Feasible computation in higher types
Feasible computation in higher types
Lambda calculus characterizations of poly-time
Fundamenta Informaticae - Special issue: lambda calculus and type theory
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
Subrecursive programming systems: complexity & succinctness
Subrecursive programming systems: complexity & succinctness
A foundational delineation of poly-time
Papers presented at the IEEE symposium on Logic in computer science
A New Characterization of Type-2 Feasibility
SIAM Journal on Computing
Programming languages capturing complexity classes
ACM SIGACT News
Types and programming languages
Types and programming languages
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Linear types and non-size-increasing polynomial time computation
Information and Computation - Special issue: ICC '99
On characterizations of the basic feasible functionals, Part I
Journal of Functional Programming
A denotational approach to measuring complexity in functional programs
A denotational approach to measuring complexity in functional programs
Time-Complexity Semantics for Feasible Affine Recursions
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
An Implicit Characterization of PSPACE
ACM Transactions on Computational Logic (TOCL)
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This paper investigates what is essentially a call-by-value version of PCF under a complexity-theoretically motivated type system. The programming formalism, ATR1, has its first-order programs characterize the poly-time computable functions, and its second-order programs characterize the type-2 basic feasible functionals of Mehlhorn and of Cook and Urquhart. (The ATR1-types are confined to levels 0, 1, and 2.) The type system comes in two parts, one that primarily restricts the sizes of values of expressions and a second that primarily restricts the time required to evaluate expressions. The size-restricted part is motivated by Bellantoni and Cook's and Leivant's implicit characterizations of poly-time. The time-restricting part is an affine version of Barber and Plotkin's DILL. Two semantics are constructed for ATR1. The first is a pruning of the naïve denotational semantics for ATR1. This pruning removes certain functions that cause otherwise feasible forms of recursion to go wrong. The second semantics is a model for ATR1's time complexity relative to a certain abstract machine. This model provides a setting for complexity recurrences arising from ATR1 recursions, the solutions of which yield second-order polynomial time bounds. The time-complexity semantics is also shown to be sound relative to the costs of interpretation on the abstract machine.