https://w3id.org/np/RA_p-Wzd6BeXHLLIoi6Cncr1guP0myeKdp4tb6fCLTDaQ
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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dc:description "analysis.py compiles revca.c and runs the exhaustive depth-first enumeration of rule tables for (k,r) = (2,1), (2,2) and (3,1). Table entries are assigned in order of the period of their neighbourhood word; after each assignment the pair graph of the de Bruijn graph is built from definite edges (both labels assigned and equal) and the branch is cut if an off-diagonal cycle or a diagonal-to-diagonal path through off-diagonal nodes exists (both are sound: they witness two distinct configurations with the same image); the balance condition (each colour exactly k^(2r) times) also prunes. At a leaf the same test is exact. The 1800 rules found for k = 3 are then checked in Python with Wolfram's ReversibleQ (distinct successors of all cyclic configurations of length <= 9), 10000 random balanced k = 3 tables not in the list are checked to fail it, all 256 elementary rules are classified by both methods, and the k = 3 rules are grouped into symmetry families under colour permutations and reflection.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 1800 reversible rules among the 3^27 three-colour nearest-neighbour cellular automata (claimed 1800) (n = 7625597484987, exact (exhaustive enumeration)). Interpretation: 'Reversible' is taken as injectivity of the global map on the full shift (bi-infinite configurations), the standard notion and the one Wolfram's note tests through periodic configurations. Rule numbering is Wolfram's (table entry for neighbourhood (l,c,r) at digit position l*k^2 + c*k + r of the base-k rule number). The count is of raw rule tables, not of symmetry classes (the note gives 172 families for k = 3). The enumeration is exact, so there is no sampling uncertainty; the only risks are implementation errors, which the k = 2 (r = 1 and r = 2) checks and the independent periodic-configuration test guard against. Note: the pruning search is written in C (compiled with gcc from analysis.py) because a Python search over the pruned tree would be too slow; this is a deviation from 'python3 only' tooling and is recorded.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch09-02: supports, confidence 0.97";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-02/result.json>;
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<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: reversible-ca-enumeration-generator, nks-note-numbers-of-reversible-rules";
<https://w3id.org/delphi/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<https://w3id.org/delphi/ontology/disconfirmingObservation> "Pre-registered. 'Refutes' if the exhaustive enumeration completes and gives a count other than 6 for k = 2, r = 1 or other than 1800 for k = 3, r = 1 (with the k = 2, r = 2 check giving 62, so the method is validated). If the k = 3 enumeration cannot be completed within the compute budget (about 1 hour), the verdict is 'mixed' or 'inconclusive' (reason: other) with the k = 2 result and a lower bound on the k = 3 count reported.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "Correctness of the pair-graph criterion is checked three ways: it reproduces the known 6 elementary rules and Wolfram's 62 for k = 2, r = 2; all 256 elementary rules are classified identically by the independent periodic-configuration test; and all 1800 three-colour rules found pass that test while 10000 random balanced tables outside the list fail it. The count of 172 symmetry families also matches Wolfram's note.",
"Reversibility is tested on bi-infinite configurations (the full shift). On finite cyclic lattices of a fixed size a rule can be a bijection without being reversible in this sense; the claim and Wolfram's own test use the infinite-line notion.",
"The search is written in C (revca.c) and analysis.py compiles it with gcc; this is a tooling deviation from the python-only guideline, recorded in the pre-registration. The search visits 25.7 million nodes for k = 3 (about 2 minutes).",
