{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c54c43ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "import spot, buddy\n",
    "spot.setup()\n",
    "from spot.jupyter import display_inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0576f64a",
   "metadata": {},
   "source": [
    "Additional testing for synthesis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e25b7989",
   "metadata": {},
   "source": [
    "Testing the different methods to solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "007107a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "si = spot.synthesis_info()\n",
    "si.s = spot.synthesis_info.algo_LAR # Use LAR algorithm\n",
    "game = spot.ltl_to_game(\"G((F(i0) && F(i1))->(G(i1<->(X(o0)))))\", [\"o0\"], si)\n",
    "spot.solve_game(game)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a7859f19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HOA: v1\n",
      "States: 21\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "spot-state-player: 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 2\n",
      "[!0&1] 4\n",
      "[0&!1] 6\n",
      "[0&1] 8\n",
      "State: 1\n",
      "[0&1] 13\n",
      "[0&!1] 18\n",
      "[!0&1] 19\n",
      "[!0&!1] 20\n",
      "State: 2\n",
      "[t] 1\n",
      "State: 3\n",
      "[0] 13\n",
      "[!0] 19\n",
      "State: 4\n",
      "[t] 3\n",
      "State: 5\n",
      "[!0&1] 10\n",
      "[0&1] 11\n",
      "[!0&!1] 15\n",
      "[0&!1] 16\n",
      "State: 6\n",
      "[t] 5\n",
      "State: 7\n",
      "[!0] 10\n",
      "[0] 11\n",
      "State: 8\n",
      "[t] 7\n",
      "State: 9\n",
      "[!0] 12\n",
      "[0] 13\n",
      "State: 10\n",
      "[2] 9\n",
      "State: 11\n",
      "[2] 7\n",
      "State: 12\n",
      "[!2] 9\n",
      "State: 13\n",
      "[!2] 7\n",
      "State: 14\n",
      "[!0&1] 12\n",
      "[0&1] 13\n",
      "[!0&!1] 17\n",
      "[0&!1] 18\n",
      "State: 15\n",
      "[2] 14\n",
      "State: 16\n",
      "[2] 5\n",
      "State: 17\n",
      "[!2] 14\n",
      "State: 18\n",
      "[!2] 5\n",
      "State: 19\n",
      "[!2] 3\n",
      "State: 20\n",
      "[!2] 1\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 7\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 1\n",
      "[!0&1] 2\n",
      "[0&!1] 3\n",
      "[0&1] 4\n",
      "State: 1\n",
      "[0&1&!2] 4\n",
      "[0&!1&!2] 3\n",
      "[!0&1&!2] 2\n",
      "[!0&!1&!2] 1\n",
      "State: 2\n",
      "[0&!2] 4\n",
      "[!0&!2] 2\n",
      "State: 3\n",
      "[!0&1&2] 5\n",
      "[0&1&2] 4\n",
      "[!0&!1&2] 6\n",
      "[0&!1&2] 3\n",
      "State: 4\n",
      "[!0&2] 5\n",
      "[0&2] 4\n",
      "State: 5\n",
      "[!0&!2] 5\n",
      "[0&!2] 4\n",
      "State: 6\n",
      "[!0&1&!2] 5\n",
      "[0&1&!2] 4\n",
      "[!0&!1&!2] 6\n",
      "[0&!1&!2] 3\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 21\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "spot-state-player: 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 2\n",
      "[!0&1] 4\n",
      "[0&!1] 6\n",
      "[0&1] 8\n",
      "State: 1\n",
      "[0&1] 13\n",
      "[0&!1] 18\n",
      "[!0&1] 19\n",
      "[!0&!1] 20\n",
      "State: 2\n",
      "[t] 1\n",
      "State: 3\n",
      "[0] 13\n",
      "[!0] 19\n",
      "State: 4\n",
      "[t] 3\n",
      "State: 5\n",
      "[!0&1] 10\n",
      "[0&1] 11\n",
      "[!0&!1] 15\n",
      "[0&!1] 16\n",
      "State: 6\n",
      "[t] 5\n",
      "State: 7\n",
      "[!0] 10\n",
      "[0] 11\n",
      "State: 8\n",
