Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Constant time factors do matter
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
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Journal of the ACM (JACM)
On Effective Procedures for Speeding Up Algorithms
Journal of the ACM (JACM)
Computational Complexity and the Existence of Complexity Gaps
Journal of the ACM (JACM)
Recursive Properties of Abstract Complexity Classes
Journal of the ACM (JACM)
Intuitionistic Light Affine Logic
ACM Transactions on Computational Logic (TOCL)
Effective Applicative Structures
CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
Experiments with Implementations of Two Theoretical Constructions
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Unsolvability considerations in computational complexity
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Classes of computable functions defined by bounds on computation: Preliminary Report
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
On light logics, uniform encodings and polynomial time
Mathematical Structures in Computer Science
Synthesis of max-plus quasi-interpretations
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
ACM Transactions on Computational Logic (TOCL)
Course of value distinguishes the intentionality of programming languages
Proceedings of the Second Symposium on Information and Communication Technology
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The proofs of major results of Computability Theory like Rice, Rice-Shapiro or Kleene's fixed point theorem hidemore information of what is usually expressed in theirrespective statements. We make this information explicit, allowing to state stronger, complexity theoretic-versions of all these theorems. In particular, we replace the notion of extensional set of indices of programs, by a set of indices of programs having not only the same extensional behavior but also similar complexity (Complexity Clique). We prove, under very weak complexity assumptions, that any recursive Complexity Clique is trivial, and any r.e. Complexity Clique is an extensional set (and thus satisfies Rice-Shapiro conditions). This allows, for instance, to use Rice's argument to prove that the property of having polynomial complexity is not decidable, and to use Rice-Shapiro to conclude that it is not even semi-decidable. We conclude the paper with a discussion of "complexity-theoretic" versions of Kleene's Fixed Point Theorem.