A -> e* | (eUe)
e -> any combination of chars from the grammar

A -> e+ | '(' A 'U' A ')'
e -> '0' | '1'

class MySyntaxError(Exception):
  def __init__(self, text, index):
    self.text = text
    self.index = index
  def __str__(self):
    return "Syntax error at index " + repr(self.index) + ": " + self.text


def parse(input):
  global index
  index = 0

  def eat_char(set):
    global index
    if index < len(input) and input[index] in set:
      index += 1
    else:
      raise MySyntaxError("expected char in " + repr(set), index)

  def e():
    eat_char(['0', '1'])

  def A():
    global index
    if index == len(input): # Successfully parsed
      return
    elif input[index] in ['0', '1']:
      while (input[index] in ['0', '1']):
        e()
    elif input[index] is '(':
      eat_char(['('])
      A()
      eat_char(['U'])
      A()
      eat_char([')'])
    else:
      raise MySyntaxError("expected char '0', '1' or '('", index)

  A()
  if index != len(input): # Parsing didn't reach the end of the string
    raise MySyntaxError("parsing ended before the end of the input", index)


def test(string):
  try:
    parse(string)
    print "The string " + string + " have been successfully parsed"
  except MySyntaxError as e:
    print "The string " + string + " can't be parsed:"
    print e

test("(01U(1U0))")
test("(01U(1U0)") # Missing parenthesis, syntax error
test("(01U(1U0)))") # Too many parenthesis, syntax error
test("01U(1U0)") # No parenthesis, syntax error

from state [1]
  read a '0' or a '1' and loop into state [1]
  read a '(', push the parenthesis and loop into state [1]
  read a 'U', when there is an open parenthesis on the top of stack, push the 'U' and loop into state [1]
  read a ')', when there is a 'U' on the top of the stack, pop the 'U', pop the opend parenthesis following, and loop into state[1]

def parse(input):
  index = 0
  stack = [];

  def top():
    if len(stack) > 0:
      return stack[len(stack)-1]
    else:
      return None

  while index < len(input):
    if input[index] in ['0', '1']:
      pass
    elif input[index] is '(':
      stack.append('(')
    elif input[index] is 'U' and top() == '(':
      stack.append('U')
    elif input[index] is ')' and top() == 'U':
      stack.pop()
      stack.pop()
    else:
      raise MySyntaxError("Unexpected char '" + input[index] + "'", index)
    index += 1

  if len(stack):
    raise MySyntaxError("unterminated input", index)