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Circuit Complexity and Decompositions of Global Constraints
 In 21st Int. Joint Conf. on AI
, 2009
"... We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a spe ..."
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Cited by 22 (5 self)
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We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the ALLDIFFERENT constraint. 1
Decompositions of All Different, Global Cardinality and Related Constraints
"... We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide ..."
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Cited by 17 (9 self)
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We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudoBoolean solver. 1
Restricted Global Grammar Constraints.
"... We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous contextfree grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as hard as parsing an unrestricted context free grammar. We also ..."
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Cited by 10 (2 self)
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We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous contextfree grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as hard as parsing an unrestricted context free grammar. We also consider the class of linear grammars and give a propagator that runs in quadratic time. Finally, to demonstrate the use of linear grammars, we show that a weighted linear GRAMMAR constraint can efficiently encode the EDITDISTANCE constraint, and a conjunction of the EDITDISTANCE constraint and the REGULAR constraint.
The polytope of contextfree grammar constraints
 INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING FOR COMBINATORIAL OPTIMIZATION PROBLEMS
, 2009
"... Contextfree grammar constraints enforce that a sequence of variables forms a word in a language defined by a contextfree grammar. The constraint has received a lot of attention in the last few years as it represents an effective and highly expressive modeling entity. Its application has been stud ..."
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Cited by 3 (1 self)
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Contextfree grammar constraints enforce that a sequence of variables forms a word in a language defined by a contextfree grammar. The constraint has received a lot of attention in the last few years as it represents an effective and highly expressive modeling entity. Its application has been studied in the field of Constraint Programming, Mixed Integer Programming, and SAT to solve complex decision problems such as shift scheduling. In this theoretical study we demonstrate how the constraint can be linearized efficiently. In particular, we propose a lifted polytope which has only integer extreme points. Based on this result, for shift scheduling problems we prove the equivalence of Dantzig’s original set covering model and a lately introduced grammarbased model.
The weighted GRAMMAR constraint
, 2011
"... We introduce the WEIGHTEDGRAMMAR constraint and propose propagation algorithms based on the CYK parser and the Earley parser. We show that the traces of these algorithms can be encoded as a weighted negation normal form (WNNF), a generalization of NNF that allows nodes to carry weights. Based on thi ..."
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Cited by 2 (0 self)
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We introduce the WEIGHTEDGRAMMAR constraint and propose propagation algorithms based on the CYK parser and the Earley parser. We show that the traces of these algorithms can be encoded as a weighted negation normal form (WNNF), a generalization of NNF that allows nodes to carry weights. Based on this connection, we prove the correctness and complexity of these algorithms. Specifically, these algorithms enforce domain consistency on the WEIGHTEDGRAMMAR constraint in time O(n 3). Further, we propose that the WNNF constraint can be decomposed into a set of primitive arithmetic constraint without hindering propagation.
Combining patternbased CRFs and weighted contextfree grammars
"... Abstract. We consider two models for the sequence labeling (tagging) problem. The first one is a PatternBased Conditional Random Field (PB), in which the energy of a string (chain labeling) x = x1... xn ∈ Dn is a sum of terms over intervals [i, j] where each term is nonzero only if the substring x ..."
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Abstract. We consider two models for the sequence labeling (tagging) problem. The first one is a PatternBased Conditional Random Field (PB), in which the energy of a string (chain labeling) x = x1... xn ∈ Dn is a sum of terms over intervals [i, j] where each term is nonzero only if the substring xi... xj equals a prespecified word w ∈ Λ. The second model is a Weighted ContextFree Grammar (WCFG) frequently used for natural language processing. PB and WCFG encode local and nonlocal interactions respectively, and thus can be viewed as complementary. We propose a Grammatical PatternBased CRF model (GPB) that combines the two in a natural way. We argue that it has certain advantages over existing approaches such as the Hybrid model of [3] that combines Ngrams and WCFGs. The focus of this paper is to analyze the complexity of inference tasks in a GPB such as computing MAP. We present a polynomialtime algorithm for general GPBs and a faster version for a special case that we call Interaction Grammars. Key words: sequence tagging, patternbased CRFs, weighted contextfree grammars 1