{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Automata\n",
    "\n",
    "Tensor trains can represent compactly *deterministic finite automata* and *weighted finite automata* that read a fixed number of symbols."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "torch.set_default_dtype(torch.float64)\n",
    "import tntorch as tn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For instance, `weight_mask` produces an automaton that accepts a string iff it has a certain amount of 1's:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4D TT tensor:\n",
       "\n",
       "  2   2   2   2\n",
       "  |   |   |   |\n",
       " (0) (1) (2) (3)\n",
       " / \\ / \\ / \\ / \\\n",
       "1   2   3   2   1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = tn.weight_mask(N=4, weight=2)\n",
    "m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All accepted input strings can be retrieved alphabetically via `accepted_inputs()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0, 0, 1, 1],\n",
       "        [0, 1, 0, 1],\n",
       "        [0, 1, 1, 0],\n",
       "        [1, 0, 0, 1],\n",
       "        [1, 0, 1, 0],\n",
       "        [1, 1, 0, 0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tn.accepted_inputs(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, `weight()` produces an automaton that is a little different. Instead of accepting or rejecting strings, it just counts how many 1's the string has:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.)\n",
      "tensor(1.)\n",
      "tensor(3.)\n"
     ]
    }
   ],
   "source": [
    "m = tn.weight(N=4)\n",
    "print(m[0, 0, 0, 0])\n",
    "print(m[0, 1, 0, 0])\n",
    "print(m[1, 0, 1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applications\n",
    "\n",
    "TT automata come in handy to group and sum tensor entries, which is important to obtain advanced [metrics for sensitivity analysis](sobol.ipynb). See also the tutorial on [Boolean logic with *tntorch*](logic.ipynb)."
   ]
  }
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