automata.py

# Copyright 2020 The HuggingFace Datasets Authors.
# Copyright 2023 Bingbin Liu, Jordan Ash, Surbhi Goel, Akshay Krishnamurthy, and Cyril Zhang.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.


import csv
import json
import os
import itertools
from sympy.combinatorics.permutations import Permutation

import datasets
import numpy as np
from copy import copy

# check python version
import sys
major, minor = sys.version_info[:2]
version = major + 0.1*minor
OLD_PY_VERSION = 1 if version < 3.8 else 0

_CITATION = """\
"""

_DESCRIPTION = """\
Online dataset mockup.
"""

_HOMEPAGE = ""

_LICENSE = ""

_URLS = {}

class SyntheticAutomataDataset(datasets.GeneratorBasedBuilder):
    """TODO: Short description of my dataset."""

    VERSION = datasets.Version("0.0.0")
    BUILDER_CONFIGS = []
    
    def __init__(self, config={}, **kwargs):
        super().__init__(**kwargs)
        
        """
        Set default configs
        """
        if 'name' not in config:
            config['name'] = 'parity'
        # if 'length' not in config: # sequence length
        #     config['length'] = 20
        if 'size' not in config: # number of sequences
            config['size'] = -1

        self.data_config = config
        self.sampler = dataset_map[config['name']](config)

    def _info(self):
        features = datasets.Features(
            {
                "input_ids": datasets.Sequence(datasets.Value("int32"), length=-1),
                "label_ids": datasets.Sequence(datasets.Value("int32"), length=-1)
            }
        )

        return datasets.DatasetInfo(
            description=_DESCRIPTION,
            features=features,
            homepage=_HOMEPAGE,
            license=_LICENSE,
            citation=_CITATION,
        )

    def _split_generators(self, dl_manager):
        return [
            datasets.SplitGenerator(
                name=datasets.Split.TRAIN,
                gen_kwargs={
                    "split": "train",
                },
            )
        ]

    def _generate_examples(self, split):
        for i in itertools.count(start=0):
            if i == self.data_config['size']:
                break
            x, y = self.sampler.sample()
            yield i, {
                "input_ids": x,
                "label_ids": y
            }


class AutomatonSampler:
  """
  This is a parent class that must be inherited.
  """
  def __init__(self, data_config):
      self.data_config = data_config

      if 'seed' in self.data_config:
          self.np_rng = np.random.default_rng(self.data_config['seed'])
      else:
          self.np_rng = np.random.default_rng()

      if 'length' not in data_config: # sequence length
          data_config['length'] = 20
      self.T = self.data_config['length']

      if 'random_length' not in data_config:
          data_config['random_length'] = 0
      self.random_length = data_config['random_length']

      self.__info__ = "  - T (int): sequence length.\n" \
          + "  - random_length (int in {0, 1}): whether to randomly sample a length per sample.\n"

  def f(self, x):
      """
      Get output sequence given an input seq
      """
      raise NotImplementedError()

  def sample(self):
      raise NotImplementedError()

  def sample_length(self):
      if self.random_length:
        return self.np_rng.choice(range(1, self.T+1))
      return self.T

  def help(self):
        print(self.__info__)




class BinaryInputSampler(AutomatonSampler):
  """
  This is a parent class that must be inherited.
  Subclasses: ParitySampler, GridworldSampler, ABABSampler
  """
  def __init__(self, data_config):
    super().__init__(data_config)

    if 'prob1' not in data_config:
      data_config['prob1'] = 0.5
    self.prob1 = data_config['prob1']
    self.__info__ = "  - prob1 (float in [0,1]): probability of token 1\n" \
         + self.__info__

  def f(self, x):
    raise NotImplementedError()

  def sample(self):
    T = self.sample_length()
    x = self.np_rng.binomial(1, self.prob1, size=T)
    return x, self.f(x)

class ParitySampler(BinaryInputSampler):
  def __init__(self, data_config):
    super().__init__(data_config)
    self.name = 'parity'

    self.__info__ = "Parity machine with 2 states: \n" \
        + "- Inputs: binary strings\n" \
        + "- Labels: binary strings of the partial parity\n" \
        + "- Config: \n" \
        + self.__info__

  def f(self, x):
    return np.cumsum(x) % 2

class GridworldSampler(BinaryInputSampler):
  """
  Note: gridworld currently doesn't include a no-op.
  """
  def __init__(self, data_config):
    super().__init__(data_config)

    if 'n' not in data_config:
      data_config['n'] = 9
    """
    NOTE: n is the number of states, and S is the id (0-indexing) of the rightmost state.
          i.e. the states are 0,1,2,...,S, where S=n-1.
    """
    self.n = data_config['n'] 
    self.S = self.n - 1

    if 'label_type' not in data_config:
      # Options: state, parity, boundary
      data_config['label_type'] = 'state'
    self.label_type = data_config['label_type']