      "[t] 7\n",
      "State: 9\n",
      "[!0] 12\n",
      "[0] 13\n",
      "State: 10\n",
      "[2] 9\n",
      "State: 11\n",
      "[2] 7\n",
      "State: 12\n",
      "[!2] 9\n",
      "State: 13\n",
      "[!2] 7\n",
      "State: 14\n",
      "[!0&1] 12\n",
      "[0&1] 13\n",
      "[!0&!1] 17\n",
      "[0&!1] 18\n",
      "State: 15\n",
      "[2] 14\n",
      "State: 16\n",
      "[2] 5\n",
      "State: 17\n",
      "[!2] 14\n",
      "State: 18\n",
      "[!2] 5\n",
      "State: 19\n",
      "[!2] 3\n",
      "State: 20\n",
      "[!2] 1\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 21\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "spot-state-player: 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 2\n",
      "[!0&1] 4\n",
      "[0&!1] 6\n",
      "[0&1] 8\n",
      "State: 1\n",
      "[0&1] 13\n",
      "[0&!1] 18\n",
      "[!0&1] 19\n",
      "[!0&!1] 20\n",
      "State: 2\n",
      "[t] 1\n",
      "State: 3\n",
      "[0] 13\n",
      "[!0] 19\n",
      "State: 4\n",
      "[t] 3\n",
      "State: 5\n",
      "[!0&1] 10\n",
      "[0&1] 11\n",
      "[!0&!1] 15\n",
      "[0&!1] 16\n",
      "State: 6\n",
      "[t] 5\n",
      "State: 7\n",
      "[!0] 10\n",
      "[0] 11\n",
      "State: 8\n",
      "[t] 7\n",
      "State: 9\n",
      "[!0] 12\n",
      "[0] 13\n",
      "State: 10\n",
      "[2] 9\n",
      "State: 11\n",
      "[2] 7\n",
      "State: 12\n",
      "[!2] 9\n",
      "State: 13\n",
      "[!2] 7\n",
      "State: 14\n",
      "[!0&1] 12\n",
      "[0&1] 13\n",
      "[!0&!1] 17\n",
      "[0&!1] 18\n",
      "State: 15\n",
      "[2] 14\n",
      "State: 16\n",
      "[2] 5\n",
      "State: 17\n",
      "[!2] 14\n",
      "State: 18\n",
      "[!2] 5\n",
      "State: 19\n",
      "[!2] 3\n",
      "State: 20\n",
      "[!2] 1\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 7\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 1\n",
      "[!0&1] 2\n",
      "[0&!1] 3\n",
      "[0&1] 4\n",
      "State: 1\n",
      "[0&1&!2] 4\n",
      "[0&!1&!2] 3\n",
      "[!0&1&!2] 2\n",
      "[!0&!1&!2] 1\n",
      "State: 2\n",
      "[0&!2] 4\n",
      "[!0&!2] 2\n",
      "State: 3\n",
      "[!0&1&2] 5\n",
      "[0&1&2] 4\n",
      "[!0&!1&2] 6\n",
      "[0&!1&2] 3\n",
      "State: 4\n",
      "[!0&2] 5\n",
      "[0&2] 4\n",
      "State: 5\n",
      "[!0&!2] 5\n",
      "[0&!2] 4\n",
      "State: 6\n",
      "[!0&1&!2] 5\n",
      "[0&1&!2] 4\n",
      "[!0&!1&!2] 6\n",
      "[0&!1&!2] 3\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 21\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "spot-state-player: 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 2\n",
      "[!0&1] 4\n",
      "[0&!1] 6\n",
      "[0&1] 8\n",
      "State: 1\n",
      "[0&1] 13\n",
      "[0&!1] 18\n",
      "[!0&1] 19\n",
      "[!0&!1] 20\n",
      "State: 2\n",
      "[t] 1\n",
      "State: 3\n",
      "[0] 13\n",
      "[!0] 19\n",
      "State: 4\n",
      "[t] 3\n",
      "State: 5\n",
      "[!0&1] 10\n",
      "[0&1] 11\n",
      "[!0&!1] 15\n",
      "[0&!1] 16\n",
      "State: 6\n",
      "[t] 5\n",
      "State: 7\n",
      "[!0] 10\n",
      "[0] 11\n",
      "State: 8\n",
      "[t] 7\n",
      "State: 9\n",
      "[!0] 12\n",
      "[0] 13\n",
      "State: 10\n",
      "[2] 9\n",
      "State: 11\n",
      "[2] 7\n",
      "State: 12\n",
      "[!2] 9\n",
      "State: 13\n",
      "[!2] 7\n",
      "State: 14\n",
      "[!0&1] 12\n",
      "[0&1] 13\n",
      "[!0&!1] 17\n",
