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__pycache__
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*.pyc
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*.swp
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CC0 1.0 Universal
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exclusive Copyright and Related Rights (defined below) upon the creator and
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@ -0,0 +1,165 @@
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import enum
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from collections import namedtuple
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from regex import lit, concat, bar, star
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NFA = namedtuple('NFA', ['start', 'accept', 'transitions'])
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||||||
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def copy_nfa(nfa):
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transitions_copy = {}
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for from_state in nfa.transitions:
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|
transitions_copy[from_state] = nfa.transitions[from_state].copy()
|
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|
||||||
|
return NFA(nfa.start, nfa.accept, transitions_copy)
|
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|
||||||
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def remove_states(nfa):
|
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|
start, accept, transitions = nfa
|
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states = transitions.keys()
|
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|
||||||
|
states_to_remove = [i for i in states if i != start and i not in accept]
|
||||||
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|
||||||
|
while len(states_to_remove) > 0:
|
||||||
|
# Select a state to remove this round
|
||||||
|
removed_state = states_to_remove.pop()
|
||||||
|
print('\nRemoving state:', removed_state)#debg
|
||||||
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|
||||||
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# Remove loops from this state back into itself
|
||||||
|
if removed_state in transitions[removed_state]:
|
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|
loop_condition = transitions[removed_state][removed_state]
|
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|
del transitions[removed_state][removed_state]
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|
||||||
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# Prepend (condition)* to all transitions leading out
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# of this state
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for to_state in transitions[removed_state]:
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condition = transitions[removed_state][to_state]
|
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transitions[removed_state][to_state] = concat(star(loop_condition), condition)
|
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||||||
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print(); prettyprint(nfa)#debg
|
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|
||||||
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# Rewrite all transitions A→this→B as A→B transitions
|
||||||
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#
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# If the condition A→this is foo and this→B is bar, the
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||||||
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# condition for A→B becomes simply foobar
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||||||
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#
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# Since we've removed all loops back into this state, this
|
||||||
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# results in there being no transitions into this state
|
||||||
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for from_state in transitions:
|
||||||
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if removed_state in transitions[from_state]:
|
||||||
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# Create a list of new transitions to add to the
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# transition table for from_state
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new_transitions = {}
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condition_to_here = transitions[from_state][removed_state]
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for to_state in transitions[removed_state]:
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||||||
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condition_from_here = transitions[removed_state][to_state]
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new_transitions[to_state] = concat(condition_to_here, condition_from_here)
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||||||
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||||||
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# Remove the transition to the state being deleted
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del transitions[from_state][removed_state]
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||||||
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# Add the new transitions
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||||||
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# Since they may lead to the same place as
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||||||
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# already-existing transitions, we may need to
