154 citations · 438 across the 55 of their papers we have counts for
5 papers · 1 filter
Computing over the Reals: Foundations for Scientific Computing
Mark Braverman, Stephen Cook
We give a detailed treatment of the ``bit-model'' of computability and complexity of real functions and subsets of R^n, and argue that this is a good way to formalize many problems…
Parabolic Julia Sets are Polynomial Time Computable
Mark Braverman
In this paper we prove that parabolic Julia sets of rational functions are locally computable in polynomial time.
On computational complexity of Riemann mapping
Ilia Binder, Mark Braverman, Michael Yampolsky
In this paper we consider the computational complexity of uniformizing a domain with a given computable boundary. We give nontrivial upper and lower bounds in two settings: when th…
On the Complexity of Real Functions
Mark Braverman
We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function…
On computational complexity of Siegel Julia sets
I. Binder, M. Braverman, M. Yampolsky
It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a lar…