      "[0&!1] 18\n",
      "State: 15\n",
      "[2] 14\n",
      "State: 16\n",
      "[2] 5\n",
      "State: 17\n",
      "[!2] 14\n",
      "State: 18\n",
      "[!2] 5\n",
      "State: 19\n",
      "[!2] 3\n",
      "State: 20\n",
      "[!2] 1\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 21\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "spot-state-player: 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 2\n",
      "[!0&1] 4\n",
      "[0&!1] 6\n",
      "[0&1] 8\n",
      "State: 1\n",
      "[0&1] 13\n",
      "[0&!1] 18\n",
      "[!0&1] 19\n",
      "[!0&!1] 20\n",
      "State: 2\n",
      "[t] 1\n",
      "State: 3\n",
      "[0] 13\n",
      "[!0] 19\n",
      "State: 4\n",
      "[t] 3\n",
      "State: 5\n",
      "[!0&1] 10\n",
      "[0&1] 11\n",
      "[!0&!1] 15\n",
      "[0&!1] 16\n",
      "State: 6\n",
      "[t] 5\n",
      "State: 7\n",
      "[!0] 10\n",
      "[0] 11\n",
      "State: 8\n",
      "[t] 7\n",
      "State: 9\n",
      "[!0] 12\n",
      "[0] 13\n",
      "State: 10\n",
      "[2] 9\n",
      "State: 11\n",
      "[2] 7\n",
      "State: 12\n",
      "[!2] 9\n",
      "State: 13\n",
      "[!2] 7\n",
      "State: 14\n",
      "[!0&1] 12\n",
      "[0&1] 13\n",
      "[!0&!1] 17\n",
      "[0&!1] 18\n",
      "State: 15\n",
      "[2] 14\n",
      "State: 16\n",
      "[2] 5\n",
      "State: 17\n",
      "[!2] 14\n",
      "State: 18\n",
      "[!2] 5\n",
      "State: 19\n",
      "[!2] 3\n",
      "State: 20\n",
      "[!2] 1\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 7\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 1\n",
      "[!0&1] 2\n",
      "[0&!1] 3\n",
      "[0&1] 4\n",
      "State: 1\n",
      "[0&1&!2] 4\n",
      "[0&!1&!2] 3\n",
      "[!0&1&!2] 2\n",
      "[!0&!1&!2] 1\n",
      "State: 2\n",
      "[0&!2] 4\n",
      "[!0&!2] 2\n",
      "State: 3\n",
      "[!0&1&2] 5\n",
      "[0&1&2] 4\n",
      "[!0&!1&2] 6\n",
      "[0&!1&2] 3\n",
      "State: 4\n",
      "[!0&2] 5\n",
      "[0&2] 4\n",
      "State: 5\n",
      "[!0&!2] 5\n",
      "[0&!2] 4\n",
      "State: 6\n",
      "[!0&1&!2] 5\n",
      "[0&1&!2] 4\n",
      "[!0&!1&!2] 6\n",
      "[0&!1&!2] 3\n",
      "--END--\n",
      "HOA: v1\n",
      "States: 21\n",
      "Start: 0\n",
      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
      "acc-name: all\n",
      "Acceptance: 0 t\n",
      "properties: trans-labels explicit-labels state-acc deterministic\n",
      "spot-state-player: 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1\n",
      "controllable-AP: 2\n",
      "--BODY--\n",
      "State: 0\n",
      "[!0&!1] 2\n",
      "[!0&1] 4\n",
      "[0&!1] 6\n",
      "[0&1] 8\n",
      "State: 1\n",
      "[0&1] 13\n",
      "[0&!1] 18\n",
      "[!0&1] 19\n",
      "[!0&!1] 20\n",
      "State: 2\n",
      "[t] 1\n",
      "State: 3\n",
      "[0] 13\n",
      "[!0] 19\n",
      "State: 4\n",
      "[t] 3\n",
      "State: 5\n",
      "[!0&1] 10\n",
      "[0&1] 11\n",
      "[!0&!1] 15\n",
      "[0&!1] 16\n",
      "State: 6\n",
      "[t] 5\n",
      "State: 7\n",
      "[!0] 10\n",
      "[0] 11\n",
      "State: 8\n",
      "[t] 7\n",
      "State: 9\n",
      "[!0] 12\n",
      "[0] 13\n",
      "State: 10\n",
      "[2] 9\n",
      "State: 11\n",
      "[2] 7\n",
      "State: 12\n",
      "[!2] 9\n",
      "State: 13\n",
      "[!2] 7\n",
      "State: 14\n",
      "[!0&1] 12\n",
      "[0&1] 13\n",
      "[!0&!1] 17\n",
      "[0&!1] 18\n",
      "State: 15\n",
      "[2] 14\n",
