https://w3id.org/np/RANel9bm6KMX8PKqR6-oSr9zY0KeSUSsmrP_rTWsWvsSc
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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dc:description "analysis.py transcribes the five rule lists into a generic ordered-pattern compiler (first matching rule wins) that produces full lookup tables, then runs the CA and an independent direct simulator of each emulated system side by side. Mobile automata (65536 rules) and Turing machines (4096 + 4 x 4096 rules) are run fully vectorised in numpy; substitution systems, register machines and logic circuits are run one instance at a time. Decodings: MA colour mod 2 and the unique dark cell; TM colour mod k and the unique cell >= k (state = colour div k); SS string read at the start of each replacement sweep; RM (program-counter colour, #(m+2) + 2#(m+3), #(m+5) + 2#(m+6)) with consecutive duplicates removed; logic circuit single surviving cell 2/4. Per-instance tables in derived/*.csv, full summary in derived/summary.json; runtime about 1 minute.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 5 number of the 5 tested system types for which every tested instance is emulated exactly (published construction; repaired RM construction; corrected SS decoder) (n = 172804, exact-emulation counts per family: MA 131072/131072, TM 40960/40960, SS 72/72 (44/72 under the pre-registered decoder), RM 300/300 repaired (255/300 published), logic 400/400). Interpretation: The claim is existential ('cellular automata can be set up to emulate ...'). The strongest finite test is to take the constructions the book itself supplies, run them against independent direct simulations of each emulated system, and look for counterexamples. Sequential substitution systems, tag systems, the multiplication CA, the RAM emulation and 'a practical computer' are not tested (the first two constructions use symbolic cell states whose decoding is not specified; the last is schematic), so a pass covers five of the eight named system types. Calibration before this pre-registration, disclosed here: the book's own examples (mobile automaton {35,57}, the 3-state Turing machine of p. 78, the substitution system {1 -> 10, 0 -> 01}, the register machine program of p. 99 and eight hand-written logic expressions) were used to fix the decodings. In that calibration the published register-machine construction failed on 14 of 60 and then 26 of 150 random programs. Tracing showed the cause: when an increment instruction fires while the register's only remaining cell is a pending-decrement signal (colour m+1 with background to its left, i.e. register value 0 whose deletion is still in flight), the published rule {_, _, p} -> m+3 converts the signal into an increment signal (worth two cells) instead of one cell. The repair adds one rule per increment instruction, {0, m+1, p} -> m+2 for i[1] and {p, m+4, 0} -> m+5 for i[2], placed before the published rules; 150/150 calibration programs were then exact. The main run uses a fresh seed.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-07: supports, confidence 0.75";
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<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: nks-emulation-constructions, emulation-test-instances";
<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. If some system type has fewer than 95% exact instances even with the repaired construction the verdict is 'inconclusive' (a failing construction does not show that no construction exists, so an existence claim cannot be refuted this way; reason: construction-failure). If every type is >= 95% but not all are 100%, or if two or more of the published constructions are not exact as printed, the verdict is 'mixed'.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "(ii) Register machines: the published RMToCA rule list fails on 45 of 300 random programs (15%) through the race condition described in interpretation (an increment firing while the register's last cell is a pending-deletion signal). The one-rule repair pre-registered before the main run ({0, m+1, p} -> m+2 for i[1], {p, m+4, 0} -> m+5 for i[2]) gives 300/300. The book's own example program (p. 99) does not trigger the race and is emulated exactly by the published rules. This is a defect in a published construction, not in the claim that an emulating CA exists.",
"All tests are finite (60 steps for MA/TM, 7 substitution steps, 40 register-machine steps, expressions of depth <= 4) with one seed; the vectorised MA/TM lookup tables were checked against the literal first-match compilation of the published rule lists on sampled rules and differ only on neighbourhoods containing two active cells or two heads, which cannot occur.",
