Pith. sign in

REVIEW 2 cited by

Shannon Information and Kolmogorov Complexity

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv cs/0410002 v1 pith:T2Z22PBJ submitted 2004-10-01 cs.IT math.IT

classification cs.ITmath.IT
keywords kolmogorovinformationshannonversuscomplexitytheoryalgorithmicmutual
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (`algorithmic') mutual information, probabilistic sufficient statistic versus algorithmic sufficient statistic (related to lossy compression in the Shannon theory versus meaningful information in the Kolmogorov theory), and rate distortion theory versus Kolmogorov's structure function. Part of the material has appeared in print before, scattered through various publications, but this is the first comprehensive systematic comparison. The last mentioned relations are new.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. How much do language models memorize?

    cs.CL 2025-05 conditional novelty 6.0 of 10

    A compression-based measurement puts GPT-style model memorization capacity at roughly 3.6 bits per parameter, with membership inference success following a sigmoid in the dataset-to-capacity ratio.

  2. Breaking through the classical Shannon entropy limit: A new frontier through logical semantics

    cs.IT 2024-12 reject novelty 6.0 of 10

    The authors state a Shannon-style rate bound for communication with deductive reasoning, governed by a function they call logical semantic entropy, but provide no proof in this text.

Pith tools