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   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'aaab', 'aaaab', 'aab', 'a', 'aaaa', 'ab', 'b'}\n",
      "['baaab', 'baa', 'baaaaa', 'baab', 'ba', 'baaaa']\n",
      "['', 'ba', 'bab', 'b', 'bba', 'bb', 'bbb']\n",
      "\n",
      "Yes because the kleen star of l1 includes all original strings in \n",
      "the language, and the string 'b', where n is zero is included in l1*, \n",
      "so it is possible for l1* to have a string where there is more bs than as. \n"
     ]
    }
   ],
   "source": [
    "l1 = ['b', 'ba']\n",
    "l2 = ['a', 'aab', 'aaaa']\n",
    "l3 = []\n",
    "for i in range(0, 5):\n",
    "    l3.append('a' * i + 'b')\n",
    "# turn all of these into sets\n",
    "l1 = set(l1)\n",
    "l2 = set(l2)\n",
    "l3 = set(l3)\n",
    "\n",
    "# l2 union l3\n",
    "l2.union(l3)\n",
    "print(l2.union(l3))\n",
    "# l1 times l2\n",
    "a = []\n",
    "for i in l1:\n",
    "    for j in l2:\n",
    "        a.append(i + j)\n",
    "print(a)\n",
    "\n",
    "# kleen star of l1 up to length 3\n",
    "a = ['']\n",
    "for i in l1:\n",
    "    a.append(i)\n",
    "    for j in l1:\n",
    "        a.append(i + j)\n",
    "        for k in l1:\n",
    "            a.append(i + j + k)\n",
    "# remove all strings of length greater than 3\n",
    "a = [x for x in a if len(x) <= 3]\n",
    "print(a)\n",
    "\n",
    "print(\"\"\"\n",
    "Yes because the kleen star of l1 includes all original strings in \n",
    "the language, and the string 'b', where n is zero is included in l1*, \n",
    "so it is possible for l1* to have a string where there is more bs than as. \n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "False\n",
      "True\n",
      "False\n",
      "True\n",
      "\n",
      "True\n",
      "False\n",
      "True\n",
      "False\n",
      "True\n",
      "False\n",
      "False\n",
      "True\n",
      "True\n",
      "False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Define a regex where a is a multiple of 2 and b is a multiple of 4 + 1\n",
    "# a = (aa)*\n",
    "# b = (bbbb)*b\n",
    "# (aa)*(bbbb)*b\n",
    "import automata.regex.regex as regex\n",
    "from automata.fa.nfa import NFA\n",
    "regex.validate('(aa)*(bbbb)*b')\n",
    "nfa = NFA.from_regex('(aa)*(bbbb)*b')\n",
    "\n",
    "print(nfa.accepts_input('aabb'))\n",
    "print(nfa.accepts_input('aabbbb'))\n",
    "print(nfa.accepts_input('aabbbbb'))\n",
    "print(nfa.accepts_input('aaabbbbbb'))\n",
    "print(nfa.accepts_input('aaaabbbbbbbbb'))\n",
    "\n",
    "print()\n",
    "# Define a regex where the number of as is 1 and the number of bs is odd\n",
    "a = \"((bb)*ba(bb)*)|((bb)*ab(bb)*)\"\n",
    "regex.validate(a)\n",
    "nfa = NFA.from_regex(a)\n",
    "\n",
    "print(nfa.accepts_input('ab'))\n",
    "print(nfa.accepts_input('bab'))\n",
    "print(nfa.accepts_input('bbab'))\n",
    "print(nfa.accepts_input('bbbab'))\n",
    "print(nfa.accepts_input('bbbabb'))\n",
    "print(nfa.accepts_input('bbbabbb'))\n",
    "print(nfa.accepts_input('abb'))\n",
    "print(nfa.accepts_input('abbb'))\n",
    "print(nfa.accepts_input('ba'))\n",
    "print(nfa.accepts_input('bba'))\n",
    "print(nfa.accepts_input('bbba'))"
   ],
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     "end_time": "2024-03-01T17:17:50.562591200Z",
     "start_time": "2024-03-01T17:17:50.534567600Z"
    }
   },
   "id": "75f2af38daefc05b",
   "execution_count": 39
  }
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