Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1811.12369 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913667102015488 |
|---|---|
| author | Bund, Johannes Lenzen, Christoph Medina, Moti |
| author_facet | Bund, Johannes Lenzen, Christoph Medina, Moti |
| contents | 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 $\mathcal{O}(n)$ 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 $2^{\mathcal{O}(s+\ell)} m n$ and depth $\mathcal{O}(s\log n + \ell)$; in particular, if $s, \ell,m\in \mathcal{O}(1)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_12369 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Small Hazard-free Transducers Bund, Johannes Lenzen, Christoph Medina, Moti Data Structures and Algorithms Computational Complexity 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 $\mathcal{O}(n)$ 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 $2^{\mathcal{O}(s+\ell)} m n$ and depth $\mathcal{O}(s\log n + \ell)$; in particular, if $s, \ell,m\in \mathcal{O}(1)$, 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. |
| title | Small Hazard-free Transducers |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/1811.12369 |