      "State: 16\n",
      "[2] 5\n",
      "State: 17\n",
      "[!2] 14\n",
      "State: 18\n",
      "[!2] 5\n",
      "State: 19\n",
      "[!2] 3\n",
      "State: 20\n",
      "[!2] 1\n",
      "--END--\n"
     ]
    }
   ],
   "source": [
    "si.minimize_lvl = 0\n",
    "mm0 = spot.solved_game_to_mealy(game, si)\n",
    "msep0 = spot.solved_game_to_separated_mealy(game, si)\n",
    "msplit0 = spot.solved_game_to_split_mealy(game, si)\n",
    "assert(spot.is_mealy(mm0))\n",
    "assert(spot.is_separated_mealy(msep0))\n",
    "assert(spot.is_split_mealy(msplit0))\n",
    "print(mm0.to_str(\"hoa\"))\n",
    "print(msep0.to_str(\"hoa\"))\n",
    "print(msplit0.to_str(\"hoa\"))\n",
    "si.minimize_lvl = 2\n",
    "mm2 = spot.solved_game_to_mealy(game, si)\n",
    "msep2 = spot.solved_game_to_separated_mealy(game, si)\n",
    "msplit2 = spot.solved_game_to_split_mealy(game, si)\n",
    "assert(spot.is_mealy(mm2))\n",
    "assert(spot.is_separated_mealy(msep2))\n",
    "assert(spot.is_split_mealy(msplit2))\n",
    "print(mm2.to_str(\"hoa\"))\n",
    "print(msep2.to_str(\"hoa\"))\n",
    "print(msplit2.to_str(\"hoa\"))\n",
    "si.minimize_lvl = 3\n",
    "mm3 = spot.solved_game_to_mealy(game, si)\n",
    "msep3 = spot.solved_game_to_separated_mealy(game, si)\n",
    "msplit3 = spot.solved_game_to_split_mealy(game, si)\n",
    "assert(spot.is_mealy(mm3))\n",
    "assert(spot.is_separated_mealy(msep3))\n",
    "assert(spot.is_split_mealy(msplit3))\n",
    "print(mm3.to_str(\"hoa\"))\n",
    "print(msep3.to_str(\"hoa\"))\n",
    "print(msplit3.to_str(\"hoa\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fb57ac53",
   "metadata": {},
   "outputs": [],
   "source": [
    "mus0 = spot.unsplit_mealy(msplit0)\n",
    "mus2 = spot.unsplit_mealy(msplit2)\n",
    "mus3 = spot.unsplit_mealy(msplit3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "40fc65b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert(mus0.equivalent_to(msep0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f6d8b29c",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert(mus2.equivalent_to(msep2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "db8d47f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert(mus3.equivalent_to(msep3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c19beeb0",
   "metadata": {},
   "source": [
    "Testing related to #495"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3736cd1b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, t)\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
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     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = spot.translate(\"i<->o\", \"parity\")\n",
    "print(a.acc())\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "da6a7802",
   "metadata": {},
   "outputs": [
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     "metadata": {},
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    "a"
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   "id": "987219a4",
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    "a_s = spot.split_2step(a, True)\n",
    "print(a.acc())\n",
    "a_s"
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       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc3486c0> >"
      ]
     },
     "execution_count": 11,
     "metadata": {},
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   "source": [
    "a = spot.make_twa_graph()\n",
    "a.acc().set_acceptance(spot.acc_code.t())\n",