"The total 7,625,597,484,987 = 3^27 is a count of rule tables, confirmed arithmetically; the enumeration does not visit them individually but prunes soundly, so the count 1800 is exact.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered. An exhaustive enumeration with an exact injectivity test (pair graph of the de Bruijn graph: a rule is injective iff the pair graph has no cycle through an off-diagonal node and no diagonal-to-diagonal path through off-diagonal nodes; used both as a sound pruning condition during depth-first assignment of the rule table and as the exact test at the leaves) yields exactly 6 reversible rules for k = 2, r = 1 and exactly 1800 for k = 3, r = 1. As a check of the method, the same program must give 62 for k = 2, r = 2 (NKS note 'Numbers of reversible rules'), and the 6 elementary rules must be {15, 51, 85, 170, 204, 240}. Also, every rule found must pass Wolfram's finite test (distinct successors for all periodic configurations of period <= 9, as his note says suffices for k = 3) and every rule not found that is sampled (10000 random balanced k = 3 rules) must fail it. 'Supports' requires the counts 6 and 1800 and the consistency checks.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. 'Refutes' if the exhaustive enumeration completes and gives a count other than 6 for k = 2, r = 1 or other than 1800 for k = 3, r = 1 (with the k = 2, r = 2 check giving 62, so the method is validated). If the k = 3 enumeration cannot be completed within the compute budget (about 1 hour), the verdict is 'mixed' or 'inconclusive' (reason: other) with the k = 2 result and a lower bound on the k = 3 count reported.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.97"^^xsd:double;
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<https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-02--claim-test--dataset-2>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "Among one-dimensional nearest-neighbour cellular automata, exactly 6 of the 256 two-colour rules and exactly 1800 of the 3^27 = 7,625,597,484,987 three-colour rules are reversible, where reversible means the global map on bi-infinite configurations is injective (equivalently bijective; equivalently, by Wolfram's note, all periodic configurations have distinct successors).";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py compiles revca.c and runs the exhaustive depth-first enumeration of rule tables for (k,r) = (2,1), (2,2) and (3,1). Table entries are assigned in order of the period of their neighbourhood word; after each assignment the pair graph of the de Bruijn graph is built from definite edges (both labels assigned and equal) and the branch is cut if an off-diagonal cycle or a diagonal-to-diagonal path through off-diagonal nodes exists (both are sound: they witness two distinct configurations with the same image); the balance condition (each colour exactly k^(2r) times) also prunes. At a leaf the same test is exact. The 1800 rules found for k = 3 are then checked in Python with Wolfram's ReversibleQ (distinct successors of all cyclic configurations of length <= 9), 10000 random balanced k = 3 tables not in the list are checked to fail it, all 256 elementary rules are classified by both methods, and the k = 3 rules are grouped into symmetry families under colour permutations and reflection.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. An exhaustive enumeration with an exact injectivity test (pair graph of the de Bruijn graph: a rule is injective iff the pair graph has no cycle through an off-diagonal node and no diagonal-to-diagonal path through off-diagonal nodes; used both as a sound pruning condition during depth-first assignment of the rule table and as the exact test at the leaves) yields exactly 6 reversible rules for k = 2, r = 1 and exactly 1800 for k = 3, r = 1. As a check of the method, the same program must give 62 for k = 2, r = 2 (NKS note 'Numbers of reversible rules'), and the 6 elementary rules must be {15, 51, 85, 170, 204, 240}. Also, every rule found must pass Wolfram's finite test (distinct successors for all periodic configurations of period <= 9, as his note says suffices for k = 3) and every rule not found that is sampled (10000 random balanced k = 3 rules) must fail it. 'Supports' requires the counts 6 and 1800 and the consistency checks.";
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dc:description "the enumerated program family and the list of reversible rules found (derived/)";
dc:license "CC0 (generated data)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Exhaustive enumeration of nearest-neighbour cellular automaton rules (generated by analysis.py + revca.c)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-02--claim-test--dataset-2>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the reversibility test Wolfram used (ReversibleQ) and the stated counts 6, 62, 1800 used as the method check";
dc:license "copyright Stephen Wolfram LLC";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: NKS notes 'Numbers of reversible rules' and 'Testing for reversibility' (p. 1017)";
prov:atLocation <https://www.wolframscience.com/nks/notes-9-2--numbers-of-reversible-cellular-automaton-rules/>,
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