"Coverage: five of the eight system types named in the claim were tested (mobile automata, Turing machines, neighbour-independent substitution systems with blocks of length 1-2, two-register machines, And/Or/Not logic expressions). Sequential substitution systems, tag systems, the multiplication-by-3 CA, the random-access-memory CA and 'a practical computer in its entirety' were not tested. The logic-circuit decoding (final single cell 2 = false, 4 = true) and the register-machine decoding were fixed from the book's examples before the main run.",
"Pre-registered decision: all five tested system types are emulated exactly in 100% of instances (172,804 instance comparisons), and four of the five published constructions are exact as printed, so the pass criterion is met. Two deviations from the pre-registration are disclosed. (i) Substitution systems: the pre-registered operationalisation of 'sweep-start configuration' (exactly one r cell, no p or m[0|1] cells) also matches mid-sweep configurations, because the r cell moves right one cell per step leaving s cells behind it, and the pre-registered run also dropped repeated strings, so non-growing systems recorded only one snapshot; under that literal reading 44/72 runs matched. Requiring in addition that the r cell be the leftmost non-background cell, which is what 'sweep start' meant, gives 72/72. The CA construction is unchanged; traces of the failing cases (e.g. 0 -> 1, 1 -> 00) show the CA producing exactly the substitution system's strings at each sweep start. Under a strict reading of the pre-registration the verdict would be 'inconclusive' (construction-failure) for this family; the confidence is lowered to reflect this post-hoc correction.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered. Five system types are tested with the rule lists given in the NKS notes, transcribed into analysis.py (first matching rule wins, as in Mathematica). (1) Mobile automata (MAToCA, 4 colours, range 2): all 65536 two-colour mobile automata in Wolfram's {colours, displacements} numbering, from the all-white initial condition and from one seeded random initial condition each; 60 steps; exact if at every step the CA colours mod 2 equal the mobile automaton's cells and the unique dark cell sits at the active position. (2) Turing machines (TMToCA, k(s+1) colours, range 1): all 4096 machines with s = 2, k = 2 and 4096 seeded random machines for each of (s,k) = (3,2), (2,3), (4,2), (3,3), each from a blank tape and from a seeded random tape; 60 steps; exact if tape, head position and head state agree at every step. (3) Substitution systems (SSToCA, 12 colours): all 36 neighbour-independent systems on {0,1} whose two blocks have length 1 or 2, from initial strings {0} and {1}; the CA is run until it has produced 8 'sweep-start' configurations (exactly one r cell, no p or m[0|1] cells), whose decoded strings must equal the substitution system's strings at steps 0..7; a run exceeding 3000 CA steps or reaching the array edge counts as not exact. (4) Register machines (RMToCA, m+7 colours): 300 seeded random programs with m = 2..6 instructions over two registers (i[r], d[r,q]) and initial registers a, b in 0..3, keeping only programs that run at least 20 steps without halting (the construction has no colour for a program counter past the end); the sequence of distinct decoded CA states (program-counter colour, r1 = #(m+2) + 2#(m+3), r2 = #(m+5) + 2#(m+6)) must equal the register machine's trajectory for up to 40 steps. Both the published construction and a one-rule repair described below are run. (5) Logic circuits (the 5-colour rule of p. 1112): 400 seeded random And/Or/Not expressions of depth <= 4 over constants, encoded with the published initial-condition rule and run for the published number of steps; exact if the final configuration has a single non-zero cell equal to 2 for false and 4 for true. The measured value is the number of system types (out of 5) for which 100% of tested instances are emulated exactly, using for register machines the repaired construction. The claim PASSES if the value is 5 and additionally at least 4 of the 5 published constructions are exact as printed.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. If some system type has fewer than 95% exact instances even with the repaired construction the verdict is 'inconclusive' (a failing construction does not show that no construction exists, so an existence claim cannot be refuted this way; reason: construction-failure). If every type is >= 95% but not all are 100%, or if two or more of the published constructions are not exact as printed, the verdict is 'mixed'.