    "i0 = buddy.bdd_ithvar(a.register_ap('i0'))\n",
    "i1 = buddy.bdd_ithvar(a.register_ap('i1'))\n",
    "o = buddy.bdd_ithvar(a.register_ap('o'))\n",
    "tt = buddy.bddtrue\n",
    "a0 = spot.mark_t([0])\n",
    "a.new_states(3)\n",
    "a.new_edge(0,1,i0&o,a0)\n",
    "a.new_edge(1,0,i1,a0)\n",
    "a.new_edge(1,2,i0&(buddy.bdd_not(o)),a0)\n",
    "spot.set_synthesis_outputs(a, o)\n",
    "a"
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     "text": [
      "(0, t)\n"
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   "source": [
    "a_snc = spot.split_2step(a, False)\n",
    "print(a_snc.acc())\n",
    "a_snc"
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   "cell_type": "code",
   "execution_count": 13,
   "id": "05b4a138",
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       "<title>4&#45;&gt;3</title>\n",
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       "<text text-anchor=\"start\" x=\"628\" y=\"-146.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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       "</svg>\n"
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      "text/plain": [
       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc345e40> >"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_s = spot.split_2step(a, True)\n",
    "print(a_s.acc())\n",
    "a_s"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ee90b2a",
   "metadata": {},
   "source": [
    "## A problematic case for merge\n",
    "\n",
    "This is an example graph for which the self-loop optimisation in merge_states does not work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "06b20a8c",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc364a20> >"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aut = spot.make_twa_graph()\n",
    "aut.set_buchi()\n",
    "aut.new_states(5)\n",
    "\n",
    "a = buddy.bdd_ithvar(aut.register_ap(\"a\"))\n",
    "b = buddy.bdd_ithvar(aut.register_ap(\"b\"))\n",
    "c = buddy.bdd_ithvar(aut.register_ap(\"c\"))\n",
    "x = buddy.bdd_ithvar(aut.register_ap(\"x\"))\n",
    "\n",
    "\n",
    "aut.new_edge(0, 1, buddy.bddtrue)\n",
    "aut.new_edge(0, 4, buddy.bddtrue)\n",
    "\n",
    "# OK, edge conditions ensure \"correct\" ordering\n",
    "aut.new_edge(1, 1, a)\n",
    "aut.new_edge(1, 2, b)\n",
    "aut.new_edge(1, 3, c)\n",
    "\n",
    "aut.new_edge(4, 4, a)\n",
    "aut.new_edge(4, 2, b)\n",
    "aut.new_edge(4, 3, c)\n",
    "\n",
    "aut.new_edge(2, 2, x)\n",
    "aut.new_edge(3, 3, buddy.bdd_not(x))\n",
    "\n",
    "aut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8a2f2e4d",
   "metadata": {},
   "outputs": [
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     "metadata": {},
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   "source": [
    "aut.merge_states()\n",
    "aut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b40f8ce7",
   "metadata": {},
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     },
     "execution_count": 16,
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   "source": [
    "aut = spot.make_twa_graph()\n",
    "aut.set_buchi()\n",
    "aut.new_states(5)\n",
    "\n",
    "a = buddy.bdd_ithvar(aut.register_ap(\"a\"))\n",
    "b = buddy.bdd_ithvar(aut.register_ap(\"b\"))\n",
    "c = buddy.bdd_ithvar(aut.register_ap(\"c\"))\n",
    "x = buddy.bdd_ithvar(aut.register_ap(\"x\"))\n",
    "\n",
    "\n",
    "aut.new_edge(0, 1, buddy.bddtrue)\n",
    "aut.new_edge(0, 4, buddy.bddtrue)\n",
    "\n",
    "# Not OK, all edge equal -> sorted by destination\n",
