Unifying lower bounds for algebraic machines, semantically

We present a new abstract method for proving lower bounds in computational complexity based on the notion of topological and measurable entropy for dynamical systems. It is shown to generalise several previous lower bounds results from the literature in algebraic complexity, thus providing a unifying framework for “topological” proofs of lower bounds. We further use this method to prove that maxflow, a ▪ complete problem, is not computable in polylogarithmic time on parallel random access machines (prams) working with real numbers. This improves on a result of Mulmuley since the class of machines considered extends the class “prams without bit operations”, making more precise the relationship between Mulmuley's result and similar lower bounds on real prams.