notebooks/examples.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PySDD: SDD Python Wrapper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Wannes Meert (KU Leuven), Arthur Choi (UCLA) - 2019*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:21:02.329354Z",
     "start_time": "2018-03-28T12:21:02.323819Z"
    }
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "sys.path.append(os.pardir)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:21:04.187538Z",
     "start_time": "2018-03-28T12:21:04.176027Z"
    }
   },
   "outputs": [],
   "source": [
    "import pysdd\n",
    "from pysdd.sdd import Vtree, SddManager, WmcManager, Fnf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:21:04.417026Z",
     "start_time": "2018-03-28T12:21:04.401482Z"
    }
   },
   "outputs": [],
   "source": [
    "from array import array\n",
    "from pathlib import Path\n",
    "from graphviz import Source\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vtree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:19:46.493163Z",
     "start_time": "2018-03-18T17:19:46.489352Z"
    }
   },
   "outputs": [],
   "source": [
    "vtree = Vtree(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:19:46.501427Z",
     "start_time": "2018-03-18T17:19:46.495863Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variable count: 4\n"
     ]
    }
   ],
   "source": [
    "print(\"variable count: {}\".format(vtree.var_count()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:19:47.232085Z",
     "start_time": "2018-03-18T17:19:46.503958Z"
    }
   },
   "outputs": [
    {
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     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Source(vtree.dot())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SDD Manager"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ask for documentation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:19:47.244926Z",
     "start_time": "2018-03-18T17:19:47.235402Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mInit signature:\u001b[0m \u001b[0mSddManager\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m/\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m     \n",
       "SddManager(long var_count=1, bool auto_gc_and_minimize=False, Vtree vtree=None)\n",
       "Creates a new SDD manager, either given a vtree or using a balanced vtree over the given number of variables.\n",
       "\n",
       "    :param var_count: Number of variables\n",
       "    :param auto_gc_and_minimize: Automatic garbage collection\n",
       "        Automatic garbage collection and automatic SDD minimization are activated in the created manager when\n",
       "        auto gc and minimize is not 0.\n",
       "    :param vtree: The manager copies the input vtree. Any manipulations performed by\n",
       "        the manager are done on its own copy, and does not affect the input vtree.\n",
       "\n",
       "    The creation and manipulation of SDDs are maintained by an SDD manager.\n",
       "    The use of an SDD manager is analogous to the use of managers in OBDD packages\n",
       "    such as CUDD [10]. For a discussion on the design and implementation of such\n",
       "    systems, see [7].\n",
       "\n",
       "    To declare an SDD manager, one provides an initial vtree. By declaring an\n",
       "    initial vtree, we also declare an initial number of variables. See the section\n",
       "    on creating vtrees, for a few ways to specify an initial vtree.\n",
       "\n",
       "    Note that variables are referred to by an index. If there are n variables\n",
       "    in an SDD manager, then the variables are referred to as 1, . . . , n. Literals\n",
       "    are referred to by signed indices. For example, given the i-th variable, we\n",
       "    refer to its positive literal by i and its negative literal by −i.\n",
       "    \n",
       "\u001b[0;31mFile:\u001b[0m           ~/Projects/Research/2017-PySDD/pysdd2_repo/pysdd/sdd.cpython-310-darwin.so\n",
       "\u001b[0;31mType:\u001b[0m           type\n",
       "\u001b[0;31mSubclasses:\u001b[0m     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SddManager?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create new manager with four variables A, B, C, and D. The variables can be requested using the `literal` function or the `var` property:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:21:15.830058Z",
     "start_time": "2018-03-28T12:21:15.808704Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SddNode(name=1,id=3)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mgr = SddManager(var_count=4)\n",
    "a = mgr.literal(1)\n",
    "b, c, d = mgr.vars[2:5]\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A negative literal can be obtained by negating a positive literal or negating the numeric representation of a literal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:21:22.607588Z",
     "start_time": "2018-03-28T12:21:22.601408Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('SddNode(name=-1,id=4)', 'SddNode(name=-1,id=4)')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(-mgr.literal(1)), str(mgr.literal(-1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most methods that require a literal accept either integer numbers or sdd nodes objects to methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:19:47.275386Z",
     "start_time": "2018-03-18T17:19:47.269972Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mgr.is_var_used(-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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       "0"
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     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mgr.is_var_used(-b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the formula $(A \\land B) \\lor (C \\land D)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:21:27.872306Z",
