Small Hazard-Free Transducers

Johannes Bund, Christoph Lenzen, Moti Medina

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 2O(s+ℓ)mn 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.

Original languageEnglish
Title of host publication13th Innovations in Theoretical Computer Science Conference, ITCS 2022
EditorsMark Braverman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772174
DOIs
StatePublished - 1 Jan 2022
Externally publishedYes
Event13th Innovations in Theoretical Computer Science Conference, ITCS 2022 - Berkeley, United States
Duration: 31 Jan 20223 Feb 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume215
ISSN (Print)1868-8969

Conference

Conference13th Innovations in Theoretical Computer Science Conference, ITCS 2022
Country/TerritoryUnited States
CityBerkeley
Period31/01/223/02/22

Keywords

  • Finite state transducers
  • Hazard-freeness
  • Parallel prefix computation

ASJC Scopus subject areas

  • Software

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