Characterizing complexity classes by higher type primitive recursive definitions
Theoretical Computer Science
Stratified functional programs and computational complexity
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
A type system for bounded space and functional in-place update
Nordic Journal of Computing
Linear Types and Non Size-Increasing Polynomial Time Computation
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Syntactical Analysis of Non-Size-Increasing Polynomial Time Computation
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
The expressive power of higher-order types or, life without CONS
Journal of Functional Programming
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We study the expressive power non-size increasing recursive definitions over lists. This notion of computation is such that the size of all intermediate results will automatically be bounded by the size of the input so that the interpretation in a finite model is sound with respect to the standard semantics. Many well-known algorithms with this property such as the usual sorting algorithms are definable in the system in the natural way. The main result is that a characteristic function is definable if and only if it is computable in time O(2p(n)) for some polynomial p. The method used to establish the lower bound on the expressive power also shows that the complexity becomes polynomial time if we allow primitive recursion only. This settles an open question posed in [1,6]. The key tool for establishing upper bounds on the complexity of derivable functions is an interpretation in a finite relational model whose correctness with respect to the standard interpretation is shown using a semantic technique.