State of the art

Terms are defined in review.md; works are listed in the bibliography.

1. The shape of the linking function f

Measure Holder Method Result Grade
Reading time, English Shain et al. 2024 6 datasets, many language models, nonlinear regression f linear in surprisal measured
Reading time, 11 languages Wilcox et al. 2023 monolingual and multilingual models f linear in surprisal measured
Reading time, super-linear claims Meister et al. 2021; Hoover et al. 2023; Xu et al. 2023 reading corpora weak or model-dependent super-linearity supported with caveat
Reading time, cloze-controlled items Brothers & Kuperberg 2021 vs Buggy et al. 2026 same items, self-paced reading vs eye-tracking linear in probability vs logarithmic contested
Acceptability Meister et al. 2021 acceptability judgments non-uniform surprisal lowers acceptability supported with caveat (one study)

2. Does spreading information evenly lower cost?

A text of n words carries surprisals s_1 ... s_n, with total S = s_1 + ... + s_n. Its total cost is C = f(s_1) + ... + f(s_n).

  • f convex: by Jensen's inequality, C ≥ n·f(S/n), with equality when every s_i = S/n; uniform is the minimum.
  • f linear, f(s) = a + b·s: C = a·n + b·S; the distribution does not matter, only n and S do.
  • f concave: uniform is the maximum; clustering information is cheaper.
  • Cost linear in probability (Brothers & Kuperberg 2021) means f(s) = a - b·2^(-s), which is concave in s.
Measure Best-supported f Consequence at fixed n and S
Reading time linear spreading buys nothing measurable; lowering S or n does
Acceptability convex uniform surprisal is judged better
  • Grade: the argument is proved; the reading-time verdict is measured; the acceptability verdict is supported with caveat.
  • Caveat: a rewrite changes n and S, so "fixed n and S" is an idealization.
  • Caveat: cost spills over to the next words, so C is not exactly a sum of independent terms.

3. Dependency length

  • Upper bound reached by languages: D between random and optimal in all 37 languages of Futrell et al. 2015.
  • Degree reached: half of 93 languages at 70% or more of the possible reduction (Ferrer-i-Cancho et al. 2022).
  • Not reached: the optimum; observed D stays above it, Indonesian coming closest (Futrell et al. 2015).
  • Processing: the cleanest effect is in controlled sentences (Grodner & Gibson 2005); naturalistic reading bounds it (Demberg & Keller 2008).

4. Nesting

  • Observed maximum of use: degree 3 in writing, practically absent in speech (Karlsson 2007); a corpus count, not a processing limit.
  • Processing: degree 2 already yields an illusion in English (Gibson & Thomas 1999) but not in German (Vasishth et al. 2010).

5. Text and text tree

  • Strongest applied evidence: model-guided revision (Britton & Gülgöz 1991), summarized by Gülgöz et al. 1999.
  • Levels effect: recall (Meyer & McConkie 1973), eye-tracking (Wu et al. 2016), conditional on reader skill (Meyer et al. 1980).
  • Coherence modelling: the entity grid is the classical baseline (Barzilay & Lapata 2008); neural successors not reviewed here.

6. Ordering complexity

Problem Bound Source Kind Grade
MinLA, general graph NP-complete Garey et al. 1976 lower measured (theorem)
MinLA, tree polynomial, O(n^2.2) (abstract only) Shiloach 1979; Chung 1984 upper measured (theorem)
Projective or planar minimum, tree linear time Alemany-Puig et al. 2022 upper measured (theorem)
Arrangement of an acyclic directed graph NP-complete Even and Shiloach, as cited in Shiloach 1979 lower supported with caveat (secondary)
Linear ordering, rooted tree (root at the left end, each node after all its ancestors) O(n log n) Adolphson & Hu 1973, section 3 upper measured (theorem)
Unit-time scheduling with precedence, weighted completion time NP-hard Lawler 1978 (proved in its 1976 report, p. 4; weights arbitrary) lower supported with caveat
  • Caveat on the acyclic directed row, cited through Shiloach 1979 (abstract only): its definition of the directed version was not read, nor was Even and Shiloach.
  • The rooted-tree row is the ordered version: Adolphson and Hu 1973 (section 2) place each node after its predecessors, so it is not MinLA on an undirected tree.
  • Futrell et al. 2015 compare to the projective minimum, not to unconstrained MinLA.
  • The unconstrained tree minimum (Chung 1984) is the baseline of Ferrer-i-Cancho et al. 2022.

Ordering notes as scheduling (derivation in this file)

  • Concepts form a directed graph: an edge u → v means v uses u; the order π must put u before v.
  • Every edge then points forward, so D(π) = Σ over edges of (π(v) - π(u)) = Σ over x of π(x)·(in(x) - out(x)).
  • That is a weighted sum of positions under precedence, with weight w(x) = in(x) - out(x).
  • With units of equal length, adding a constant to every weight changes D by a constant, so negative weights are harmless.
  • It is then unit-time single-machine scheduling with precedence, minimizing weighted completion time.
  • Known: with series-parallel precedence, rooted forests included, that problem is solvable in O(n log n) time once the decomposition is given (Lawler 1978; its 1976 report read, the published chapter not). An undirected path need not be series-parallel.
  • With sections of unequal length, positions become start offsets and the weights keep both signs; standard results assume non-negative weights, so none is claimed.
  • Not found: whether weights of the form in(x) - out(x) keep the general case NP-hard; this file makes no such claim.

7. Measurement

  • Readability: models built from NLP features beat Flesch-Kincaid for adult comprehension, processing and familiarity (Crossley et al. 2017).
  • Surprisal source: larger transformer models with lower perplexity fit reading time worse (Oh & Schuler 2023).

8. Most adopted, kept apart from best evidence

Sub-question Most adopted (practice record) Best evidence (research record)
Sentence length average 20 words (EC 2011); average 15, cap 25 (Style Manual AU 2024) dependency length, not word count (Futrell et al. 2015; corpus evidence, no comprehension test)
Readability number Flesch floor of 40 to 50 in US state law (NAIC 2025); grade 9 default (Hemingway 2026) NLP-feature models beat Flesch for adults (Crossley et al. 2017)
Nesting advice to avoid legalese register of legalese hurt recall, with center-embedding the strongest feature in an exploratory, underpowered model; N = 184 over two experiments (Martinez et al. 2022)
  • No source read here states a comprehension test of any word cap.
  • The practice record is convention, untested; the adoption counts are measured, descriptive.