Created by W.Langdon from gp-bibliography.bib Revision:1.4780
We present a compilation scheme for real-valued arithmetic expressions to fixed-point arithmetic programs. Given a real-valued polynomial expression t, we find an expression t' that is equivalent to t over the reals, but whose implementation as a series of fixed-point operations minimises the error between the fixed-point value and the value of t over the space of all inputs. We show that the corresponding decision problem, checking whether there is an implementation t' of t whose error is less than a given constant, is NP-hard. We then propose a solution technique based on genetic programming. Our technique evaluates the fitness of each candidate program using a static analysis based on affine arithmetic. We show that our tool can significantly reduce the error in the fixed-point implementation on a set of linear control system benchmarks. For example, our tool found implementations whose errors are only one half of the errors in the original fixed-point expressions.",
Genetic Programming entries for Eva Darulova Viktor Kuncak Rupak Majumdar Indranil Saha