Relational queries computable in polynomial time
Information and Control
The expressiveness of a family of finite set languages
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Tractable query languages for complex object databases
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On the expressive power of database queries with intermediate types
Journal of Computer and System Sciences
Type systems for programming languages
Handbook of theoretical computer science (vol. B)
A new recursion-theoretic characterization of the polytime functions (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Bounded linear logic: a modular approach to polynomial-time computability
Theoretical Computer Science
Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
A simple proof of a theorem of Statman
Theoretical Computer Science
On the complexity of queries in the logical data model
ICDT Selected papers of the 4th international conference on Database theory
Lambda calculus characterizations of poly-time
Fundamenta Informaticae - Special issue: lambda calculus and type theory
Functional database query languages as typed lambda calculi of fixed order (extended abstract)
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Principles of programming with complex objects and collection types
ICDT '92 Selected papers of the fourth international conference on Database theory
Finite model theory in the simply typed lambda calculus
Finite model theory in the simply typed lambda calculus
The Expressiveness of Simple and Second-Order Type Structures
Journal of the ACM (JACM)
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
The Definition of Standard ML
Space Usage in Functional Query Languages
ICDT '95 Proceedings of the 5th International Conference on Database Theory
Tailoring Recursing for Complexity
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Towards a theory of type structure
Programming Symposium, Proceedings Colloque sur la Programmation
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Algebras of feasible functions
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
In Memoriam: Paris C. Kanellakis
PCK50 Proceedings of the Paris C. Kanellakis memorial workshop on Principles of computing & knowledge: Paris C. Kanellakis memorial workshop on the occasion of his 50th birthday
The expressive power of higher-order types or, life without CONS
Journal of Functional Programming
Light types for polynomial time computation in lambda calculus
Information and Computation
The complexity of β-reduction in low orders
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Complexity of higher-order queries
Proceedings of the 14th International Conference on Database Theory
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We present a functional framework for descriptive computational complexity, in which the Regular, First-order, Ptime, Pspace, k-Exptime, k-Expspace (k = 1), and Elementary sets have syntactic characterizations. In this framework, typed lambda terms represent inputs and outputs as well as programs. The lambda calculi describing the above computational complexity classes are simply or Let-polymorphically typed with functionalities of fixed order. They consist of: order 0 atomic constants, order 1 equality among these constants, variables, application, and abstraction. Increasing functionality order by one for these languages corresponds to increasing the computational complexity by one alternation. This exact correspondence is established using a semantic evaluation of languages for each fixed order, which is the primary technical contribution of this paper.