    "# Fails to merge\n",
    "aut.new_edge(1, 1, a)\n",
    "aut.new_edge(1, 2, a)\n",
    "aut.new_edge(1, 3, a)\n",
    "\n",
    "aut.new_edge(4, 4, a)\n",
    "aut.new_edge(4, 2, a)\n",
    "aut.new_edge(4, 3, a)\n",
    "\n",
    "aut.new_edge(2, 2, x)\n",
    "aut.new_edge(3, 3, buddy.bdd_not(x))\n",
    "\n",
    "aut"
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  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1f596284",
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   "outputs": [
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     "execution_count": 18,
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   "source": [
    "aut = spot.make_twa_graph()\n",
    "aut.set_buchi()\n",
    "aut.new_states(8)\n",
    "\n",
    "a = buddy.bdd_ithvar(aut.register_ap(\"a\"))\n",
    "b = buddy.bdd_ithvar(aut.register_ap(\"b\"))\n",
    "c = buddy.bdd_ithvar(aut.register_ap(\"c\"))\n",
    "x = buddy.bdd_ithvar(aut.register_ap(\"x\"))\n",
    "\n",
    "\n",
    "aut.new_edge(0, 1, buddy.bddtrue)\n",
    "aut.new_edge(0, 4, buddy.bddtrue)\n",
    "\n",
    "aut.new_edge(1, 1, a)\n",
    "aut.new_edge(1, 2, b)\n",
    "aut.new_edge(1, 3, c)\n",
    "\n",
    "aut.new_edge(4, 4, a)\n",
    "aut.new_edge(4, 2, b)\n",
    "aut.new_edge(4, 3, c)\n",
    "\n",
    "aut.new_edge(2, 2, x)\n",
    "aut.new_edge(3, 3, buddy.bdd_not(x))\n",
    "\n",
    "aut.new_edge(5, 1, a)\n",
    "aut.new_edge(5, 2, b)\n",
    "aut.new_edge(5, 3, c)\n",
    "\n",
    "display(aut.show_storage())\n",
    "aut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d4e09261",
   "metadata": {},
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    "## Splitting can inhibit merging\n",
    "\n",
    "In split automata, no self-loops exist.\n",
    "Therefore states that can be merged pre-split can not be merged in a split automaton"
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      "text/plain": [
       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc3910f0> >"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aut = spot.make_twa_graph()\n",
    "aut.set_buchi()\n",
    "aut.new_states(5)\n",
    "\n",
    "a = buddy.bdd_ithvar(aut.register_ap(\"a\"))\n",
    "b = buddy.bdd_ithvar(aut.register_ap(\"b\"))\n",
    "c = buddy.bdd_ithvar(aut.register_ap(\"c\"))\n",
    "x = buddy.bdd_ithvar(aut.register_ap(\"x\"))\n",
    "\n",
    "\n",
    "aut.new_edge(0, 1, buddy.bddtrue)\n",
    "aut.new_edge(0, 4, buddy.bddtrue)\n",
    "\n",
    "aut.new_edge(1, 1, a)\n",
    "aut.new_edge(1, 2, b)\n",
    "aut.new_edge(1, 3, c)\n",
    "\n",
    "aut.new_edge(4, 4, a)\n",
    "aut.new_edge(4, 2, b)\n",
    "aut.new_edge(4, 3, c)\n",
    "\n",
    "aut.new_edge(2, 2, x)\n",
    "aut.new_edge(3, 3, buddy.bdd_not(x))\n",
    "\n",
    "display(aut)\n",
    "\n",
    "aut = spot.split_2step(aut, x, False)\n",
    "\n",
    "display(aut.show_storage())\n",
    "aut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2009f279",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
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     },
     "execution_count": 21,
     "metadata": {},
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    }
   ],
   "source": [
    "print(aut.merge_states())\n",
    "aut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "17c8d6bc",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc35a9c0> >"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Merging possible even in split case\n",
    "aut = spot.make_twa_graph()\n",
