diff --git a/langtons_highway/README.md b/langtons_highway/README.md index 8b14501..9f9b284 100644 --- a/langtons_highway/README.md +++ b/langtons_highway/README.md @@ -117,6 +117,52 @@ implement exactly this check and agree on every pattern in position sequence is `P`-periodic with drift `d`, found by walking backwards from the certified period. For the empty grid that is step 9,977. +## The catalogue: is the 104-highway the *only* highway? + +The brute-force survey above can only ever say "every seed we tried ended +on the classic highway". A stronger question is whether any *other* +highway shape exists at all: a periodic-with-drift orbit of the ant on a +white background, of any period, that is not the classic one. Such an +orbit would be reachable from a finite starting pattern (its own +truncated trail), so finding one would refute the strong form of the +conjecture ("the 104-highway is the unique attractor"), and proving none +exists below some size narrows what a counterexample can look like. + +`highway_catalogue.py` turns "period-P orbit with drift d" into SAT: one-hot +ant position and heading per step, per-cell colour epochs, the read / flip / +move rules, and the periodicity constraint *colour of q+d after the period += colour of q before it, white beyond the window*. CaDiCaL enumerates every +solution (blocking all cyclic shifts of each), and every solution is +re-verified with nothing but its read sequence: the walk determines the only +consistent starting configuration (parity of visits along the forward ray +q+d, q+2d, ...), and the plain ant from `ant.py` must replay the reads from +it. Convexity of the window then makes the cycle repeat forever. + +**Result.** Within the searched scope there is exactly one highway, and it +is the classic one (period 104, drift (2,2) up to rotation, 41 cells per +period, 46 black reads). + +| scope | instances | solve time | highways found | +|-------|-----------|------------|----------------| +| every even P <= 50, every drift with \|d\|_1 <= 6, **unrestricted** window (any walk that returns to d) | 284 | 35 min | 0 | +| every even P <= 104, **every** drift, one-period footprint fitting a **9 x 9** box | 1,754 | 2.4 h | **1: the classic highway** | + +The (P, d) grid is complete for both scopes (`catalogue_summary.py` checks +it), no solution failed verification, and the box-window run reproduces the +classic highway exactly where it must (P = 104, d = (2, 2)), which is the +encoding's end-to-end check. + +What this does and does not say: any highway with period at most 104 whose +one-period footprint fits in a 9 x 9 box *is* the classic highway. A +counterexample to the strong conjecture must therefore have a longer period, +or a footprint wider than 9 cells, or both. The unrestricted window was only +affordable to period 50; the exponential cost of the full window (about x1.2 +per unit of period) is what forces the box. Raising the box to 11 x 11 or +the period past 104 is a matter of machine time, not new ideas. + +Data: `data/catalogue/instances_*.jsonl` (one line per (P, d) instance with +timing and any solutions) and `data/catalogue/summary.json`. + ## Honest limitations * Only patterns inside a centred *n*×*n* box with the ant at the box @@ -139,11 +185,13 @@ python survey.py --n 4 --full # 2 s python survey.py --n 5 # ~6 min on 4 cores python survey.py --n 8 --random 100000 # random sample of a bigger box python make_movie.py # renders output/langtons_highway.mp4 +python highway_catalogue.py --pmax 104 --radius 8 # the