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||||||
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# combine the conditions with pre-existing ones
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||||||
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for to_state in new_transitions:
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if to_state in transitions[from_state]:
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||||||
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# Already a transition leading
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||||||
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# to the same state
|
||||||
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# If its condition is foo and
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||||||
|
# ours is bar, then the new
|
||||||
|
# condition will be foo|bar
|
||||||
|
other_condition = transitions[from_state][to_state]
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||||||
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our_condition = new_transitions[to_state]
|
||||||
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transitions[from_state][to_state] = bar(other_condition, our_condition)
|
||||||
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||||||
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else:
|
||||||
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# No pre-existing transition
|
||||||
|
transitions[from_state][to_state] = new_transitions[to_state]
|
||||||
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|
||||||
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# Finally, remove the state we no longer need
|
||||||
|
del transitions[removed_state]
|
||||||
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||||||
|
print(); prettyprint(nfa)#debg
|
||||||
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|
||||||
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return NFA(start, accept, transitions)
|
||||||
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|
||||||
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def to_regex(nfa):
|
||||||
|
# Rewrite the NFA so that there are no transitions leading in to the
|
||||||
|
# start state or any leading out of an accept state. The easy way to
|
||||||
|
# do this is by creating a new start state that leads to the old one
|
||||||
|
# with empty condition (i.e. it consumes no input), and creating a new
|
||||||
|
# accept state that has similar empty condition transitions from all
|
||||||
|
# the old ones. Since we have an NFA and not a DFA, that operation is
|
||||||
|
# safe
|
||||||
|
#
|
||||||
|
# As a bonus, this rewrite gives us two useful properties:
|
||||||
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# a) There is exactly one start state and one accept state
|
||||||
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# b) After running remove_state() there will be only one transition,
|
||||||
|
# that of start to accept
|
||||||
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#
|
||||||
|
# S
|
||||||
|
class _(enum.Enum): start, end = range(2)
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||||||
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|
||||||
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start, accept, transitions = copy_nfa(nfa)
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||||||
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||||||
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# Add new start state
|
||||||
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transitions[_.start] = {start: lit('')}
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||||||
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||||||
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# Add new accept state and transitions to it
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||||||
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transitions[_.end] = {}
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for state in accept:
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transitions[state][_.end] = lit('')
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||||||
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||||||
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# Package everything into a new NFA
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nfa = NFA(_.start, [_.end], transitions)
|
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print();prettyprint(nfa)#debg
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processed = remove_states(nfa)
|
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|
||||||
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return processed.transitions[_.start][_.end]
|
||||||
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|
||||||
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def prettyprint(nfa):
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||||||
|
def process_state(state):
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nonlocal start, accept
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t = ''
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if state == start:
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# Bold
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t += '\x1b[1m'
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if state in accept:
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# Green
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||||||
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t += '\x1b[32m'
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||||||
