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Fast synchronization of inhomogenous random automata

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Balázs Gerencsér, Zsombor Várkonyi

Combinatorics · Submitted 10 Jun 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n} \big)$ with high probability, assuming only certain partial independence of the letters.

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arXiv ID2206.05043 (version 2)
Pith IDOXHYD5FA, Pith's permanent record of this paper and its review
CitationBal\'azs Gerencs\'er, Zsombor V\'arkonyi. "Fast synchronization of inhomogenous random automata." arXiv:2206.05043 (2022). https://pith.science/paper/OXHYD5FA
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,667 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.70 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.07 · states quantitative result 0.98 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We examine the reset threshold of randomly generated deterministic automata. We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n} \big)$ with high probability, assuming only certain partial independence of the letters. Our observation is motivated by Nicaud (2014) providing a near-linear bound in the case of two random mapping letters, among multiple other results. The upper bound for the latter case has been recently improved by the breakthrough work of Chapuy and Perarnau (2023) to $\mathcal{O}(\sqrt{n} \log n)$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We examine the reset threshold of randomly generated deterministic automata. contribution 0.56 0.74 0.04 asserted 0.58
s1 We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n} \big)$ with high probability, assuming only certain partial independence of the letters. result 0.84 0.93 0.89 asserted 1.00
s2 Our observation is motivated by Nicaud (2014) providing a near-linear bound in the case of two random mapping letters, among multiple other results. background 1.00 0.07 0.03 asserted 0.97
s3 The upper bound for the latter case has been recently improved by the breakthrough work of Chapuy and Perarnau (2023) to $\mathcal{O}(\sqrt{n} \log n)$. background 0.99 0.03 0.04 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We examine the reset threshold of randomly generated deterministic automata. We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n} \big)$ with high probability, assuming only certain partial independence of the letters. Our observation is motivated by Nicaud (2014) providing a near-linear bound in the case of two random mapping letters, among multiple other results. The upper bound for the latter case has been recently improved by the breakthrough work of Chapuy and Perarnau (2023) to $\mathcal{O}(\sqrt{n} \log n)$.

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