catalogue sweep (~2.4 h on 4 cores) +python catalogue_summary.py # -> data/catalogue/summary.json pytest tests # from the repo root: pytest langtons_highway/tests ``` Dependencies: a C compiler for the survey; `numpy`, `pillow` and -`imageio-ffmpeg` (bundles ffmpeg) for the video. +`imageio-ffmpeg` (bundles ffmpeg) for the video; `python-sat` for the catalogue. ## Files @@ -153,6 +201,8 @@ Dependencies: a C compiler for the survey; `numpy`, `pillow` and | `ant_core.c` | fast C ant + certificate, one CSV line per pattern | | `survey.py` | compiles the core, sweeps a pattern space over all cores, writes `data/` | | `make_movie.py` | renders the vertical video and `output/poster.png` from the simulator and `data/` | +| `highway_catalogue.py` | SAT enumeration of every highway (periodic drifting orbit) up to a period, with independent verification | +| `catalogue_summary.py` | aggregates catalogue runs, checks grid completeness, groups highways | | `tests/test_ant.py` | rule sanity, empty-grid onset 9,977, certificate rejects chaos, C vs Python | | `data/` | survey results (see above) | | `output/` | the video and its poster frame | diff --git a/langtons_highway/catalogue_summary.py b/langtons_highway/catalogue_summary.py new file mode 100644 index 0000000..75f07c8 --- /dev/null +++ b/langtons_highway/catalogue_summary.py @@ -0,0 +1,74 @@ +#!/usr/bin/env python3 +""" +Summarise highway_catalogue.py runs into data/catalogue/summary.json. + +Reads every data/catalogue/instances_*.jsonl, checks that every solution +passed independent verification, groups solutions by canonical read +sequence, and records the exact scope (periods, drifts, window) that was +searched exhaustively. + +Author: Claude (with Stephen) +Created: 2026-09-20 +""" + +from __future__ import annotations + +import json +from collections import defaultdict +from pathlib import Path + +HERE = Path(__file__).resolve().parent +CAT = HERE / "data" / "catalogue" + + +def main() -> None: + summary = {"runs": {}, "highways": {}} + for path in sorted(CAT.glob("instances_*.jsonl")): + rows = [json.loads(line) for line in path.read_text().splitlines() if line.strip()] + if not rows: + continue + tag = path.stem.replace("instances_", "") + by_p = defaultdict(list) + for r in rows: + by_p[r["P"]].append(r) + run = { + "instances": len(rows), + "periods": sorted(by_p), + "drift_l1_max": max(abs(r["d"][0]) + abs(r["d"][1]) for r in rows), + "radius": rows[0].get("radius", 0), + "solve_seconds": round(sum(r["total_s"] for r in rows)), + "slowest_instance_seconds": max(r["total_s"] for r in rows), + "solutions": sum(len(r["solutions"]) for r in rows), + "unverified_solutions": sum(1 for r in rows for s in r["solutions"] if not s["verified"]), + } + # completeness: every (P, d) expected for the scope must be present + missing = [] + for P in run["periods"]: + have = {tuple(r["d"]) for r in by_p[P]} + if run["radius"]: + R = run["radius"] + want = {(dx, dy) for dx in range(1, R + 1) for dy in range(0, R + 1) + if (dx + dy) % 2 == P % 2 and dx + dy <= P} + else: + D = run["drift_l1_max"] + want = {(dx, dy) for dx in range(1, D + 1) for dy in range(0, D + 1 - dx) + if (dx + dy) % 2 == P % 2 and dx + dy <= P} + missing += [(P, d) for d in sorted(want - have)] + run["missing_instances"] = missing + summary["runs"][tag] = run + for r in rows: + for s in r["solutions"]: + if s["primitive_period"] != r["P"]: + continue + key = s["canonical"] + h = summary["highways"].setdefault(key, { + "period": r["P"], "cells_per_period": s["cells_visited"], + "black_reads": sum(s["reads"]), "found_in": [], "verified": True}) + h["found_in"].append({"run": tag, "d": r["d"], "h0": s["h0"]}) + h["verified"] = h["verified"] and s["verified"] + (CAT / "summary.json").write_text(json.dumps(summary, indent=2)) + print(json.dumps(summary, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/langtons_highway/data/catalogue/instances_r8.jsonl b/langtons_highway/data/catalogue/instances_r8.jsonl new file mode 100644 index 0000000..b077ec9 --- /dev/null +++ b/langtons_highway/data/catalogue/instances_r8.jsonl @@ -0,0 +1,1754 @@ +{"P": 2, "d": [1, 1], "radius": 8, "vars": 25, "clauses": 95, "lens_cells": 4, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 4, "d": [2, 0], "radius": 8, "vars": 57, "clauses": 252, "lens_cells": 10, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 4, "d": [2, 2], "radius": 8, "vars": 50, "clauses": 203, "lens_cells": 9, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 4, "d": [3, 1], "radius": 8, "vars": 47, "clauses": 187, "lens_cells": 8, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 4, "d": [4, 0], "radius": 8, "vars": 38, "clauses": 139, "lens_cells": 5, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 6, "d": [1, 1], "radius": 8, "vars": 109, "clauses": 550, "lens_cells": 18, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 6, "d": [1, 3], "radius": 8, "vars": 95, "clauses": 452, "lens_cells": 16, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 6, "d": [1, 5], "radius": 8, "vars": 69, "clauses": 279, "lens_cells": 12, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 6, "d": [2, 0], "radius": 8, "vars": 110, "clauses": 549, "lens_cells": 19, "build_s": 0.0, "total_s": 0.0, "solutions": []} +{"P": 6, "d": [2, 2], "radius": 8, "vars": 103, "clauses": 499, 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diff --git a/langtons_highway/data/catalogue/summary.json b/langtons_highway/data/catalogue/summary.json new file mode 100644 index 0000000..248f604 --- /dev/null +++ b/langtons_highway/data/catalogue/summary.json @@ -0,0 +1,123 @@ +{ + "runs": { + "r8": { + "instances": 1754, + "periods": [ + 2, + 4, + 6, + 8, + 10, + 12, + 14, + 16, + 18, + 20, + 22, + 24, + 26, + 28, + 30, + 32, + 34, + 36, + 38, + 40, + 42, + 44, + 46, + 48, + 50, + 52, + 54, + 56, + 58, + 60, + 62, + 64, + 66, + 68, + 70, + 72, + 74, + 76, + 78, + 80, + 82, + 84, + 86, + 88, + 90, + 92, + 94, + 96, + 98, + 100, + 102, + 104 + ], + "drift_l1_max": 16, + "radius": 8, + "solve_seconds": 8610, + "slowest_instance_seconds": 379.4, + "solutions": 1, + "unverified_solutions": 0, + "missing_instances": [] + }, + "unrestricted": { + "instances": 284, + "periods": [ + 2, + 4, + 6, + 8, + 10, + 12, + 14, + 16, + 18, + 20, + 22, + 24, + 26, + 28, + 30, + 32, + 34, + 36, + 38, + 40, + 42, + 44, + 46, + 48, + 50 + ], + "drift_l1_max": 6, + "radius": 0, + "solve_seconds": 2118, + "slowest_instance_seconds": 191.6, + "solutions": 0, + "unverified_solutions": 0, + "missing_instances": [] + } + }, + "highways": { + "00001000011110100001011001111001100001100101101101011000011011000011000011010000101111000010010000111101": { + "period": 104, + "cells_per_period": 41, + "black_reads": 46, + "found_in": [ + { + "run": "r8", + "d": [ + 2, + 2 + ], + "h0": 0 + } + ], + "verified": true + } + } +} \ No newline at end of file diff --git a/langtons_highway/highway_catalogue.py b/langtons_highway/highway_catalogue.py new file mode 100644 index 0000000..c2230fa --- /dev/null +++ b/langtons_highway/highway_catalogue.py @@ -0,0 +1,383 @@ +#!