## 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 2^{O(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 language | English |
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Title of host publication | 13th Innovations in Theoretical Computer Science Conference, ITCS 2022 |

Editors | Mark Braverman |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959772174 |

DOIs | |

State | Published - 1 Jan 2022 |

Event | 13th Innovations in Theoretical Computer Science Conference, ITCS 2022 - Berkeley, United States Duration: 31 Jan 2022 → 3 Feb 2022 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 215 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 13th Innovations in Theoretical Computer Science Conference, ITCS 2022 |
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Country/Territory | United States |

City | Berkeley |

Period | 31/01/22 → 3/02/22 |

### Bibliographical note

Funding Information:Johannes Bund: 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). Christoph Lenzen: 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). Moti Medina: The author was supported by the Israel Science Foundation under Grant 867/19.

Funding Information:

Funding Johannes Bund: 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). Christoph Lenzen: 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). Moti Medina: The author was supported by the Israel Science Foundation under Grant 867/19.

Publisher Copyright:

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

## Keywords

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