Small Hazard-Free Transducers

Abstract

In digital circuits, hazardous input signals are a result of spurious operation of bistable elements. For example, the problem occurs in circuits with asynchronous inputs or clock domain crossings. Marino (TC’81) showed that hazards in bistable elements are inevitable. Hazard-free circuits compute the “most stable” output possible on hazardous inputs, under the constraint that it returns the same output as the circuit on stable inputs. Ikenmeyer et al. (JACM’19) proved an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions. Despite that, asymptotically optimal hazard-free sorting circuit are possible (Bund et al., TC’19). This raises the question: Which classes of functions permit efficient hazard-free circuits? 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 that computes the hazard-free extension of the function. For transducers with constant state space, the circuit has asymptotically optimal size, with small constants if the state space is small.