add sampler for symmetric groups

automata.py

@@ -22,6 +22,8 @@ import itertools
 import datasets
 import numpy as np
 
+# Local imports
+# from symmetric import SymmetricSampler
 
 _CITATION = """\
 """
@@ -159,8 +161,89 @@ class FlipFlopSampler(AutomatonSampler):
         return x, self.f(x)
 
 
+class SymmetricSampler(AutomatonSampler):
+  """
+  TODO: add options for labels as functions of states
+  - parity (whether a state is even): this may need packages (e.g. Permutation from sympy)
+  - position / toggle: for S3 ~ D6, we can add labels for substructures as in Dihedral groups.
+  """
+  def __init__(self, data_config):
+    super().__init__(data_config)
+    self.name = 'symmetric'
+    self.data_config = data_config
+
+    if 'n' not in data_config:
+      data_config['n'] = 5 # Default to S5
+    if 'n_actions' not in data_config:
+      data_config['n_actions'] = 3
+    if 'label_type' not in data_config:
+      # Options: 'state', 'first_chair'
+      data_config['label_type'] = 'state'
+    
+    self.n = data_config['n']
+    self.label_type = data_config['label_type']
+
+    """
+    Get states
+    """
+    self.state_encode = lambda state: ''.join([str(int(each)) for each in state])
+    self.state_label_map = {}
+    for si, state in enumerate(itertools.permutations(range(self.n))):
+      enc = self.state_encode(state)
+      self.state_label_map[enc] = si
+
+    """
+    Get actions (3 defaults: id, shift-by-1, swap-first-two)
+    """
+    self.n_actions = data_config['n_actions']
+    self.actions = {0: np.eye(self.n)}
+    # shift all elements to the right by 1
+    shift_idx = list(range(1, self.n)) + [0]
+    self.actions[1] = np.eye(self.n)[shift_idx]
+    # swap the first 2 elements
+    shift_idx = [1, 0] + list(range(2, self.n))
+    self.actions[2] = np.eye(self.n)[shift_idx]
+
+    if self.n_actions > 3:
+      # add permutations in the order given by itertools.permutations
+      self.all_permutations = list(itertools.permutations(range(self.n)))[1:]
+      cnt = 2
+      for each in self.all_permutations:
+        action = np.eye(self.n)[list(each)]
+        if np.linalg.norm(action - self.actions[0]) == 0:
+          continue
+        elif np.linalg.norm(action - self.actions[1]) == 0:
+          continue
+        self.actions[cnt] = action
+        cnt += 1
+        if cnt == self.n_actions: break
+
+  def get_state_label(self, state):
+    enc = self.state_encode(state)
+    return self.state_label_map[enc]
+
+  def f(self, x):
+    curr_state = np.arange(self.n)
+    labels = []
+    for action in x:
+      curr_state = self.actions[action].dot(curr_state)
+
+      if self.label_type == 'state':
+        labels += self.get_state_label(curr_state),
+      elif self.label_type == 'first_chair':
+        labels += curr_state[0],
+
+    return np.array(labels)
+
+  def sample(self):
+    x = np.random.choice(range(self.n_actions), replace=True, size=self.T)
+
+    return x, self.f(x)
+
+
 dataset_map = {
   'parity': ParitySampler,
   'flipflop': FlipFlopSampler,
+  'symmetric': SymmetricSampler,
   # TODO: more datasets
-  }
+  }