fade2black / Ntm

Nondeterministic Turing machine simulator

Ntm

Ntm simulates nondeterministic Turing machines. It may also be used to simulate deterministic Turing machines.

Installation

Add this line to your application's Gemfile:

gem 'ntm'

And then execute:

$ bundle

Or install it yourself as:

$ gem install ntm

Ntm examples

Example 1

state	symbol	move
q0	0	(q1,0,R), (q1,1,R)
q1	1	(q2,0,R), (q2,1,R)

  require "ntm"
  
  ntm = Ntm.new(initial_state: 0) do
    given({state:0, symbol: '0'}) do
      transition(state:1, symbol:'0', move: :right)
      transition(state:1, symbol:'1', move: :right)
    end

    given({state:1, symbol: '1'}) do
      transition(state:2, symbol:'0', move: :right)
      transition(state:2, symbol:'1', move: :right)
    end
  end

  configurations = ntm.run({max_depth:250, tape_content: "011" })

  configurations.each do |conf|
    conf.path.each do |p|
      instr = p[:instr]
      print p[:config] + " (#{instr[:state]},#{instr[:symbol]},#{instr[:move][0]}) => "
    end
    puts conf.to_s
  end

Output: four possible computations

[q0]011 (1,0,r) => 0[q1]11 (2,0,r) => 00[q2]1

[q0]011 (1,0,r) => 0[q1]11 (2,1,r) => 01[q2]1

[q0]011 (1,1,r) => 1[q1]11 (2,0,r) => 10[q2]1

[q0]011 (1,1,r) => 1[q1]11 (2,1,r) => 11[q2]1

Example 2: a deterministic TM accepting language the language {0ⁿ1ⁿ | n > 0 } - n 0s followed by n 1s

state	symbol	move
q0	0	(q1,X,R)
q0	Y	(q3,Y,R)
q1	0	(q1,0,R)
q1	1	(q2,Y,L)
q1	Y	(q1,Y,R)
q2	0	(q2,0,L)
q2	X	(q0,X,R)
q2	Y	(q2,Y,L)
q3	Y	(q3,Y,R)
q3	#	(q4,#,R)

Accept state: q₄

require "ntm"

ntm = Ntm.new(initial_state: 0) do
  given({state:0, symbol:'0'}) { transition(state:1, symbol:'X', move: :right) }
  given({state:0, symbol:'Y'}) { transition(state:3, symbol:'Y', move: :right) }
  given({state:1, symbol:'0'}) { transition(state:1, symbol:'0', move: :right) }
  given({state:1, symbol:'1'}) { transition(state:2, symbol:'Y', move: :left)  }
  given({state:1, symbol:'Y'}) { transition(state:1, symbol:'Y', move: :right) }
  given({state:2, symbol:'0'}) { transition(state:2, symbol:'0', move: :left)  }
  given({state:2, symbol:'X'}) { transition(state:0, symbol:'X', move: :right) }
  given({state:2, symbol:'Y'}) { transition(state:2, symbol:'Y', move: :left)  }
  given({state:3, symbol:'Y'}) { transition(state:3, symbol:'Y', move: :right) }
  given({state:3, symbol:'#'}) { transition(state:4, symbol:'#', move: :right) }
end

configurations = ntm.run({max_depth:250, tape_content: "0011", accept_states:[4] })

configurations.each do |conf|
  conf.path.each do |p|
    instr = p[:instr]
    print p[:config] + " (#{instr[:state]},#{instr[:symbol]},#{instr[:move][0]}) => "
  end
  puts conf.to_s
end

Output

[q0]0011 (1,X,r) => X[q1]011 (1,0,r) => X0[q1]11 (2,Y,l) => X[q2]0Y1 (2,0,l) => [q2]X0Y1 (0,X,r) => X[q0]0Y1 (1,X,r) => XX[q1]Y1 (1,Y,r) => XXY[q1]1 (2,Y,l) => XX[q2]YY (2,Y,l) => X[q2]XYY (0,X,r) => XX[q0]YY (3,Y,r) => XXY[q3]Y (3,Y,r) => XXYY[q3] (4,#,r) => XXYY#[q4]

Development

After checking out the repo, run bin/setup to install dependencies. Then, run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release to create a git tag for the version, push git commits and tags, and push the .gem file to rubygems.org.

Contributing

1. Fork it ( https://github.com/[my-github-username]/ntm/fork )
2. Create your feature branch (git checkout -b my-new-feature)
3. Commit your changes (git commit -am 'Add some feature')
4. Push to the branch (git push origin my-new-feature)
5. Create a new Pull Request