private static void Benchmark(List <MuFormula> list)
{
Log("Formula; LTS Size; Algorithm; Time");
double[,] results = new double[list.Count * 2, 13];
bool lastResult = false;
foreach (var formula in list)
{
int num_runs = 4;
for (int i = 2; i <= 13; i++)
{
if (i >= 11)
{
num_runs = 1;
}
var sw = Stopwatch.StartNew();
var lts = LTS.Parse("../demanding/demanding_" + i.ToString(CultureInfo.InvariantCulture) + ".aut");
Log("Read input set in {0}ms", sw.ElapsedMilliseconds);
sw.Reset(); sw.Start();
for (int j = 0; j < num_runs; j++)
{
lastResult = NaiveSolver.Solve(formula, lts, new Environment()).Contains(lts.InitialState);
}
results[list.IndexOf(formula) * 2 + 0, i - 2] = (double)sw.ElapsedMilliseconds / num_runs;
Log("{0}\t{1}\t{2}\t{3}\t{4}", list.IndexOf(formula) + 1, i, "Naive ", (double)sw.ElapsedMilliseconds / (double)num_runs, lastResult);
sw.Reset(); sw.Start();
for (int j = 0; j < num_runs; j++)
{
lastResult = EmersonLei.Solve(formula, lts, new Environment()).Contains(lts.InitialState);
}
results[list.IndexOf(formula) * 2 + 1, i - 2] = (double)sw.ElapsedMilliseconds / num_runs;
Log("{0}\t{1}\t{2}\t{3}\t{4}", list.IndexOf(formula) + 1, i, "Emerson-Lei", (double)sw.ElapsedMilliseconds / (double)num_runs, lastResult);
logWriter.Flush();
lts = null;
}
}
Log("");
Log("");
Log("Results table:");
Log("lts size\tformula1 naive\tformula1 emers\tformula2 naive\tformula2 emers\tformula3 naive\tformula3 emers\tformula4 naive\tformula4 emers");
for (int j = 0; j < results.GetLength(1); j++)
{
var sb = new StringBuilder();
sb.Append((j + 2).ToString());
for (int i = 0; i < results.GetLength(0); i++)
{
sb.AppendFormat("\t{0}", results[i, j]);
}
Log(sb.ToString());
}
}
static LTS ChessBoard(int boardSize)
{
// this procedure outputs a board of size boardSize x boardSize in aldebaran format
var lts = new LTS();
var board = new LTSState[boardSize, boardSize];
int stateNum = 0;
var initial = new LTSState(stateNum++.ToString(), lts);
lts.InitialState = initial;
for (int i = 0; i < boardSize; i++)
{
for (int j = 0; j < boardSize; j++)
{
var cell = new LTSState(stateNum++.ToString(), lts);
board[i, j] = cell;
lts.States.Add(cell);
}
}
lts.States.Add(initial);
for (int i = 0; i < boardSize; i++)
{
lts.Transitions.Add(new LTSTransition(initial, board[boardSize - 1, i], "start(" + (boardSize - 1) + "," + i + ")"));
if (i != boardSize - 1) // don't want 2 transitions to same init
{
lts.Transitions.Add(new LTSTransition(initial, board[i, boardSize - 1], "start(" + i + "," + (boardSize - 1) + ")"));
}
}
for (int y = boardSize - 1; y >= 0; y--)
{
for (int x = boardSize - 1; x >= 0; x--)
{
var thisCell = board[x, y];
// horizontal moves
for (int i = x - 1; i >= 0; i--)
{
lts.Transitions.Add(new LTSTransition(thisCell, string.Format("to({0},{1})", i, y), board[i, y]));
}
// vertical moves
for (int j = y - 1; j >= 0; j--)
{
lts.Transitions.Add(new LTSTransition(thisCell, string.Format("to({0},{1})", x, j), board[x, j]));
}
// diagonal moves
int k = x - 1, l = y - 1;
while (k >= 0 && l >= 0)
{
lts.Transitions.Add(new LTSTransition(thisCell, string.Format("to({0},{1})", k, l), board[k--, l--]));
}
}
}
return(lts);
}
private static LTSState GetState(string stateName, LTS lts) {
LTSState state;
if (lts.StatesMap.TryGetValue(stateName, out state))
return state;
else {
state = new LTSState(stateName, lts);
lts.StatesMap[stateName] = state;
lts.States.Add(state);
}
return state;
}
public static HashSet<LTSState> LFP(PredicateTransformer tau, LTS lts, Environment env)
{
var Q = Tuple.Create(new HashSet<LTSState>(), lts, env);
var QPrime = tau(Q);
