Chapt_12_model_time.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 13: Modeling Running Time\n",
    "\n",
    "Code related to [Chapter 13: Modeling Running Time](https://introtcs.org/public/lec_11_running_time.html) in __Introduction to Theoretical Computer Science__ by Boaz Barak. [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/boazbk/tcscode/blob/master/Chapt_12_model_time.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!wget https://raw.githubusercontent.com/boazbk/tcscode/master/Utilities.ipynb\n",
    "!pip install schemdraw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# utility code \n",
    "%run \"Utilities.ipynb\"\n",
    "from IPython.display import clear_output\n",
    "clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unrolling the loop\n",
    "\n",
    "Proof that $\\mathbf{P} \\subseteq \\mathbf{P_{/poly}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unroll(P,n,T, index = lambda t:t):\n",
    "    Q = '''temp = NAND(X[0],X[0])'\n",
    "one= NAND(temp,X[0])\n",
    "zero = NAND(one,one)\n",
    "'''\n",
    "    P = \"\\n\".join([l in P.split('\\n') if l[:len('Y_nonblank')] != 'Y_nonblank']) + \"\\n\"\n",
    "    defined = [\"one\",\"temp\",\"zero\"] + [f\"X[{i}]\" for i in range(n)]\n",
    "    for t in range(T):\n",
    "        for line in P.split('\\n')\n",
    "            line =  line.replace('Xvalid[i]','one' if index(t)<n else 'zero').replace('[i]',f'[{index(t)}]')\n",
    "            \n",
    "    return Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "xorline = r'''\n",
    "temp_0 = NAND(X[0],X[0])\n",
    "one = NAND(X[0],temp_0)\n",
    "Y[0] = NAND(one,one)\n",
    "temp_2 = NAND(X[0],Y[0])\n",
    "temp_3 = NAND(X[0],temp_2)\n",
    "temp_4 = NAND(Y[0],temp_2)\n",
    "Y[0] = NAND(temp_3,temp_4)\n",
    "temp_2 = NAND(X[1],Y[0])\n",
    "temp_3 = NAND(X[1],temp_2)\n",
    "temp_4 = NAND(Y[0],temp_2)\n",
    "Y[0] = NAND(temp_3,temp_4)\n",
    "temp_2 = NAND(X[2],Y[0])\n",
    "temp_3 = NAND(X[2],temp_2)\n",
    "temp_4 = NAND(Y[0],temp_2)\n",
    "Y[0] = NAND(temp_3,temp_4)\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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       "   </g>\r\n",
       "  </g>\r\n",
       " </g>\r\n",
       " <defs>\r\n",
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       "   <rect height=\"295.554515\" width=\"592.095536\" x=\"7.2\" y=\"7.2\"/>\r\n",
       "  </clipPath>\r\n",
       " </defs>\r\n",
       "</svg>\r\n"
      ],
      "text/plain": [
       "<Figure size 657.884x381.361 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "C=circuit(xorline)\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C(1,0,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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