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DOI: 10.4230/LIPIcs.ITCS.2022.32

Small Hazard-Free Transducers

Authors: Johannes Bund, Christoph Lenzen, and Moti Medina

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

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 n*m*2^{𝒪(s+𝓁)} and depth 𝒪(s*log(n) + 𝓁); in particular, if s, 𝓁,m ∈ 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.

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Johannes Bund, Christoph Lenzen, and Moti Medina. Small Hazard-Free Transducers. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 32:1-32:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bund_et_al:LIPIcs.ITCS.2022.32,
  author =	{Bund, Johannes and Lenzen, Christoph and Medina, Moti},
  title =	{{Small Hazard-Free Transducers}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{32:1--32:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.32},
  URN =		{urn:nbn:de:0030-drops-156281},
  doi =		{10.4230/LIPIcs.ITCS.2022.32},
  annote =	{Keywords: Hazard-Freeness, Parallel Prefix Computation, Finite State Transducers}
}

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Small Hazard-Free Transducers

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