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On Independence and Capacity of Multidimensional Semiconstrained Systems

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Ohad Elishco, Tom Meyerovitch, Moshe Schwartz

Dynamical Systems · Submitted 15 Sep 2017

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

The authors' main claim We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity.

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arXiv ID1709.05105 (version 1)
Pith IDI34NA7UV, Pith's permanent record of this paper and its review
CitationMoshe Schwartz, Ohad Elishco, Tom Meyerovitch. "On Independence and Capacity of Multidimensional Semiconstrained Systems." arXiv:1709.05105 (2017). https://pith.science/paper/I34NA7UV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,283 input tokens.

What the abstract itself states, as probabilities: claims first 0.13 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.60 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. Using the independence entropy, we obtain new lower bounds on the capacity of multidimensional semiconstrained systems in general, and $d$-dimensional axial-product systems in particular. In the case of the latter, we prove our bound is asymptotically tight, giving the exact limiting capacity in terms of the independence entropy. We show the new bound improves upon the best-known bound in a case study of $(0,k,p)$-RLL.

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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 find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. result 0.95 0.97 0.85 asserted 1.00
s1 We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. method 0.92 0.92 0.05 asserted 0.99
s2 Using the independence entropy, we obtain new lower bounds on the capacity of multidimensional semiconstrained systems in general, and $d$-dimensional axial-product systems in particular. result 0.80 0.96 0.16 asserted 1.00
s3 In the case of the latter, we prove our bound is asymptotically tight, giving the exact limiting capacity in terms of the independence entropy. result 0.99 0.96 0.36 asserted 1.00
s4 We show the new bound improves upon the best-known bound in a case study of $(0,k,p)$-RLL. result 0.97 0.95 0.09 asserted 1.00

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

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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 find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. Using the independence entropy, we obtain new lower bounds on the capacity of multidimensional semiconstrained systems in general, and $d$-dimensional axial-product systems in particular. In the case of the latter, we prove our bound is asymptotically tight, giving the exact limiting capacity in terms of the independence entropy. We show the new bound improves upon the best-known bound in a case study of $(0,k,p)$-RLL.

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