/usr/bin/env python3 +""" +Catalogue every "highway" of Langton's Ant up to a given period. + +A highway is a periodic-with-drift orbit on an otherwise white plane: after +P steps the whole picture (cells + ant) has moved by a vector d != 0. +Equivalently: a configuration C and a P-step walk such that running the ant +for P steps on C yields C translated by d. For fixed (P, d) that +fixed-point condition is a finite SAT problem; this module builds it, +enumerates every solution with CaDiCaL, and re-verifies each one by plain +simulation (``verify``), independently of the encoding. + +Scope of an exhaustive run: all even P <= PMAX, every drift d with +|dx|+|dy| <= DMAX (one representative per 90-degree rotation class; the +initial heading is left free so rotations are covered). Within that scope +the enumeration is complete: the walk may wander anywhere it can while still +returning to d after P steps (the "lens" |c|_1 + |c-d|_1 <= P). + +Usage: + python highway_catalogue.py --pmax 120 --dmax 10 --workers 4 + python highway_catalogue.py --single 104 2 2 # one (P, d) instance + +Author: Claude (with Stephen) +Created: 2026-09-20 +""" + +from __future__ import annotations + +import argparse +import bisect +import json +import os +import sys +import time +from concurrent.futures import ProcessPoolExecutor, as_completed +from pathlib import Path +from typing import Dict, List, Tuple + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +from ant import Ant # noqa: E402 + +HERE = Path(__file__).resolve().parent +OUT = HERE / "data" / "catalogue" + +DX = (0, 1, 0, -1) # N E S W +DY = (1, 0, -1, 0) + +Cell = Tuple[int, int] + + +def m1(c: Cell) -> int: + return abs(c[0]) + abs(c[1]) + + +# ---------------------------------------------------------------------- +# CNF construction +# ---------------------------------------------------------------------- +class Instance: + """SAT encoding of 'period-P highway with drift d'.""" + + def __init__(self, P: int, d: Cell, radius: int = 0): + assert P % 2 == 0 and (d[0] + d[1]) % 2 == 0 and d != (0, 0) + assert m1(d) <= P, "drift longer than the period is impossible" + self.P, self.d, self.radius = P, d, radius + self.nv = 0 + self.clauses: List[List[int]] = [] + self._build() + + def new(self) -> int: + self.nv += 1 + return self.nv + + def add(self, *lits: int) -> None: + self.clauses.append(list(lits)) + + def _build(self) -> None: + P, d = self.P, self.d + dx, dy = d + # lens: every cell a P-step walk from 0 to d can touch + # Window. Unrestricted: the lens of all P-step walks from 0 to d. + # With a radius R: the period is anchored at the footprint's + # leftmost-bottom cell (x >= 0, and y >= 0 when x == 0), so any + # highway whose footprint bounding box is at most (R+1) x (R+1) + # appears with x in [0, R] and y in [-R, R]. The window used for + # colour/periodicity constraints stays convex (x >= 0 only); the + # anchor rule is applied to the position variables. + R = self.radius + if R: + assert 1 <= dx <= R and 0 <= dy <= R + lens = [(x, y) for x in range(0, R + 1) for y in range(-R, R + 1) + if m1((x, y)) + m1((x - dx, y - dy)) <= P] + else: + lens = [(x, y) for x in range(-P, P + 1) for y in range(-P, P + 1) + if m1((x, y)) + m1((x - dx, y - dy)) <= P] + self.lens = lens + lens_set = set(lens) + + def allowed(c: Cell) -> bool: + return not (R and c[0] == 0 and c[1] < 0) + + # reach(i): cells the ant can occupy before step i + reach: List[List[Cell]] = [] + for i in range(P + 1): + reach.append([c for c in lens + if m1(c) <= i and