Relational queries computable in polynomial time
Information and Control
Capturing complexity classes by fragments of second-order logic
Theoretical Computer Science - Special issue on logic and applications to computer science
Information and Computation - Special issue: logic and computational complexity
The OPL optimization programming language
The OPL optimization programming language
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Some Decision Problems of Enormous Complexity
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Predicate-calculus-based logics for modeling and solving search problems
ACM Transactions on Computational Logic (TOCL)
Automated reformulation of specifications by safe delay of constraints
Artificial Intelligence
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
The Design of the Zinc Modelling Language
Constraints
A framework for representing and solving NP search problems
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
The design of ESSENCE: a constraint language for specifying combinatorial problems
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
The rules of constraint modelling
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
GrinGo: a new grounder for answer set programming
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Detecting and breaking symmetries by reasoning on problem specifications
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
NP-SPEC: an executable specification language for solving all problems in NP
Computer Languages
Declarative programming of search problems with built-in arithmetic
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
PBINT, a logic for modelling search problems involving arithmetic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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Development of languages for specifying or modelling problems is an important direction in constraint modelling. To provide greater abstraction and modelling convenience, these languages are becoming more syntactically rich, leading to a variety of questions about their expressive power. In this paper, we consider the expressiveness of Essence, a specification language with a rich variety of syntactic features. We identify natural fragments of Essence that capture the complexity classes P, NP, all levels $\Sigma_i^p$ of the polynomial-time hierarchy, and all levels k-NEXP of the nondeterministic exponential-time hierarchy. The union of these classes is the very large complexity class ELEMENTARY. One goal is to begin to understand which features play a role in the high expressive power of the language and which are purely features of convenience. We also discuss the formalization of arithmetic in Essence and related languages, a notion of capturing NP-search which is slightly different than that of capturing NP, and a conjectured limit to the expressive power of Essence. Our study is an application of descriptive complexity theory, and illustrates the value of taking a logic-based view of modelling and specification languages.