This is example bash shell session, demonstrating the MPCP.py program.
Note '$' is the shell prompt.

First we run MPCP.py from the command line. The output shows that
the string w='ababab' (embedded in the first domino) leads to a match,
using the other dominos from L_dominos. So we say this w is in the
language defined by L_dominos.


$ python3 MPCP.py
Solving MPCP: #/#Sababab# a/a b/b #/# Sa/S Sb/T Ta/T Tb/S #T#/#
FOUND MATCH: 0 4 2 1 2 1 2 3 5 1 2 1 2 3 6 2 1 2 3 7 1 2 3 4 2 3 5 8
# Sa b a b a b # Sb a b a b # Ta b a b # Tb a b # Sa b # Sb #T#
#Sababab# S b a b a b # T a b a b # T b a b # S a b # S b # T #


Second, we start python in interactive mode, loading MPCP as a 'module'.
First we solve some textbook examples (page227, pag227b, page239).
Then for a few strings w in {a,b}*, we test whether dominos(w) has
a match.


$ python3
Python 3.6.9 (default, Nov  7 2019, 10:44:02)
[GCC 8.3.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> from MPCP import *
>>> mpcp(page227)
Solving MPCP: b/ca a/ab ca/a abc/c
NO MATCH (no solution exists)

>>> mpcp(page227b)
Solving MPCP: a/ab b/ca ca/a abc/c
FOUND MATCH: 0 1 2 0 3
a b ca a abc
ab ca a ab c

>>> mpcp(page239)
Solving MPCP: ab/abab b/a aba/b aa/a
FOUND MATCH: 0 0 2 1 1 3 3
ab ab aba b b aa aa
abab abab b a a a a

>>> mpcp(dominos('a'))
Solving MPCP: #/#Sa# a/a b/b #/# Sa/S Sb/T Ta/T Tb/S #T#/#
NO MATCH (no solution exists)

>>> mpcp(dominos('aba'))
Solving MPCP: #/#Saba# a/a b/b #/# Sa/S Sb/T Ta/T Tb/S #T#/#
FOUND MATCH: 0 4 2 1 3 5 1 3 6 8
# Sa b a # Sb a # Ta #T#
#Saba# S b a # T a # T #

>>> mpcp(dominos('abbab'))
Solving MPCP: #/#Sabbab# a/a b/b #/# Sa/S Sb/T Ta/T Tb/S #T#/#
FOUND MATCH: 0 4 2 2 1 2 3 5 2 1 2 3 7 1 2 3 4 2 3 5 8
# Sa b b a b # Sb b a b # Tb a b # Sa b # Sb #T#
#Sabbab# S b b a b # T b a b # S a b # S b # T #

>>> mpcp(dominos('abbaba'))
Solving MPCP: #/#Sabbaba# a/a b/b #/# Sa/S Sb/T Ta/T Tb/S #T#/#
FOUND MATCH: 0 4 2 2 1 2 1 3 5 2 1 2 1 3 7 1 2 1 3 4 2 1 3 5 1 3 6 8
# Sa b b a b a # Sb b a b a # Tb a b a # Sa b a # Sb a # Ta #T#
#Sabbaba# S b b a b a # T b a b a # S a b a # S b a # T a # T #

>>> mpcp(dominos('abbabb'))
Solving MPCP: #/#Sabbabb# a/a b/b #/# Sa/S Sb/T Ta/T Tb/S #T#/#
NO MATCH FOUND (gave up after 10000 steps)

>>>


Say that L_dominos defines the language:
    L = { w in {a,b}*:  dominos(w) has a match }
As given, L is the strings with an odd number of b's.
In homework, you are asked to edit 'L_dominos' so that it
defines some other language in {a,b}*.