Functions computable in polynomial space

Polynomial time computable real functions

In this paper, we study computability and complexity of real functions. We extend these notions, already defined for functions over closed intervals or over the real line to functions over particular real open sets and give some results and characterizations, especially for polynomial time computable functions. Our representation of real numbers as sequences of rational numbers allows us to imp...

Differentiability of polynomial time computable functions

We show that a real z is polynomial time random if and only if each nondecreasing polynomial time computable function is differentiable at z. This establishes an analog in feasible analysis of a recent result of Brattka, Miller and Nies, who characterized computable randomness in terms of differentiability of nondecreasing computable functions. Further, we show that a Martin-Löf random real z i...

On Functions Computable in Nondeterministic Polynomial Time: Some Characterizations

It is shown how certain refutation methods can be extended into semi-decision procedures that are complete for both unsatisfiability and finite satisfiability. The proposed extension is justified by a new characterization of finite satisfiability. This research was motivated by a database design problem: Deduction rules and integrity constraints in definite databases have to be finitely satisfi...

Polynomial differential equations compute all real computable functions on computable compact intervals

In the last decade, the field of analog computation has experienced renewed interest. In particular, there have been several attempts to understand which relations exist between the many models of analog computation. Unfortunately, most models are not equivalent. It is known that Euler’s Gamma function is computable according to computable analysis, while it cannot be generated by Shannon’s Gen...

Computable Bounds for Polynomial Ergodicity