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STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A shorter model theory
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Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
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A Dichotomy Theorem for Constraints on a Three-Element Set
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The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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SIAM Journal on Computing
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Quantified Equality Constraints
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
The complexity of temporal constraint satisfaction problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Quantified Positive Temporal Constraints
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
The complexity of equality constraint languages
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Qualitative temporal and spatial reasoning revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Syntactically characterizing local-to-global consistency in ORD-Horn
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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A positive temporal template (or a positive temporal constraint language) is a relational structure whose relations can be defined over a dense linear order of rational numbers using a relational symbol ≤, logical conjunction and disjunction. We provide a complexity characterization for quantified constraint satisfaction problems (QCSP ) over positive temporal languages. The considered QCSP problems are decidable in LOGSPACE or complete for one of the following classes: NLOGSPACE, P, NP, PSPACE. Our classification is based on so-called algebraic approach to constraint satisfaction problems: we first classify positive temporal languages depending on their surjective polymorphisms and then give the complexity of QCSP for each obtained class. The complete characterization is quite complex and does not fit into one paper. Here we prove that QCSP for positive temporal languages is either NP-hard or belongs to P and we give the whole description of the latter case, that is, we show for which positive temporal languages the problem QCSP is in LOGSPACE, and for which it is NLOGSPACE-complete or P-complete. The classification of NP-hard cases is given in a separate paper.