TY - GEN

T1 - Small Hazard-Free Transducers

AU - Bund, Johannes

AU - Lenzen, Christoph

AU - Medina, Moti

N1 - Publisher Copyright:
© Johannes Bund, Christoph Lenzen, and Moti Medina; licensed under Creative Commons License CC-BY 4.0

PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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.

AB - 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.

KW - Finite state transducers

KW - Hazard-freeness

KW - Parallel prefix computation

UR - http://www.scopus.com/inward/record.url?scp=85124010540&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ITCS.2022.32

DO - 10.4230/LIPIcs.ITCS.2022.32

M3 - Conference contribution

AN - SCOPUS:85124010540

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 13th Innovations in Theoretical Computer Science Conference, ITCS 2022

A2 - Braverman, Mark

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 13th Innovations in Theoretical Computer Science Conference, ITCS 2022

Y2 - 31 January 2022 through 3 February 2022

ER -