Turing machine class:
definition initialization(self, tape, transition, initial state, accept state, reject state):
self.tape = list(tape) # tape is a list of characters
self.head = 0 # The head position starts from the beginning
self.state = initial state
self.transitions = transitions
self.accept_state = Accept_state
self.reject_state = reject state
def step(self):
"""Perform one step of the Turing machine."""
symbol = self.tape[self.head] if self.head < len(self.tape) else ' ' # Read the current symbol (blank if out of bounds)
if (self.state, symbol) in self.transitions:
new_state, write_symbol, move = self.transitions[(self.state, symbol)]
# Write the new symbol on the tape
if self.head < len(self.tape):
self.tape[self.head] = write_symbol
else:
self.tape.append(write_symbol)
# Move the head
if move == 'R':
self.head += 1
elif move == 'L':
self.head -= 1
if self.head < 0:
self.tape.insert(0, ' ') # Extend tape on the left
# Update the state
self.state = new_state
else:
# Transition not defined for current state and symbol
self.state = self.reject_state
def run(self):
"""Run the Turing machine until it reaches an accept or reject state."""
while self.state != self.accept_state and self.state != self.reject_state:
self.step()
return self.state == self.accept_state
def display_tape(self):
"""Display the tape and head position."""
tape_view = ''.join(self.tape).rstrip() # Remove trailing blanks
print("Tape:", tape_view)
print("Head:", ' ' * self.head + '^')
Tape = list(“1011”) # Initial tape
convert = {
#(current state, current symbol): (new state, written symbol, moving direction)
(‘q0’, ‘1’): (‘q0’, ‘1’, ‘R’),
(‘q0’, ‘0’): (‘q0’, ‘0’, ‘R’),
(‘q0’, ‘ ‘): (‘q_accept’, ‘ ‘, ‘N’), # N: Do not move
}
initial state=”q0″
Accept status = “q_accept”
Deny status = “q_deny”
tm = Turing machine (tape, transition, initial state, accept state, reject state)
tm.display_tape()
If tm.run():
print(“The Turing machine accepted the input.”)
Others:
print(“The Turing machine rejected the input.”)
tm.display_tape()
Draft article below
Simulate Turing machine with Python
Turing machine is a basic concept in computer science, representing a computational theoretical model that defines what it means for a system to be “computable.” Although this is an abstract idea, we can use Python to simulate a Turing machine, demonstrating the Turing completeness of the language.
In this article, we will explore the basics of Turing machines, implement a Python simulator, and test it using various examples.
What is a Turing machine?
Turing machines include:
Tape: An infinitely long sequence of cells that can hold symbols. The tape served as both input and memory.
Head: A pointer that can read and write symbols on a tape and move it left and right.
Status: A machine can be in one of several states, including initial, accepting, and rejecting.
Transition Rule: A set of instructions that instructs the machine what to do based on its current state and the symbol under the header.
Why use Python to simulate a Turing machine?
As a Turing-complete language, Python can simulate any computing process. Implement Turing machine through Python:
You can better understand how computing works at a fundamental level.
It’s a practical example of Python’s computing power.
Python implementation of Turing machine
The following is the Python code for the Turing machine simulator:
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Turing machine class:
definition initialization(self, tape, transition, initial state, accept state, reject state):
self.tape = list(tape) # tape is a list of characters
self.head = 0 # The head position starts from the beginning
self.state = initial state
self.transitions = transitions
self.accept_state = Accept_state
self.reject_state = reject state
def step(self):
"""Perform one step of the Turing machine."""
symbol = self.tape[self.head] if self.head < len(self.tape) else ' ' # Read the current symbol (blank if out of bounds)
if (self.state, symbol) in self.transitions:
new_state, write_symbol, move = self.transitions[(self.state, symbol)]
# Write the new symbol on the tape
if self.head < len(self.tape):
self.tape[self.head] = write_symbol
else:
self.tape.append(write_symbol)
# Move the head
if move == 'R':
self.head += 1
elif move == 'L':
self.head -= 1
if self.head < 0:
self.tape.insert(0, ' ') # Extend tape on the left
# Update the state
self.state = new_state
else:
# Transition not defined for current state and symbol
self.state = self.reject_state
def run(self):
"""Run the Turing machine until it reaches an accept or reject state."""
while self.state != self.accept_state and self.state != self.reject_state:
self.step()
return self.state == self.accept_state
def display_tape(self):
"""Display the tape and head position."""
tape_view = ''.join(self.tape).rstrip() # Remove trailing blanks
print("Tape:", tape_view)
print("Head:", ' ' * self.head + '^')
Example: Testing a Turing Machine
Configuration
Let’s configure the Turing machine to read a binary string and accept it if it reaches the end without error.
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Tape = list(“1011”) # Initial tape
convert = {
#(current state, current symbol): (new state, written symbol, moving direction)
(‘q0’, ‘1’): (‘q0’, ‘1’, ‘R’),
(‘q0’, ‘0’): (‘q0’, ‘0’, ‘R’),
(‘q0’, ‘ ‘): (‘q_accept’, ‘ ‘, ‘N’), # N: Do not move
}
initial state=”q0″
Accept status = “q_accept”
Deny status = “q_deny”
tm = Turing machine (tape, transition, initial state, accept state, reject state)
tm.display_tape()
If tm.run():
print(“The Turing machine accepted the input.”)
Others:
print(“The Turing machine rejected the input.”)
tm.display_tape()
expected output
For input 1011, the output will be:
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Tape: 1011
Header: ^
A Turing machine takes input.
Tape: 1011
Header: ^
how it works
The machine starts from the first position and reads the tape.
It moves to the right until it encounters a space (‘ ‘).
It transitions to the accept state (q_accept) and stops.
Extended example
You can extend this example to handle more complex operations. For example:
Replace symbols on tape
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convert = {
(‘q0’, ‘1’): (‘q1’, ‘X’, ‘R’), # Replace 1 with X
(‘q1’, ‘0’): (‘q0’, ‘Y’, ‘R’), # Replace 0 with Y
(‘q1’, ‘ ‘): (‘q_accept’, ‘ ‘, ‘N’),
}
For Tape = list(“1011”), this produces:
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Tape: XYX1
Header: ^
A Turing machine takes input.
Add rejection status
To handle invalid input, define a reject status:
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convert = {
(‘q0’, ‘1’): (‘q0’, ‘1’, ‘R’),
(‘q0’, ‘2’): (‘q_reject’, ‘2’, ‘N’), # Reject if symbol 2 is encountered
}
For Tape = list(“12”) this will produce:
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Tape: 12
Header: ^
The Turing machine rejected the input.
focus
Simulate a Turing machine: Python can effectively simulate a Turing machine and demonstrate its computing power.
Understanding Computation: This program provides insights into how basic computational models work.
Customization: Various computing tasks can be simulated by modifying conversion rules and tapes.
in conclusion
This simple Python Turing machine simulator is a great way to explore computing theory. It demonstrates how complex operations can arise from simple rules and provides a platform for experimenting with theoretical computer science concepts.
If you want to delve deeper, consider building a visualization or extending the simulator for more advanced calculations. The possibilities are endless!