FSM
in Python

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This module implements a Finite State Machine (FSM). In addition to state this FSM also maintains a user defined "something". This "something" is effectively memory, so this FSM could be considered a Push-down Automata (PDA) since a PDA is a FSM + memory.

The following describes how the FSM works, but you will probably also need to see the example to understand how the FSM is used in practice.

You define an FSM by building tables of transitions. For a given input symbol the process() method uses these tables to decide what action to call and what the next state will be. The FSM has a table of transitions that associate:

        (input_symbol, current_state) --> (action, next_state)

where "action" is a function you define. The symbols and states can be any objects. You use the add_transition() and add_transition_list() methods to add to the transition table. The FSM also has a table of transitions that associate:

        (current_state) --> (action, next_state)

You use the add_transition_any() method to add to this transition table. The FSM also has one default transition that is not associated with any specific input_symbol or state. You use the set_default_transition() method to set the default transition.

When an action function is called it is passed a reference to the FSM. The action function may then access attributes of the FSM such as input_symbol, current_state, or "something". The "something" attribute can be any object that you want to pass along to the action functions. It is not used by the FSM. For parsing you would typically pass a list to be used as a stack.

The processing sequence is as follows. The process() method is given an input_symbol to process. The FSM will search the table of transitions that associate:

        (input_symbol, current_state) --> (action, next_state)

If the pair (input_symbol, current_state) is found then process() will call the associated action function and then set the current state to the next_state.

If the FSM cannot find a match for (input_symbol, current_state) it will then search the table of transitions that associate:

        (current_state) --> (action, next_state)

If the current_state is found then the process() method will call the associated action function and then set the current state to the next_state. Notice that this table lacks an input_symbol. It lets you define transitions for a current_state and ANY input_symbol. Hence, it is called the "any" table. Remember, it is always checked after first searching the table for a specific (input_symbol, current_state).

For the case where the FSM did not match either of the previous two cases the FSM will try to use the default transition. If the default transition is defined then the process() method will call the associated action function and then set the current state to the next_state. This lets you define a default transition as a catch-all case. You can think of it as an exception handler. There can be only one default transition.

Finally, if none of the previous cases are defined for an input_symbol and current_state then the FSM will raise an exception. This may be desirable, but you can always prevent this just by defining a default transition.

Noah Spurrier 20020822

Modules

Classes

exceptions.Exception

ExceptionFSM

FSM

class ExceptionFSM(exceptions.Exception)
	This is the FSM Exception class.

class FSM

This is a Finite State Machine (FSM).

Methods defined here:

__init__(self, initial_state, something): This creates the FSM. You set the initial state here. The "something" attribute is any object that you want to pass along to the action functions. It is not used by the FSM. For parsing you would typically pass a list to be used as a stack.

add_transition(self, input_symbol, state, action, next_state): This adds a transition that associates
(input_symbol, current_state) --> (action, next_state)
The action may be set to None in which case the process() method will ignore the action and only set the next_state. You can also set transitions for a list of symbols by using add_transition_list().

add_transition_any(self, state, action, next_state): This adds a transition that associates
(current_state) --> (action, next_state)
The process() method checks these associations if it cannot first find a match of an (input_symbol, current_state).

add_transition_list(self, list_input_symbols, state, action, next_state): This adds the same transition for lots of different input symbols. You can pass a list or a string. Note that it is handy to use string.digits, string.whitespace, string.letters, etc. to add transitions that match character classes.

get_transition(self, input_symbol, state): This returns (action, next state) given an input_symbol and state. This leaves the FSM unchanged. This does not update the current state nor does it trigger the output action. Normally you do not call this method. It is called by process().

The sequence of steps to check for a defined transition goes from the most specific to the least specific.
1. Check state_transitions[] that match (input_symbol, state)
2. Check state_transitions_any[] that match (state) In other words, match a specific state and ANY input_symbol.
3. Check if the default_transition is defined. This catches any input_symbol and any state. This is a handler for errors, undefined states, or defaults.
4. No transition was defined. If we get here then raise an exception.

process(self, input_symbol): This is the main method that you call to process input. This may cause the FSM to change state and call an action. This method calls get_transition() to find the action and next_state associated with the input_symbol and current_state. If the action is None then the action is not called and only the current state is changed. This method processes one input symbol. You can process a list of symbols (or a string) by calling process_list().

process_list(self, s): This takes a list and sends each element to process(). The list may be a string.

reset(self): This sets the current_state to the initial_state and sets input_symbol to None. The initial state was set by the constructor __init__().

set_default_transition(self, action, next_state): This sets the default transition. This defines an action and next_state if the FSM cannot find the input symbol and the current state in the transition list and if the FSM cannot find the current_state in the transition_any list. This is useful for catching errors and undefined states.

The default transition can be removed by setting the attribute default_transition to None.

Data and non-method functions defined here:

Example

##########################################################################
# The following example demonstrates the use of the FSM class in 
# processing RPN expressions. Run this module from the command line.
# You will get a prompt ] for input. 
# Enter an RPN Expression.
# Numbers may be integers. Operators are * / + -
# Use the = sign to evaluate and print the expression.
# For example: 
#    167 3 2 2 * * * 1 - =
# will print:
#    2003
##########################################################################

import string

#
# These define the actions. 
# Note that "something" is a list being used as a stack.
#
def BeginBuildNumber (fsm):
    fsm.something.append (fsm.input_symbol)
def BuildNumber (fsm):
    s = fsm.something.pop ()
    s = s + fsm.input_symbol
    fsm.something.append (s)
def EndBuildNumber (fsm):
    s = fsm.something.pop ()
    fsm.something.append (int(s))
def DoOperator (fsm):   
    ar = fsm.something.pop()
    al = fsm.something.pop()
    if fsm.input_symbol == '+':
        fsm.something.append (al + ar)
    elif fsm.input_symbol == '-':
        fsm.something.append (al - ar)
    elif fsm.input_symbol == '*':
        fsm.something.append (al * ar)
    elif fsm.input_symbol == '/':
        fsm.something.append (al / ar)
def DoEqual (fsm):
    print str(fsm.something.pop())
def Error (fsm):
    print 'That does not compute.'
    print str(fsm.input_symbol)

#
# This is where the example starts and the FSM state transitions are defined.
# Note that states (such as 'INIT') are strings. This is not necessary, but
# it makes the example easier to read.
#
def example ():
    f = FSM ('INIT', []) # "something" will be used as a stack.
    f.set_default_transition (Error, 'INIT')
    f.add_transition_any  ('INIT', None, 'INIT')
    f.add_transition      ('=',               'INIT',            DoEqual,          'INIT')
    f.add_transition_list (string.digits,     'INIT',            BeginBuildNumber, 'BUILDING_NUMBER')
    f.add_transition_list (string.digits,     'BUILDING_NUMBER', BuildNumber,      'BUILDING_NUMBER')
    f.add_transition_list (string.whitespace, 'BUILDING_NUMBER', EndBuildNumber,   'INIT')
    f.add_transition_list ('+-*/',            'INIT',            DoOperator,       'INIT')
    
    print
    print 'Enter an RPN Expression.'
    print 'Numbers may be integers. Operators are * / + -'
    print 'Use the = sign to evaluate and print the expression.'
    print 'For example: '
    print '    167 3 2 2 * * * 1 - ='
    inputs = raw_input (']')
    for s in inputs:
        f.process (s)

if __name__ == '__main__':
    example ()

FSM in Python

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FSM
in Python