Point algebras for temporal reasoning: Algorithms and complexity

Broxvall, Mathias; Jönsson, Peter

doi:10.1016/s0004-3702(03)00075-4

Cited by 28 publications

(18 citation statements)

References 24 publications

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“…The class of temporal constraint languages is of fundamental importance for infinite domain constraint satisfaction, since CSPs for such languages appear as important special cases in several other classes of CSPs that have been studied, e.g., constraint languages about branching time, partially ordered time, spatial reasoning, and set constraints [9,22,32]. Moreover, several polynomial-time solvable classes of constraint languages on time intervals [21,34,37] can be solved by translation into polynomial-time solvable temporal constraint languages.…”

mentioning

confidence: 99%

The complexity of temporal constraint satisfaction problems

Bodirsky

Kára

2008

Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing

144

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A temporal constraint language is a set of relations that has a first-order definition in (Q; <), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint languages, then the CSP can be solved in polynomial time; otherwise, the CSP is NP-complete. Our proof combines model-theoretic concepts with techniques from universal algebra, and also applies the so-called product Ramsey theorem, which we believe will useful in similar contexts of constraint satisfaction complexity classification.An extended abstract of this paper appeared in the proceedings of STOC'08.

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confidence: 99%

The complexity of temporal constraint satisfaction problems

Bodirsky

Kára

2008

Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing

144

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“…Yet another algorithm with a running time that is quadratic in the input size has been described in [BK02]. The complexity of the CSP of disjunctive reducts of (S 2 ; ≤, ≺) has been determined in [BJ03]; a disjunctive reduct is a reduct each of whose relations can be defined by a disjunction of the basic relations in such a way that the disjuncts do not share common variables.…”

Section: Applications In Constraint Satisfactionmentioning

confidence: 99%

“…The structure (S 2 ; ≤) plays an important role in the study of a natural class of constraint satisfaction problems (CSPs) in theoretical computer science. CSPs from this class have been studied in artificial intelligence for qualitative reasoning about branching time [Due05,Hir96,BJ03], and, independently, in computational linguistics [Cor94,BK02] under the name tree description or dominance constraints.…”

Section: Introductionmentioning

confidence: 99%

The universal homogeneous binary tree

Bodirsky

Bradley-Williams

Pinsker

et al. 2018

Journal of Logic and Computation

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A partial order is called semilinear if the upper bounds of each element are linearly ordered and any two elements have a common upper bound. There exists, up to isomorphism, a unique countable existentially closed semilinear order, which we denote by (S2; ≤). We study the reducts of (S2; ≤), that is, the relational structures with domain S2, all of whose relations are first-order definable in (S2; ≤). Our main result is a classification of the model-complete cores of the reducts of S2. From this, we also obtain a classification of reducts up to first-order interdefinability, which is equivalent to a classification of all subgroups of the full symmetric group on S2 that contain the automorphism group of (S2; ≤) and are closed with respect to the pointwise convergence topology.

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“…Interactive points control the starting or ending time of so-called static temporal objects. A partial order among temporal objects is given by point-to-point relations without disjunction nor inequality: Qualitative temporal relations between the start or end of two temporal objects; for instance, the start of a is executed before the end of b, or the start of a is executed at the same time than the start of b [7]. A score is a tuple consisting of an object hierarchy, a set of temporal relations over those objects and a set of point identifiers, such that two interactive points cannot start at the same time, for simplicity.…”

Section: Interactive Scoresmentioning

confidence: 99%

Backtracking-free Interactive Music Scores with Temporal Relations over Rythms

Toro¹

2018

Preprint

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Another alternative to solve CSP s is to use (incomplete) local search algorithmsto find interatively an approximative solution. Local search is a metaheuristic forsolving computationally hard optimization problems. An example of local searchis adaptive search: A computational method that optimizes a problem by iterativelytrying to improve a candidate solution with regard to the problem constraints (andpossibly an optimization function). In spite of the advances in constraint solving for music compositions problems,as far as we know, there is little research on solving CSP s during real-time music interaction. In this paper we will focus on interactive scores, a formalism for thedesign of interactive scenarios closely related to constraint programming. we do not have a polynomial algorythm to solve all instances ofthe problem. Consider, for instance, the case where the durations of the temporalobjects are not singles values nor intervals, but discrete values.

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Point algebras for temporal reasoning: Algorithms and complexity

Cited by 28 publications

References 24 publications

The complexity of temporal constraint satisfaction problems

The complexity of temporal constraint satisfaction problems

The universal homogeneous binary tree

Backtracking-free Interactive Music Scores with Temporal Relations over Rythms

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