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It is currently not clear what the potential is of neuromorphic hardwarebeyond machine learning and neuroscience. In this project, a problem isinvestigated that is inherently difficult to fully implement in neuromorphichardware by introducing a new machine model in which a conventional Turingmachine and neuromorphic oracle work together to solve such types of problems.We show that the P-complete Max Network Flow problem is intractable in modelswhere the oracle may be consulted only once (`create-and-run' model) butbecomes tractable using an interactive (`neuromorphic co-processor') model ofcomputation. More in specific we show that a logspace-constrained Turingmachine with access to an interactive neuromorphic oracle with linear space,time, and energy constraints can solve Max Network Flow. A modified variant ofthis algorithm is implemented on the Intel Loihi chip; a neuromorphic manycoreprocessor developed by Intel Labs. We show that by off-loading the search foraugmenting paths to the neuromorphic processor we can get energy efficiencygains, while not sacrificing runtime resources. This result demonstrates howP-complete problems can be mapped on neuromorphic architectures in atheoretically and potentially practically efficient manner.

A spiking neural algorithm for the Network Flow problem