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DOI: 10.4230/LIPIcs.ITCS.2022.32
URN: urn:nbn:de:0030-drops-156281
URL: https://drops.dagstuhl.de/opus/volltexte/2022/15628/
Bund, Johannes ; Lenzen, Christoph ; Medina, Moti
Small Hazard-Free 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 πͺ(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^{πͺ(s+π)} and depth πͺ(s*log(n) + π); in particular, if s, π,m β πͺ(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.
BibTeX - Entry
@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/opus/volltexte/2022/15628},
URN = {urn:nbn:de:0030-drops-156281},
doi = {10.4230/LIPIcs.ITCS.2022.32},
annote = {Keywords: Hazard-Freeness, Parallel Prefix Computation, Finite State Transducers}
}
| Keywords: | Hazard-Freeness, Parallel Prefix Computation, Finite State Transducers | |
| Seminar: | 13th Innovations in Theoretical Computer Science Conference (ITCS 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 25.01.2022 |