    "aut.set_buchi()\n",
    "aut.new_states(5)\n",
    "\n",
    "a = buddy.bdd_ithvar(aut.register_ap(\"a\"))\n",
    "b = buddy.bdd_ithvar(aut.register_ap(\"b\"))\n",
    "c = buddy.bdd_ithvar(aut.register_ap(\"c\"))\n",
    "x = buddy.bdd_ithvar(aut.register_ap(\"x\"))\n",
    "\n",
    "\n",
    "aut.new_edge(0, 1, buddy.bddtrue)\n",
    "aut.new_edge(0, 4, buddy.bddtrue)\n",
    "\n",
    "aut.new_edge(1, 2, b)\n",
    "aut.new_edge(1, 3, c)\n",
    "\n",
    "aut.new_edge(4, 2, b)\n",
    "aut.new_edge(4, 3, c)\n",
    "\n",
    "aut.new_edge(2, 2, x)\n",
    "aut.new_edge(3, 3, buddy.bdd_not(x))\n",
    "\n",
    "display(aut)\n",
    "\n",
    "aut = spot.split_2step(aut, x, False)\n",
    "\n",
    "display(aut.show_storage())\n",
    "aut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b3e90235",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
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       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc35a9c0> >"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(aut.merge_states())\n",
    "aut"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05785bb1",
   "metadata": {},
   "source": [
    "Fail case for alternate_players"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "df4aa681",
   "metadata": {},
   "outputs": [
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       "<!-- 3&#45;&gt;2 -->\n",
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      ],
      "text/plain": [
       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc3646c0> >"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aut = spot.make_twa_graph()\n",
    "aut.set_buchi()\n",
    "i = buddy.bdd_ithvar(aut.register_ap(\"i\"))\n",
    "o = buddy.bdd_ithvar(aut.register_ap(\"o\"))\n",
    "\n",
    "spot.set_synthesis_outputs(aut, o)\n",
    "\n",
    "aut.new_states(2)\n",
    "aut.new_edge(0,1,i)\n",
    "aut.new_edge(1,0,o,spot.mark_t([0]))\n",
    "display(aut)\n",
    "spot.alternate_players(aut)\n",
    "display(aut)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7efe7450",
   "metadata": {},
   "source": [
    "# Test improved aiger INF encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "31872ccc",
   "metadata": {},
   "outputs": [
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       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fbccc3911e0> >"
      ]
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     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "si = spot.synthesis_info()\n",
    "\n",
    "aut = spot.ltl_to_game(\"(a|b|c|d)->x\", [\"x\"], si)\n",
    "aut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9064bc60",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print(spot.solve_game(aut))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "303ada1e",
   "metadata": {},
   "outputs": [
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     "execution_count": 27,
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   ],
   "source": [
    "ctrl = spot.solved_game_to_split_mealy(aut)\n",
    "ctrl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9874a530",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<spot.aig; proxy of <Swig Object of type 'std::shared_ptr< spot::aig > *' at 0x7fbccc33adb0> >"
      ]
     },
     "execution_count": 28,
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   "source": [
    "aig = spot.mealy_machine_to_aig(ctrl, \"ite\")\n",
    "aig"
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