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Small Hazard-Free Transducers

Talkat ITCS 2022 · 2022-01-31..02-03
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Claims that every Mealy transducer on n inputs admits a hazard-free circuit of size O(n · 2^{|S|+e}) and depth O(|S| log n + e) where |S| is state count and e is input-encoding size, built by adapting Lauter Fisher parallel-prefix composition and using state-subset transition matrices that record transitions for every subset to avoid information loss under u inputs. Construction yields logarithmic depth for constant |S| and e. Application to addition uses a unary+Gray encoding and assumes bounded uncertainty; circuits are explicit though constants may be large.

AI-written summary · about

  1. 0:00Intro
  2. 0:14Circuit Complexity in Ternary Logic
  3. 1:29Motivation
  4. 2:07From Ternary to Binary and Back
  5. 3:40Definition of a Hazard
  6. 4:51Hazard-Free Circuit Complexity
  7. 7:12Parallel Prefix Computation
  8. 8:31Universal Function Encoding
  9. 10:27Application - Addition
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