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@InProceedings{Darulova:2013:EMSOFT, author = "Eva Darulova and Viktor Kuncak and Rupak Majumdar and Indranil Saha", booktitle = "Proceedings of the International Conference on Embedded Software (EMSOFT 2013)", title = "Synthesis of fixed-point programs", year = "2013", month = sep # " 29-" # oct # " 4", keywords = "genetic algorithms, genetic programming, SBSE, Software Engineering, Design-Methodologies, synthesis, stochastic optimisation, embedded control software", URL = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.368.1023", DOI = "doi:10.1109/EMSOFT.2013.6658600", abstract = "Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the real numbers into an imperative program using fixed-point arithmetic. Fixed-point arithmetic only approximates real values, and its operators do not have the fundamental properties of real arithmetic, such as associativity. Consequently, a naive compilation process can yield a program that significantly deviates from the real polynomial, whereas a different order of evaluation can result in a program that is close to the real value on all inputs in its domain. 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.", notes = "Also known as \cite{6658600}", }

Genetic Programming entries for Eva Darulova Viktor Kuncak Rupak Majumdar Indranil Saha