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.75"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-07--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-07--claim-test--dataset-2>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "The explicit cellular-automaton constructions Wolfram publishes for emulating mobile automata, Turing machines, neighbour-independent substitution systems, register machines and logic circuits (NKS notes pp. 1111-1112) reproduce the evolution of every instance of those systems exactly, under the decoding implied by each construction.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py transcribes the five rule lists into a generic ordered-pattern compiler (first matching rule wins) that produces full lookup tables, then runs the CA and an independent direct simulator of each emulated system side by side. Mobile automata (65536 rules) and Turing machines (4096 + 4 x 4096 rules) are run fully vectorised in numpy; substitution systems, register machines and logic circuits are run one instance at a time. Decodings: MA colour mod 2 and the unique dark cell; TM colour mod k and the unique cell >= k (state = colour div k); SS string read at the start of each replacement sweep; RM (program-counter colour, #(m+2) + 2#(m+3), #(m+5) + 2#(m+6)) with consecutive duplicates removed; logic circuit single surviving cell 2/4. Per-instance tables in derived/*.csv, full summary in derived/summary.json; runtime about 1 minute.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. Five system types are tested with the rule lists given in the NKS notes, transcribed into analysis.py (first matching rule wins, as in Mathematica). (1) Mobile automata (MAToCA, 4 colours, range 2): all 65536 two-colour mobile automata in Wolfram's {colours, displacements} numbering, from the all-white initial condition and from one seeded random initial condition each; 60 steps; exact if at every step the CA colours mod 2 equal the mobile automaton's cells and the unique dark cell sits at the active position. (2) Turing machines (TMToCA, k(s+1) colours, range 1): all 4096 machines with s = 2, k = 2 and 4096 seeded random machines for each of (s,k) = (3,2), (2,3), (4,2), (3,3), each from a blank tape and from a seeded random tape; 60 steps; exact if tape, head position and head state agree at every step. (3) Substitution systems (SSToCA, 12 colours): all 36 neighbour-independent systems on {0,1} whose two blocks have length 1 or 2, from initial strings {0} and {1}; the CA is run until it has produced 8 'sweep-start' configurations (exactly one r cell, no p or m[0|1] cells), whose decoded strings must equal the substitution system's strings at steps 0..7; a run exceeding 3000 CA steps or reaching the array edge counts as not exact. (4) Register machines (RMToCA, m+7 colours): 300 seeded random programs with m = 2..6 instructions over two registers (i[r], d[r,q]) and initial registers a, b in 0..3, keeping only programs that run at least 20 steps without halting (the construction has no colour for a program counter past the end); the sequence of distinct decoded CA states (program-counter colour, r1 = #(m+2) + 2#(m+3), r2 = #(m+5) + 2#(m+6)) must equal the register machine's trajectory for up to 40 steps. Both the published construction and a one-rule repair described below are run. (5) Logic circuits (the 5-colour rule of p. 1112): 400 seeded random And/Or/Not expressions of depth <= 4 over constants, encoded with the published initial-condition rule and run for the published number of steps; exact if the final configuration has a single non-zero cell equal to 2 for false and 4 for true. The measured value is the number of system types (out of 5) for which 100% of tested instances are emulated exactly, using for register machines the repaired construction. The claim PASSES if the value is 5 and additionally at least 4 of the 5 published constructions are exact as printed.";
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dc:description "the constructions under test, transcribed into analysis.py";
dc:license "copyright Stephen Wolfram LLC; rule lists transcribed for research";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Wolfram, A New Kind of Science, notes to 'Emulating Other Systems with Cellular Automata' (MAToCA, TMToCA, SSToCA, RMToCA, logic-circuit rule)";
prov:wasDerivedFrom <https://www.wolframscience.com/nks/notes-11-5--mobile-automata-from-cellular-automata/> .
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dc:description "instances whose direct evolution is compared with the decoded CA evolution";
dc:license "generated data";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Mobile automata, Turing machines, substitution systems, register machine programs and logic expressions (generated by analysis.py)";
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