bump

flower_snarks.py

@@ -223,9 +223,87 @@ Petersen = join_gadgets(
   []
 )
 
-#print(join_gadgets([CUBIC_VERTEX]*2, [((1,1), (2,1))], []))
-#for i in range(1, 10):
-#  print(i, necklace(i))
+
+
+def stabilize(base_gadget, operation, finalize = None):
+  from sage.all import SR, matrix, ZZ
+  boundaries = set()
+  new_boundaries = set(base_gadget.keys())
+
+  i = 0
+  while True:
+    i += 1
+    new_boundaries.update(boundaries)
+    if new_boundaries == boundaries: break
+    boundaries = new_boundaries
+    gadget = { k: SR.symbol() for k in boundaries }
+    out = operation(gadget)
+    new_boundaries = set(out.keys())
+    print("Loop %i done - %i boundaries (%i new)" % \
+      (i, len(new_boundaries), len(new_boundaries.difference(boundaries))))
+
+  sorted_gadget = tuple(gadget.items())
+  out = { k: v.expand() for k, v in out.items() }
+  rename = { v: i for i, (_, v) in enumerate(sorted_gadget) }
+  m = matrix(ZZ, len(gadget), len(gadget), {
+    (rename[gadget[row]], rename[col]): formula.coefficient(col)
+    for row, formula in out.items()
+    for col in formula.free_variables()
+  })
+
+  iv = matrix(ZZ, len(gadget), 1, {
+    (rename[gadget[row]], 0): v for row, v in base_gadget.items()
+  })
+
+  if finalize is not None:
+    fin = finalize(gadget)
+    assert(len(fin) == 1 and (None,) in fin)
+    fin = next(iter(fin.values())).expand()
+    fin = matrix(ZZ, 1, len(gadget), {
+      (0, rename[col]): fin.coefficient(col) for col in fin.free_variables()
+    })
+  else:
+    fin = None
+
+  return {
+    'variables': sorted_gadget,
+    'step_matrix': m,
+    'initial_vector': iv,
+    'finalize': fin
+  }
+
+def flower_matrix():
+  return stabilize(flower_gadget(1),
+    lambda x: flower_snark_join(x, FLOWER_SNARK_BASIC_GADGET),
+    lambda gadget: join_gadgets(
+      [ gadget ],
+      [
+        ((1, 2), (1, 1)),
+        ((1, 4), (1, 3)),
+        ((1, 6), (1, 5)),
+      ],
+      []
+    )
+  )
+
+
+def count_cdc_naive(G):
+  assert(G.degree() == [3]*G.num_verts())
+
+  vert_map = { v: i for i, v in enumerate(G.vertices()) }
+  vert_used = [ 1 ] * len(vert_map)
+
+  joins = []
+  for u, v, _ in G.edges():
+    u = vert_map[u]
+    v = vert_map[v]
+    joins.append(((u+1, vert_used[u]), (v+1, vert_used[v])))
+    vert_used[u] += 1
+    vert_used[v] += 1
+
+  b = join_gadgets([ CUBIC_VERTEX ] * G.num_verts(), joins, [])
+  assert(list(b.keys()) == [(None,)])
+  return (b[(None,)], 2**(G.num_verts() // 2) // 2)
 
 assert(K4 == {(None,): 2})
 for i in range(2, 10):
@@ -233,6 +311,7 @@ for i in range(2, 10):
 assert(Petersen == {(None,): 52})
 assert(flower_snark(3) == {(None,): 104})
 
+if False:
   print(flower_snark(5))
 
   print("basic", len(FLOWER_SNARK_BASIC_GADGET))

utils.py

@@ -29,3 +29,15 @@ def select(pat, l):
 def prod(iterable):
   return reduce(operator.mul, iterable, 1)
 
+def arg_min(fn, it):
+  ret = next(it)
+  v = fn(ret)
+
+  for i in it:
+    v_ = fn(i)
+    if v_ < v:
+      v = v_
+      ret = i
+
+  return ret
+