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Small Hazard-Free Transducers

Authors Johannes Bund , Christoph Lenzen, Moti Medina

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ACM Subject Classification
  • Hardware → Fault tolerance
  • Theory of computation → Circuit complexity
Keywords
  • Hazard-Freeness
  • Parallel Prefix Computation
  • Finite State Transducers

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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) https://doi.org/10.4230/LIPIcs.ITCS.2022.32

Author Details

Johannes Bund
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Christoph Lenzen
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Moti Medina
  • Faculty of Engineering, Bar-Ilan University, Ramat Gan, Israel

Funding

  • Bund, Johannes: The author has received support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 716562).
  • Lenzen, Christoph: The author has received support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 716562).
  • Medina, Moti: The author was supported by the Israel Science Foundation under Grant 867/19.

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