    self.name = f'Grid{self.n}'

    self.__info__ = f"1d Gridworld of n={self.n} states:\n" \
        + "- Inputs: binary strings, i.e. move left(0) or right(1)\n" \
        + "- Labels: depending on 'label_type'. \n" \
        + "- Config: \n" \
        + "  - n (int): number of states; i.e. the states are 0,1,2,...,n-1.\n" \
        + "  - label_type (str): choosing from the following options:\n" \
        + "    - 'state' (default): the state id, i.e. 0 to n-1.\n" \
        + "    - 'parity': the state id mod 2.\n" \
        + "    - 'boundary': whether the current state is in {0, n-1} or not.\n" \
        + self.__info__


  def f(self, x):
    x = copy(x)
    x[x == 0] = -1
    if OLD_PY_VERSION:
      # NOTE: for Python 3.7 or below, accumulate doesn't have the 'initial' argument.
      x = np.concatenate([np.array([0]), x]).astype(np.int64)
      states = list(itertools.accumulate(x, lambda a,b: max(min(a+b, self.S), 0)))
      states = states[1:]
    else:
      states = list(itertools.accumulate(x, lambda a,b: max(min(a+b, self.S), 0), initial=0))
      states = states[1:] # remove the 1st entry with is the (meaningless) initial value 0
    return np.array(states).astype(np.int64)


class ABABSampler(BinaryInputSampler):
  def __init__(self, data_config):
    super().__init__(data_config)
    self.name = 'abab'

    if 'prob_abab_pos_sample' not in data_config:
      # The probability of having a positive sequence, i.e. 010101010101...
      data_config['prob_abab_pos_sample'] = 0.25
    if 'label_type' not in data_config:
      # Options: 'state', 'boundary'
      data_config['label_type'] = 'state'

    self.prob_abab_pos_sample = data_config['prob_abab_pos_sample']
    self.label_type = data_config['label_type']

    self.transition = np.array(
      [[4, 1], # state 0
       [2, 4], # state 1
       [4, 3], # state 2
       [0, 4], # state 3
       [4, 4], # state 4
       ])

    self.__info__ = "abab: an automaton with 4 states + 1 absorbing state:\n" \
        + "- Inputs: binary strings\n" \
        + "- Labels: depending on 'label_type'.\n" \
        + "- Config:\n" \
        + "  - prob_abab_pos_sample (float in [0,1]): probability of having a 'positive' sequence, i.e. 01010101010...\n" \
        + "  - label_type (str): choosing from the following options:\n" \
        + "    - 'state' (default): the state id.\n" \
        + "    - 'boundary': whether the state is in state 3 (the states are 0,1,2,3).\n" \
        + self.__info__ 

  def f(self, x):
    labels = []
    curr_state = 3
    for each in x:
      curr_state = self.transition[curr_state, each]
      labels += curr_state,
    labels = np.array(labels).astype(np.int64)
    if self.label_type == 'boundary':
      labels = (labels == 3).astype(np.int64)
    return labels

  def sample(self):
    pos_sample = self.np_rng.random() < self.prob_abab_pos_sample
    if pos_sample:
      T = self.sample_length()
      x = [0,1,0,1] * (T//4)
      x += [0,1,0,1][:(T%4)]
      x = np.array(x)
      return x, self.f(x)
    else:
      return super().sample()




class FlipFlopSampler(AutomatonSampler):
  def __init__(self, data_config):
    super().__init__(data_config)
    self.name = 'flipflop'

    if 'n' not in data_config:
        data_config['n'] = 2
    
    self.n_states = data_config['n'] 
    self.n_actions = self.n_states + 1
    self.transition = np.array([list(range(self.n_actions))] + [[i+1]*self.n_actions for i in range(self.n_states)]).T

    self.__info__ = f"Flipflop with n={self.n_states} states:\n" \
        +f"- Inputs: tokens are either 0 (read) or 1:{self.n} (write).\n" \
        + "- Labels: depending on 'label_type'.\n" \
        + "- Config:\n" \
        + "  - n (int): number of write states; i.e. the states are 1,2,...,n, plus a default start state 0.\n" \
        + self.__info__ 

  def f(self, x):
    state, states = 0, []
    for action_id in x:
        state = self.transition[state, action_id]
        states += state,
    return np.array(states)

  def sample(self):
    T = self.sample_length()
    rand = self.np_rng.uniform(size=T)
    nonzero_pos = (rand < 0.5).astype(np.int64)
    writes = self.np_rng.choice(range(1, self.n_states+1), size=T)
    x = writes * nonzero_pos
    return x, self.f(x)




class PermutationSampler(AutomatonSampler):
  """
  This is a parent class that must be inherited.
  Subclasses: SymmetricSampler, AlternatingSampler
  """
  def __init__(self, data_config):
    super().__init__(data_config)

    if 'n' not in data_config:
      data_config['n'] = 5
    if 'label_type' not in data_config:
      # Options: 'state', 'first_chair'
      data_config['label_type'] = 'state'
    
    self.n = data_config['n'] # the symmetric group Sn
    self.label_type = data_config['label_type']

    self.__info__ = \
          "  - label_type (str): choosing from the following options:\n" \
        + "    - 'state' (default): the state id.\n" \
        + "    - 'first_chair': the element in the first position of the permutation.\n" \
        + "          e.g. if the current permutation is [2,1,4,3], then 'first_chair' is 2.\n" \
        + self.__info__

