of detecting properties for a problem model -and thus all its instances -are efficient but not accurate enough. This paper presents a new method for inferring symmetries in constraint satisfaction models that combines the high accuracy of instance-based methods with the efficiency of model-based methods; the key insight is that symmetries detected for small instances of the model can be generalised to the model itself. Experimental evaluation shows that this approach is able to find all symmetries in almost all the benchmark problems used. The generality of our method is then illustrated by showing how it can be applied to infer other properties.

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“…Mears et al have detected symmetries on small instances of a constraint model, and used this to identify symmetries that might occur in the more general model [20]. More recently, Mears et al have shown how a limited form of symmetry detection in MiniZinc can be reduced to deciding sentences in Presburger arithmetic [21].…”

Section: Related Workmentioning

confidence: 99%

Reasoning about Constraint Models

Bessière

Hébrard

Katsirelos³

et al. 2014

Lecture Notes in Computer Science

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Abstract. We propose a simple but powerful framework for reasoning about properties of models specified in languages like AMPL, OPL, Zinc or Essence. Using this framework, we prove that reasoning problems like detecting symmetries, redundant constraints or dualities between models are undecidable even for a very limited modelling language that only generates simple problem instances. To provide tools to help the human modeller (for example, to identify when a model has a particular symmetry), it would nevertheless be useful to automate many of these reasoning tasks. To explore the possibility of doing this, we describe two case-studies. The first uses the ACL2 inductive prover to prove inductively that a model contains a symmetry. The second identifies a tractable fragment of MiniZinc and uses a decision procedure to prove that a model implies a parameterized constraint.

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A Novel Approach For Detecting Symmetries in CSP Models

Cited by 15 publications

References 13 publications

Detection and exploitation of functional dependencies for model generation

Detection and exploitation of functional dependencies for model generation

A method for detecting symmetries in constraint models and its generalisation

Reasoning about Constraint Models

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