Class: Lernen::Automaton::TransitionSystem

Inherits:
Object
  • Object
show all
Defined in:
lib/lernen/automaton/transition_system.rb

Overview

TransitionSystem represents a labelled transition system.

We assume that this transition system is deterministic and complete; thus, the transition function should be defined for all states and input characters, and the destination configuration of a transition should be one.

Also, this transition system has an output value for each transition. From this point of view, this definition is much like Mealy machines. However, this class is more generic. Actually, this is a superclass of Moore machines, DFA, etc.

Note that this class is abstract. We should implement the following method:

  • ‘#type`

  • ‘#initial_conf`

  • ‘#step(conf, input)`

  • ‘#to_graph`

Direct Known Subclasses

Mealy, MooreLike

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.find_separating_word(alphabet, automaton1, automaton2) ⇒ Object

Finds a separating word between ‘automaton1` and `automaton2`.

: [Conf, In, Out] (

  Array[In] alphabet,
  TransitionSystem[Conf, In, Out] automaton1,
  TransitionSystem[Conf, In, Out] automaton2
) -> (Array[In] | nil)



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# File 'lib/lernen/automaton/transition_system.rb', line 104

def self.find_separating_word(alphabet, automaton1, automaton2)
  unless automaton2.is_a?(automaton1.class)
    raise ArgumentError, "Cannot find a separating word for different type automata"
  end
  queue = []
  prefix_hash = {}

  initial_pair = [automaton1.initial_conf, automaton2.initial_conf]
  queue << initial_pair
  prefix_hash[initial_pair] = []

  until queue.empty?
    conf1, conf2 = queue.shift
    prefix = prefix_hash[[conf1, conf2]]

    alphabet.each do |input|
      word = prefix + [input]

      output1, next_conf1 = automaton1.step(conf1, input)
      output2, next_conf2 = automaton2.step(conf2, input)

      return word if output1 != output2 # steep:ignore

      next_pair = [next_conf1, next_conf2]
      unless prefix_hash.include?(next_pair)
        queue << next_pair
        prefix_hash[next_pair] = word
      end
    end
  end

  nil
end

.random_transition_function(alphabet:, min_state_size: 5, max_state_size: 10, num_reachable_paths: 2, random: Random) ⇒ Object

Generates a transition function randomly.

To make a transition function connected, this method generates a transition function in the following mannar.

  1. Decide a number of states within ‘min_state_size..max_state_size` randomly.

  2. Divides the states into ‘num_reachable_paths` partitions.

  3. Generate a path from the initial state for each paratition.

  4. Generate transition for all ‘state` and `input`.

This method returns a pair of a transition function and an array of reachable paths. The initial state of the result transition function is ‘0`.

: [In] (

  alphabet: Array[In],
  ?min_state_size: Integer,
  ?max_state_size: Integer,
  ?num_reachable_paths: Integer,
  ?random: Random,
) -> [Hash[[Integer, In], Integer], Array[Array[Integer]]]



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# File 'lib/lernen/automaton/transition_system.rb', line 158

def self.random_transition_function(
  alphabet:,
  min_state_size: 5,
  max_state_size: 10,
  num_reachable_paths: 2,
  random: Random
)
  state_size = random.rand(min_state_size..max_state_size)
  num_reachable_paths = [num_reachable_paths, alphabet.size, state_size].min #: Integer

  initial_state = 0
  reachable_paths = []
  transition_function = {}

  partitions = (0...state_size).to_a + ([nil] * (num_reachable_paths - 1))
  partitions.shuffle!(random:)
  partitions.push(nil)

  initial_alphabet = alphabet.dup
  initial_alphabet.shuffle!(random:)

  until partitions.empty?
    reachable_path = [initial_state]
    state = initial_state
    input = initial_alphabet.shift
    loop do
      next_state = partitions.shift
      break if next_state.nil?
      next if next_state == initial_state

      reachable_path << next_state

      transition_function[[state, input]] = next_state

      input = alphabet.sample(random:)
    end
    reachable_paths << reachable_path
  end

  state_size.times do |state|
    alphabet.each do |input|
      next if transition_function[[state, input]]
      next_state = random.rand(state_size)
      transition_function[[state, input]] = next_state
    end
  end

  [transition_function, reachable_paths]
end

Instance Method Details

#initial_conf ⇒ Object

Returns the initial configuration.

This is an abstract method.

: () -> Conf

Raises:

  • (TypeError) 


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# File 'lib/lernen/automaton/transition_system.rb', line 44

def initial_conf
  raise TypeError, "abstract method: `initial_conf`"
end

#run(word) ⇒ Object

Runs transitions from the initial configuration with the given word.

It returns a pair of the output values and the final configuration of the transitions.

: (Array word) -> [Array, Conf]



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# File 'lib/lernen/automaton/transition_system.rb', line 77

def run(word)
  conf = initial_conf
  outputs = []
  word.each do |input|
    output, conf = step(conf, input)
    outputs << output
  end
  [outputs, conf]
end

#step(conf, input) ⇒ Object

Runs a transition from the given configuration with the given input.

It returns a pair of the output value and the next configuration of this transition.

This is an abstract method.

: (Conf conf, In input) -> [Out, Conf]

Raises:

  • (TypeError) 


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# File 'lib/lernen/automaton/transition_system.rb', line 56

def step(conf, input)
  raise TypeError, "abstract method: `step`"
end

#to_dot ⇒ Object

Returns a [GraphViz](graphviz.org) DOT diagram of this transition system.

: () -> String



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# File 'lib/lernen/automaton/transition_system.rb', line 95

def to_dot = to_graph.to_dot

#to_graph ⇒ Object

Returns a graph of this transition system.

This is an abstract method.

: () -> Graph

Raises:

  • (TypeError) 


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# File 'lib/lernen/automaton/transition_system.rb', line 65

def to_graph
  raise TypeError, "abstract method: `to_graph`"
end

#to_mermaid(direction: "TD") ⇒ Object

Returns a [Mermaid](mermaid.js.org) diagram of this transition system.

: (?direction: Graph::mermaid_direction) -> String



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# File 'lib/lernen/automaton/transition_system.rb', line 90

def to_mermaid(direction: "TD") = to_graph.to_mermaid(direction:)

#type ⇒ Object

Returns the automaton type.

This is an abstract method.

: () -> transition_system_type

Raises:

  • (TypeError) 


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# File 'lib/lernen/automaton/transition_system.rb', line 35

def type
  raise TypeError, "abstract method: `type`"
end