     "start_time": "2018-03-28T12:21:27.865428Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'SddNode(name=Decision,id=12)'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fab   = mgr.conjoin(a, b)\n",
    "fcd   = mgr.conjoin(c, d)\n",
    "fabcd = mgr.disjoin(fab, fcd)\n",
    "str(fcd)"
   ]
  },
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   "execution_count": 20,
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    "Use shorter syntax by mapping `&`/`|` to `*`/`+`:"
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     "start_time": "2018-03-28T12:21:37.450738Z"
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   "source": [
    "mgr = SddManager(var_count=4)\n",
    "a, b, c, d = mgr.vars"
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     "text": [
      " node size      : 2\n",
      " sdd size       : 8\n",
      " sdd node count : 4\n"
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fabcd = (a & b) | (c & d)\n",
    "print(f\" node size      : {fabcd.node_size()}\")\n",
    "print(f\" sdd size       : {fabcd.size()}\")\n",
    "print(f\" sdd node count : {fabcd.count()}\")\n",
    "Source(fabcd.dot())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which can be minimized using:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:19:48.684091Z",
     "start_time": "2018-03-18T17:19:48.674072Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " node size      : 2\n",
      " sdd size       : 6\n",
      " sdd node count : 3\n"
     ]
    }
   ],
   "source": [
    "fabcd.ref()\n",
    "mgr.minimize_limited()\n",
    "print(f\" node size      : {fabcd.node_size()}\")\n",
    "print(f\" sdd size       : {fabcd.size()}\")\n",
    "print(f\" sdd node count : {fabcd.count()}\")\n",
    "Source(fabcd.dot())\n",
    "fabcd.deref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or we can minimize cardinality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:19:49.377654Z",
     "start_time": "2018-03-18T17:19:48.687019Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " node size      : 2\n",
      " sdd size       : 10\n",
      " sdd node count : 5\n"
     ]
    },
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   ],
   "source": [
    "fabcd = mgr.global_minimize_cardinality(fabcd)\n",
    "print(f\" node size      : {fabcd.node_size()}\")\n",
    "print(f\" sdd size       : {fabcd.size()}\")\n",
    "print(f\" sdd node count : {fabcd.count()}\")\n",
    "Source(fabcd.dot())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: API documentation example 1"
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   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:22:09.812655Z",
     "start_time": "2018-03-28T12:22:09.806298Z"
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   "outputs": [],
   "source": [
    "var_count = 4\n",
    "var_order = array(\"l\", [2,1,4,3])\n",
    "tree_type = \"balanced\""
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    "vtree = Vtree(var_count=var_count, var_order=var_order, vtree_type=tree_type)\n",
    "Source(vtree.dot())"
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    "mgr = SddManager(vtree=vtree)"
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    "construct a formula $(A \\land B) \\lor (B \\land C) \\lor (C \\land D)$"
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    "f_a, f_b, f_c, f_d = mgr.vars"
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    "beta  = f_a & f_b\n",
    "alpha = alpha | beta\n",
    "beta  = f_b & f_c"
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    "Source(alpha.dot())"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Load from CNF file"
   ]
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  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:20:22.250402Z",
     "start_time": "2018-03-18T17:20:22.241338Z"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read CNF: vars=6 clauses=3\n"
     ]
    }
   ],
   "source": [
    "cnf_str = \"\"\"p cnf 6 3\n",
    "1 4 0\n",
    "-1 2 5 0\n",
    "-1 -2 3 6 0\n",
    "\"\"\"\n",
    "mgr, f = SddManager.from_cnf_string(cnf_str)"
   ]
  },
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   "cell_type": "markdown",
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    "#### Change the SDD after loading the CNF"
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   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
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     "text": [
      "Var count before: 6\n",
      "Var count after:  8\n"
     ]
    }
   ],
   "source": [
    "print(f\"Var count before: {mgr.var_count()}\")\n",
    "mgr.add_var_after_last()\n",
    "mgr.add_var_after_last()\n",
    "print(f\"Var count after:  {mgr.var_count()}\")"
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     "execution_count": 38,
     "metadata": {},
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   ],
   "source": [
    "g = mgr.literal(7)\n",
    "h = mgr.literal(8)\n",
    "\n",
    "fp = g & h\n",
    "Source(fp.dot())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:20:55.293979Z",
     "start_time": "2018-03-18T17:20:54.628961Z"
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     "execution_count": 39,
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   "source": [
    "fpp = f | fp\n",
    "Source(fpp.dot())"
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   "cell_type": "markdown",
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   "source": [
    "### Example: API documentation example 6"
   ]
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   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:26:24.954415Z",
     "start_time": "2018-03-18T17:26:24.948234Z"
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   "outputs": [],
   "source": [
    "vtree_path = Path(\"../examples/input/opt-swap.vtree\")\n",
    "if not vtree_path.exists():\n",
    "    print(f\"File not found: {vtree_path}\")\n",
