Small Hazard-Free Transducers

Summary

Ikenmeyer et al. (JACM'19) proved an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions. This raises the question: which classes of functions permit efficient hazard-free circuits? In this work, we prove that circuit implementations of transducers with small state space are such a class. A transducer is a finite state machine that transcribes, symbol by symbol, an input string of length n into an output string of length n. We present a construction that transforms any function arising from a transducer into an efficient circuit of size O(n) computing the hazard-free extension of the function. More precisely, given a transducer with s states, receiving n input symbols encoded by l bits, and computing n output symbols encoded by m bits, the transducer has a hazard-free circuit of size m*n*2^O(s+l) and depth O(s*log(n) + l); in particular, if s, l, m are element of O(1), size and depth are asymptotically optimal. In light of the strong hardness results by Ikenmeyer et al. (JACM'19), we consider this a surprising result.