m1((c[0] - dx, c[1] - dy)) <= P - i + and (c[0] + c[1]) % 2 == i % 2 and allowed(c)]) + self.reach = reach + pos: Dict[Tuple[int, Cell], int] = {} + for i in range(P + 1): + for c in reach[i]: + pos[(i, c)] = self.new() + self.pos = pos + hd = [[self.new() for _ in range(4)] for _ in range(P + 1)] + self.hd = hd + r = [self.new() for _ in range(P)] + self.r = r + # colour epochs per cell + vis: Dict[Cell, List[int]] = {c: [] for c in lens} + for i in range(P): + for c in reach[i]: + vis[c].append(i) + colv: Dict[Cell, List[int]] = {} + for c in lens: + colv[c] = [self.new() for _ in range(len(vis[c]) + 1)] + self.vis, self.colv = vis, colv + + def col_at(i: int, c: Cell) -> int: + return colv[c][bisect.bisect_left(vis[c], i)] + + self.col_at = col_at + + # start: ant at origin (heading free), end: at d with the same heading + self.add(pos[(0, (0, 0))]) + self.add(*hd[0]) + for k in range(4): + for k2 in range(k + 1, 4): + self.add(-hd[0][k], -hd[0][k2]) + assert (P, d) in pos + self.add(pos[(P, d)]) + for k in range(4): + self.add(-hd[P][k], hd[0][k]) + self.add(hd[P][k], -hd[0][k]) + + for i in range(P): + # heading update: white -> right (k+1), black -> left (k-1) + for k in range(4): + self.add(-hd[i][k], r[i], hd[i + 1][(k + 1) % 4]) + self.add(-hd[i][k], -r[i], hd[i + 1][(k + 3) % 4]) + for k in range(4): + for k2 in range(k + 1, 4): + self.add(-hd[i + 1][k], -hd[i + 1][k2]) + reach_next = set(reach[i + 1]) + for c in reach[i]: + pv = pos[(i, c)] + cv = col_at(i, c) + # read + self.add(-pv, -cv, r[i]) + self.add(-pv, cv, -r[i]) + # flip + nv = colv[c][bisect.bisect_left(vis[c], i) + 1] + self.add(-pv, -cv, -nv) + self.add(-pv, cv, nv) + self.add(pv, -cv, nv) + self.add(pv, cv, -nv) + # move forward + for k in range(4): + nc = (c[0] + DX[k], c[1] + DY[k]) + if nc in reach_next: + self.add(-pv, -hd[i + 1][k], pos[(i + 1, nc)]) + else: + self.add(-pv, -hd[i + 1][k]) + # move backward (keeps position unique) + for nc in reach[i + 1]: + nv_ = pos[(i + 1, nc)] + preds = [] + for k in range(4): + pc = (nc[0] - DX[k], nc[1] - DY[k]) + if (i, pc) in pos: + preds.append(pos[(i, pc)]) + self.add(-nv_, -hd[i + 1][k], pos[(i, pc)]) + else: + self.add(-nv_, -hd[i + 1][k]) + self.add(-nv_, *preds) + # periodicity: C(q) == colour of q+d after the period, white beyond + for q in lens: + qd = (q[0] + dx, q[1] + dy) + c0 = colv[q][0] + if qd in lens_set: + cP = colv[qd][-1] + self.add(-c0, cP) + self.add(c0, -cP) + else: + self.add(-c0) + + # ------------------------------------------------------------------ + def decode(self, model: List[int]) -> dict: + val = set(v for v in model if v > 0) + reads = [1 if self.r[i] in val else 0 for i in range(self.P)] + h0 = [k for k in range(4) if self.hd[0][k] in val][0] + C = sorted(q for q in self.lens if self.colv[q][0] in val) + return {"P": self.P, "d": list(self.d), "h0": h0, "reads": reads, "C": C} + + def block(self, solver, reads: List[int], h0: int) -> None: + """Forbid this exact (reads, h0) assignment.""" + clause = [-self.hd[0][h0]] + for i, b in enumerate(reads): + clause.append(-self.r[i] if b else self.r[i]) + solver.add_clause(clause) + + +# ---------------------------------------------------------------------- +# independent verification and canonical form +# ---------------------------------------------------------------------- +def walk_from_reads(reads: List[int], h0: int) -> Tuple[List[Cell], List[int]]: + """Positions p_0..p_P and headings h_0..h_P implied by the reads.""" + x = y = 0 + h = h0 + ps, hs = [(0, 0)], [h0] + for b in reads: + h = (h + 3) % 4 if b else (h + 1) % 4 + x += DX[h] + y += DY[h] + ps.append((x, y)) + hs.append(h) + return ps, hs + + +def verify(sol: dict) -> bool: + """Independent check that (reads, h0, d) really is a highway. + + Uses nothing from the SAT model except the read sequence and the initial + heading. The walk determines the visit counts N; the only configuration + consistent with a periodic drift is C(q) = parity of N(q+d) + N(q+2d) + ... + (cells written by earlier periods). Simulating the plain ant on C must + reproduce the reads and end at d with the same heading. Given that, the + picture after the period equals C shifted by d on every cell the next + period can read (the window is convex), so the cycle repeats forever. + """ + from collections import Counter + + P, (dx, dy), h0, reads = sol["P"], sol["d"], sol["h0"], sol["reads"] + ps, hs = walk_from_reads(reads, h0) + if ps[-1] != (dx, dy) or hs[-1] != h0: + return False + N = Counter(ps[:-1]) + lens = [(x, y) for x in range(-P, P + 1) for y in range(-P, P + 1) + if m1((x, y)) + m1((x - dx, y - dy)) <= P] + C = set() + for q in lens: + par, m = 0, 1 + while m * m1((dx, dy)) <= 2 * P: + par ^= N[(q[0] + m * dx, q[1] + m * dy)] & 1 + m += 1 + if par: + C.add(q) + ant = Ant(x=0, y=0, heading=h0, black=C) + for i in range(P): + if ant.colour((ant.x, ant.y)) != reads[i]: + return False + ant.step() + return (ant.x, ant.y, ant.heading) == (dx, dy, h0) + + +def canonical(reads: List[int]) -> str: + s = "".join(map(str, reads)) + return min(s[i:] + s[:i] for i in range(len(s))) + + +def primitive_period(reads: List[int]) -> int: + n = len(reads) + for k in range(1, n + 1): + if n % k == 0 and reads == reads[k:] + reads[:k]: + return k + return n + + +# ---------------------------------------------------------------------- +# enumeration for one (P, d) +# ---------------------------------------------------------------------- +def solve_instance(P: int, d: Cell, radius: int = 0, verbose: bool = False) -> dict: + from pysat.solvers import Solver + + t0 = time.time() + inst = Instance(P, d, radius) + t_build = time.time() - t0 + sols: List[dict] = [] + seen = set() + with Solver(name="cadical153", bootstrap_with=inst.clauses) as s: + while s.solve(): + sol = inst.decode(s.get_model()) + reads, h0 = sol["reads"], sol["h0"] + sol["verified"] = verify(sol) + sol["canonical"] = canonical(reads) + sol["primitive_period"] = primitive_period(reads) + ps, hs = walk_from_reads(reads, h0) + sol["cells_visited"] = len(set(ps[:-1])) + if sol["canonical"] not in seen: + seen.add(sol["canonical"]) + sols.append(sol) + # block every cyclic shift of this solution (same highway, other phase) + for sft in range(P): + shifted = reads[sft:] + reads[:sft] + inst.block(s, shifted, hs[sft]) + return { + "P": P, "d": list(d), "radius": radius, "vars": inst.nv, "clauses": len(inst.clauses), + "lens_cells": len(inst.lens), "build_s": round(t_build, 1), + "total_s": round(time.time() - t0, 1), "solutions": sols, + } + + +def fundamental_drifts(P: int, dmax: int, radius: int = 0) -> List[Cell]: + """One representative per rotation class: dx >= 1, dy >= 0. + + Unrestricted window: |d|_1 <= dmax. Box window: every d that fits the + window (1 <= dx <= radius, 0 <= dy <= radius), which is all of them. + """ + out = [] + if radius: + for dx in range(1, radius + 1): + for dy in range(0, radius + 1): + if (dx + dy) % 2 == P % 2 and dx + dy <= P: + out.append((dx, dy)) + return out + for dx in range(1, dmax + 1): + for dy in range(0, dmax + 1 - dx): + if (dx + dy) % 2 == P % 2 and dx + dy <= P: + out.append((dx, dy)) + return out + + +def _job(args): + P, d, radius = args + return solve_instance(P, d, radius) + + +def main() -> None: + ap = argparse.ArgumentParser(description=__doc__, + formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument("--pmax", type=int, default=104) + ap.add_argument("--pmin", type=int, default=2) + ap.add_argument("--dmax", type=int, default=8) + ap.add_argument("--workers", type=int, default=os.cpu_count() or 1) + ap.add_argument("--radius", type=int, default=0, + help="restrict the footprint to a box of this radius (0 = unrestricted)") + ap.add_argument("--single", type=int, nargs=3, metavar=("P", "DX", "DY")) + ap.add_argument("--out", type=Path, default=OUT) + a = ap.parse_args() + a.out.mkdir(parents=True, exist_ok=True) + + if a.single: + P, dx, dy = a.single + res = solve_instance(P, (dx, dy), a.radius, verbose=True) + print(json.dumps({k: v for k, v in res.items() if k != "solutions"})) + for s in res["solutions"]: + print(" solution: verified=%s primitive=%d cells=%d h0=%d reads=%s" % ( + s["verified"], s["primitive_period"], s["cells_visited"], s["h0"], + "".join(map(str, s["reads"])))) + return + + jobs = [(P, d, a.radius) for P in range(a.pmin, a.pmax + 1, 2) + for d in fundamental_drifts(P, a.dmax, a.radius)] + scope = f"footprint box {a.radius + 1}x{a.radius + 1}" if a.radius else f"|d|_1 <= {a.dmax}, unrestricted" + print(f"{len(jobs)} instances, P in [{a.pmin},{a.pmax}], {scope}", flush=True) + tag = f"r{a.radius}" if a.radius else "unrestricted" + log = open(a.out / f"instances_{tag}.jsonl", "a") + found = 0 + t0 = time.time() + with ProcessPoolExecutor(max_workers=a.workers) as pool: + futs = {pool.submit(_job, j): j for j in jobs} + for n, f in enumerate(as_completed(futs), 1): + res = f.result() + log.write(json.dumps(res) + "\n") + log.flush() + prim = [s for s in res["solutions"] if s["primitive_period"] == res["P"]] + found += len(prim) + flag = f" <-- {len(prim)} primitive highway(s)!" if prim else "" + print(f"[{n}/{len(jobs)}] P={res['P']:4d} d={tuple(res['d'])} " + f"{res['total_s']:7.1f}s sols={len(res['solutions'])}{flag}", flush=True) + print(f"done in {time.time() - t0:.0f}s; primitive highways found: {found}") + + +if __name__ == "__main__": + main() diff --git a/langtons_highway/tests/test_ant.py b/langtons_highway/tests/test_ant.py index ae14926..35ed40c 100644 --- a/langtons_highway/tests/test_ant.py +++ b/langtons_highway/tests/test_ant.py @@ -85,3 +85,28 @@ def test_c_core_agrees_with_python_reference(): assert row[1] == "HIGHWAY" assert (int(row[2]), int(row[3]), int(row[4]), int(row[5]), int(row[6])) == ( r["onset"], r["cert_step"], r["period"], r["dx"], r["dy"]) + + +def test_catalogue_verifier_accepts_classic_and_rejects_corruption(): + from highway_catalogue import verify, canonical + + ant = Ant() + r = ant.find_highway(200_000) + s, P = r["cert_step"], 104 + reads = [ant.history[s - P + i][2] for i in range(P)] + h0 = ant.history[s - P][3] + sol = {"P": P, "d": [r["dx"], r["dy"]], "h0": h0, "reads": reads} + # the SAT catalogue normalises drift to the quadrant dx>=1, dy>=0 by + # rotation; the verifier itself works for any drift + assert verify(sol) + bad = dict(sol, reads=reads[:10] + [1 - reads[10]] + reads[11:]) + assert not verify(bad) + assert len(canonical(reads)) == P + + +def test_catalogue_small_period_has_no_highway(): + pytest.importorskip("pysat") + from highway_catalogue import solve_instance + + res = solve_instance(12, (2, 0)) + assert res["solutions"] == []