    "sdd_path = Path(\"../examples/input/opt-swap.sdd\")\n",
    "if not sdd_path.exists():\n",
    "    print(f\"File not found: {sdd_path}\")"
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    "ExecuteTime": {
     "end_time": "2018-03-18T17:26:30.589339Z",
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      ],
      "text/plain": [
       "<graphviz.sources.Source at 0x106a8d750>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vtree = Vtree(filename=bytes(vtree_path))    \n",
    "Source(vtree.dot())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:27:18.660542Z",
     "start_time": "2018-03-18T17:27:18.654184Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size alpha: 116\n"
     ]
    }
   ],
   "source": [
    "mgr = SddManager.from_vtree(vtree)\n",
    "alpha = mgr.read_sdd_file(bytes(sdd_path))\n",
    "print(f\"Size alpha: {alpha.size()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:27:21.358154Z",
     "start_time": "2018-03-18T17:27:20.669253Z"
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   "outputs": [
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    "Source(alpha.dot())"
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     "end_time": "2018-03-18T17:27:24.097197Z",
     "start_time": "2018-03-18T17:27:24.093754Z"
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   "source": [
    "alpha.ref()"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Minimize the SDD"
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  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
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     "end_time": "2018-03-18T17:27:28.768281Z",
     "start_time": "2018-03-18T17:27:28.754490Z"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size alpha: 8\n"
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   "source": [
    "mgr.minimize()\n",
    "print(f\"Size alpha: {alpha.size()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
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    "ExecuteTime": {
     "end_time": "2018-03-18T17:27:31.969918Z",
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    "Source(alpha.dot())"
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   "metadata": {},
   "source": [
    "Show the new vtree after minimization."
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  },
  {
   "cell_type": "code",
   "execution_count": 47,
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    "ExecuteTime": {
     "end_time": "2018-03-18T17:27:40.555101Z",
     "start_time": "2018-03-18T17:27:39.902614Z"
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    "beta = alpha * (mgr.literal(4) + mgr.literal(5))\n",
    "print(f\"Size beta: {beta.size()}\")"
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    "Source(beta.dot())"
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    "Perform minimization again on new SDD"
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   "cell_type": "code",
   "execution_count": 50,
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    "ExecuteTime": {
     "end_time": "2018-03-18T17:27:54.234484Z",
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    "beta.ref()"
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     "text": [
      "Size: 21\n"
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    "mgr.minimize()\n",
    "print(f\"Size: {beta.size()}\")"
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     "end_time": "2018-03-18T17:27:56.545888Z",
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       "<graphviz.sources.Source at 0x10685d9c0>"
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     },
     "execution_count": 52,
     "metadata": {},
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   ],
   "source": [
    "Source(beta.dot())"
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  {
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   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-18T17:27:56.552970Z",
     "start_time": "2018-03-18T17:27:56.549307Z"
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   "source": [
    "beta.deref()"
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  {
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     "end_time": "2017-09-22T08:43:00.203500Z",
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    "### Example: WMC"
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    "ExecuteTime": {
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    "a, b, c, d = mgr.vars\n",
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     "start_time": "2018-03-28T12:24:15.095135Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 1.0)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wmc = f.wmc(log_mode=True)\n",
    "math.exp(wmc.literal_weight(a)), math.exp(wmc.literal_weight(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:24:22.947781Z",
     "start_time": "2018-03-28T12:24:22.942739Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of models: 7\n"
     ]
    }
   ],
   "source": [
    "w = wmc.propagate()\n",
    "print(f\"Number of models: {round(math.exp(w))}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:24:35.595397Z",
     "start_time": "2018-03-28T12:24:35.591666Z"
    }
   },
   "outputs": [],
   "source": [
    "wmc.set_literal_weight(a, math.log(0.5))\n",
    "wmc.set_literal_weight(-a, math.log(0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-28T12:24:38.931087Z",
     "start_time": "2018-03-28T12:24:38.926824Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weighted model count: 3.5\n"
     ]
    }
   ],
   "source": [
    "w = wmc.propagate()\n",
    "print(f\"Weighted model count: {math.exp(w)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `PySDD` package can be downloaded from https://github.com/wannesm/PySDD/. More examples are available in the `examples` directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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