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||||||
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if t != '':
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||||||
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return t + str(state) + '\x1b[0m'
|
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|
else:
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||||||
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return str(state)
|
||||||
|
|
||||||
|
start, accept, transitions = nfa
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|
states = transitions.keys()
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||||||
|
|
||||||
|
print('\t' + '\t'.join(map(process_state, states)))
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|
for from_state in states:
|
||||||
|
t = []
|
||||||
|
for to_state in states:
|
||||||
|
if to_state in transitions[from_state]:
|
||||||
|
t.append(str(transitions[from_state][to_state]))
|
||||||
|
else:
|
||||||
|
t.append('\x1b[90m-\x1b[0m')
|
||||||
|
|
||||||
|
print(process_state(from_state) + '\t' + '\t'.join(t))
|
||||||
|
|
||||||
|
def main():
|
||||||
|
nfa = NFA('start', ['end'], {
|
||||||
|
'start': {'0': lit('s')},
|
||||||
|
'0': {'0': lit('0'), '1': lit('1'), 'end': lit('e'), 'start': lit('r')},
|
||||||
|
'1': {'0': lit('1'), '1': lit('0'), 'start': lit('r')},
|
||||||
|
'end': {'end': lit('e'), 'start': lit('n')}
|
||||||
|
})
|
||||||
|
|
||||||
|
prettyprint(nfa)
|
||||||
|
|
||||||
|
print(to_regex(nfa))
|
||||||
|
|
||||||
|
if __name__ == '__main__':
|
||||||
|
main()
|
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@ -0,0 +1,118 @@
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|
class Literal:
|
||||||
|
def __init__(self, text):
|
||||||
|
self.text = text
|
||||||
|
self.single_char = len(text) == 1
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
return 'Literal(%s)' % repr(self.text)
|
||||||
|
|
||||||
|
def __str__(self):
|
||||||
|
# ERE-style quotation rules
|
||||||
|
# A-Za-z0-9 and space are safe, as are non-ASCII
|
||||||
|
# Everything else is safe to quote with backslash
|
||||||
|
return ''.join(
|
||||||
|
char if ord('A') <= ord(char) <= ord('Z') else
|
||||||
|
char if ord('a') <= ord(char) <= ord('z') else
|
||||||
|
char if ord('0') <= ord(char) <= ord('9') else
|
||||||
|
char if char == ' ' else
|
||||||
|
char if ord(char) >= 128 else # Non-ASCII
|
||||||
|
'\\' + char # Quote
|
||||||
|
|
||||||
|
for char in self.text
|
||||||
|
)
|
||||||
|
|
||||||
|
class Concatenation:
|
||||||
|
def __init__(self, *elements):
|
||||||
|
self.elements = elements
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
return 'Concatenation(%s)' % ', '.join(map(repr, self.elements))
|
||||||
|
|
||||||
|
def __str__(self):
|
||||||
|
return ''.join(
|
||||||
|
# Only alternation binds looser than concatenation,
|
||||||
|
# so we can pass everything else pass through with
|
||||||
|
# no parenthesizing
|
||||||
|
str(element) if type(element) != Alternation else
|
||||||
|
'(' + str(element) + ')'
|
||||||
|
|
||||||
|
for element in self.elements
|
||||||
|
)
|
||||||
|
|
||||||
|
class Alternation:
|
||||||
|
def __init__(self, *elements):
|
||||||
|
self.elements = elements
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
return 'Alternation(%s)' % ', '.join(map(repr, self.elements))
|
||||||
|
|
||||||
|
def __str__(self):
|
||||||
|
if all(type(i) == Literal and i.single_char for i in self.elements):
|
||||||
|
# Special case: [abc]
|
||||||
|
return '[%s]' % ''.join(map(str, self.elements))
|
||||||
|
else:
|
||||||
|
# Nothing binds looser than alternation, so just
|
||||||
|
# pass everything through as-is
|
||||||
|
return '|'.join(map(str, self.elements))
|
||||||
|
|
||||||
|
class Star:
|
||||||
|
def __init__(self, element):
|
||||||
|
self.element = element
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
return 'Star(%s)' % repr(self.element)
|
||||||
|
|
||||||
|
def __str__(self):
|
||||||
|
# * applies to the previous character or a parenthesized
|
||||||
|
# group. Therefore, we parentesize unless we havea Literal
|
||||||
|
# and it is one-char long
|
||||||
|
if type(self.element) == Literal and self.element.single_char:
|
||||||
|
return str(self.element) + '*'
|
||||||
|
else:
|
||||||
|
return '(%s)*' % str(self.element)
|
||||||
|
|
||||||
|
def lit(text):
|
||||||
|
return Literal(text)
|
||||||
|
|
||||||
|
def concat(*elements):
|
||||||
|
flattened = []
|
||||||
|
for element in elements:
|
||||||
|
if type(element) == Concatenation:
|
||||||
|
flattened.extend(element.elements)
|
||||||
|
else:
|
||||||
|
flattened.append(element)
|
||||||
|
|
||||||
|
combined = []
|
||||||
|
for element in flattened:
|
||||||
|
if len(combined) > 0 and type(combined[-1]) == Literal and type(element) == Literal:
|
||||||
|
# Combine two literals next to each other
|
||||||
|
# into one literal
|
||||||
|
previous = combined.pop()
|
||||||
|
combined.append(Literal(previous.text + element.text))
|
||||||
|
|
||||||
|
else:
|
||||||
|
combined.append(element)
|
||||||
|
|
||||||
|
if len(combined) == 1:
|
||||||
|
element, = combined
|
||||||
|
return element
|
||||||
|
else:
|
||||||
|
return Concatenation(*combined)
|
||||||
|
|
||||||
|
def bar(*elements):
|
||||||
|
# TODO: rewrite (foo|foo) → foo
|
||||||
|
flattened = []
|
||||||
|
for element in elements:
|
||||||
|
if type(element) == Alternation:
|
||||||
|
flattened.extend(element.elements)
|
||||||
|
else:
|
||||||
|
flattened.append(element)
|
||||||
|
|
||||||
|
if len(flattened) == 1:
|
||||||
|
element, = flattened
|
||||||
|
return element
|
||||||
|
else:
|
||||||
|
return Alternation(*flattened)
|
||||||
|
|
||||||
|
def star(element):
|
||||||
|
return Star(element)
|
Loading…
Reference in New Issue