  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_id in x:
      curr_state = self.actions[action_id].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):
    T = self.sample_length()
    x = self.np_rng.choice(range(self.n_actions), replace=True, size=T)

    return x, self.f(x)


class SymmetricSampler(PermutationSampler):
  """
  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 = f'S{self.n}'

    """
    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)
    """
    if 'n_actions' not in data_config:
      data_config['n_actions'] = 3
    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

    self.__info__ = f"Symmetric group on n={self.n} objects:\n" \
        +f"- Inputs: tokens are either 0 (no-op), or 1:{self.n_actions} (corresponding to {self.n_actions} permutations).\n" \
        + "- Labels: depending on 'label_type'.\n" \
        + "- Config:\n" \
        + "  - n (int): number of objects, i.e. there are n! states.\n" \
        + "  - n_actions (int): number of permutations to include in the generator set;\n" \
        + "        the ordering is given by itertools.permutations, and the first 'n_actions' permutations will be included.\n" \
        + self.__info__ 


class AlternatingSampler(PermutationSampler):
  """
  TODO: other choices of generators (currently using (12x))?
  """
  def __init__(self, data_config):
    super().__init__(data_config)

    self.name = f'A{self.n}'

    """
    Get states
    """
    self.state_label_map = {}
    self.state_encode = lambda state: ''.join([str(int(each)) for each in state])
    cnt = 0
    for si, state in enumerate(itertools.permutations(range(self.n))):
      if not Permutation(state).is_even:
        continue
      enc = self.state_encode(state)
      self.state_label_map[enc] = cnt
      cnt += 1

    """
    Get actions: all 3 cycles of the form (12x)
    """
    self.actions = {0: np.eye(self.n)}
    for idx in range(2, self.n):
      # (1, 2, idx) 
      shift_idx = list(range(self.n))
      shift_idx[0],shift_idx[1], shift_idx[idx] = shift_idx[1], shift_idx[idx], shift_idx[0]
      self.actions[idx-1] = np.eye(self.n)[shift_idx]
    self.n_actions = len(self.actions)

    self.__info__ = f"Alternating group on n={self.n} objects:\n" \
        +f"- Inputs: tokens from 0 to n-3, corresponding to all 3-cycles of the form (12x).\n" \
        + "- Labels: depending on 'label_type'.\n" \
        + "- Config:\n" \
        + "  - n (int): number of objects, i.e. there are n!/2 states.\n" \
        + self.__info__ 




class CyclicSampler(AutomatonSampler):
  def __init__(self, data_config):
    super().__init__(data_config)

    if 'n' not in data_config:
      data_config['n'] = 5
    self.n = data_config['n']

    """
    Get actions: shift by i positions, for i = 0 to n_actions-1
    """
    if 'n_actions' not in data_config:
      data_config['n_actions'] = 2
    self.n_actions = data_config['n_actions']
    shift_idx = list(range(1, self.n)) + [0]
    self.actions = {}
    for i in range(self.n_actions):
      shift_idx = list(range(i, self.n)) + list(range(0, i))
      self.actions[i] = np.eye(self.n)[shift_idx]


  def f(self, x):
    if OLD_PY_VERSION:
      # NOTE: for Python 3.7 or below, accumulate doesn't have the 'initial' argument.
      x_padded = np.concatenate([np.array([0]), x]).astype(np.int64)
      states = list(itertools.accumulate(x_padded, lambda a,b: (a+b)%self.n ))
      states = states[1:]
    else:
      states = list(itertools.accumulate(x, lambda a,b: (a+b)%self.n, initial=0))
      states = states[1:] # remove the 1st entry with is the (meaningless) initial value 0

    return np.array(states).astype(np.int64)

  def sample(self):
    T = self.sample_length()
    x = self.np_rng.choice(range(self.n_actions), replace=True, size=T)

    return x, self.f(x)



dataset_map = {
  'abab': ABABSampler,
  'alternating': AlternatingSampler,
  'cyclic': CyclicSampler,
  'flipflop': FlipFlopSampler,
  'gridworld': GridworldSampler,
  'parity': ParitySampler,
  'symmetric': SymmetricSampler,
  # TODO: more datasets
  }