while (QPrime.Item1.Count() != Q.Item1.Count()) {
Q = QPrime;
QPrime = tau(QPrime);
}
return Q.Item1;
}
public static HashSet <LTSState> GFP(PredicateTransformer tau, LTS lts, Environment env)
{
var Q = Tuple.Create(new HashSet <LTSState>(lts.States), lts, env);
var QPrime = tau(Q);
while (QPrime.Item1.Count() != Q.Item1.Count())
{
Q = QPrime;
QPrime = tau(QPrime);
}
return(Q.Item1);
}
private static void OutputResult(MuFormula f, LTS lts)
{
Log("Formula {0}", f);
Log("\t ND: {0}, AD: {1}, DAD: {2}", f.NestingDepth, f.AlternationDepth, f.DependentAlternationDepth);
var naiveSol = NaiveSolver.Solve(f, lts, new Environment());
Log("\tNAIVE: {0}", naiveSol.Contains(lts.InitialState));
var emersonLeiSol = EmersonLei.Solve(f, lts, new Environment());
Log("\tEMLEI: {0}", emersonLeiSol.Contains(lts.InitialState));
}
private static void Init(IEnumerable <Variable> variables, LTS lts, Environment env)
{
foreach (var v in variables)
{
if (v.Binder is Mu)
{
env[v] = new HashSet <LTSState>();
}
else if (v.Binder is Nu)
{
env[v] = lts.States;
}
}
}
private static LTSState GetState(string stateName, LTS lts)
{
LTSState state;
if (lts.StatesMap.TryGetValue(stateName, out state))
{
return(state);
}
else
{
state = new LTSState(stateName, lts);
lts.StatesMap[stateName] = state;
lts.States.Add(state);
}
return(state);
}
public static LTS Parse(string file)
{
// parse aldebran format
var ret = new LTS();
var sr = new StreamReader(file, Encoding.Default);
var lineRE = new Regex(@"\((\w+)\s*,\s*""([^\""]+?)""\s*,\s*(\w+)\s*\)");
string initial = string.Empty;
while (!sr.EndOfStream)
{
var line = sr.ReadLine();
if (line.StartsWith("des"))
{
var m = Regex.Match(line, @"des\s*\((\w+?),(\w+?),(\w+?)\)");
if (m.Success)
{
initial = m.Groups[1].Captures[0].Value;
}
continue;
}
var match = lineRE.Match(line);
if (match.Success)
{
string start = match.Groups[1].Captures[0].Value;
string label = match.Groups[2].Captures[0].Value;
string end = match.Groups[3].Captures[0].Value;
LTSState startState = GetState(start, ret);
LTSState endState = GetState(end, ret);
LTSTransition trans = new LTSTransition(startState, label, endState);
ret.Actions.Add(label);
ret.Transitions.Add(trans);
startState.AddOutTransition(trans);
//endState.AddInTransition(trans);
}
else
{
int i = 0;
}
}
ret.InitialState = GetState(initial, ret);
return(ret);
}
static LTS ChessBoard(int boardSize)
{
// this procedure outputs a board of size boardSize x boardSize in aldebaran format
var lts = new LTS();
var board = new LTSState[boardSize, boardSize];
int stateNum = 0;
var initial = new LTSState(stateNum++.ToString(), lts);
lts.InitialState = initial;
for (int i = 0; i < boardSize; i++) {
for (int j = 0; j < boardSize; j++) {
var cell = new LTSState(stateNum++.ToString(), lts);
board[i, j] = cell;
lts.States.Add(cell);
}
}
lts.States.Add(initial);
for (int i = 0; i < boardSize; i++) {
lts.Transitions.Add(new LTSTransition(initial, board[boardSize - 1, i], "start(" + (boardSize - 1) + "," + i + ")"));
if (i != boardSize - 1) // don't want 2 transitions to same init
lts.Transitions.Add(new LTSTransition(initial, board[i, boardSize - 1], "start(" + i + "," + (boardSize - 1) + ")"));
}
for (int y = boardSize - 1; y >= 0; y--) {
for (int x = boardSize - 1; x >= 0; x--) {
var thisCell = board[x, y];
// horizontal moves
for (int i = x - 1; i >= 0; i--)
lts.Transitions.Add(new LTSTransition(thisCell, string.Format("to({0},{1})", i, y), board[i, y]));
// vertical moves
for (int j = y - 1; j >= 0; j--)
lts.Transitions.Add(new LTSTransition(thisCell, string.Format("to({0},{1})", x, j), board[x, j]));
// diagonal moves
int k = x - 1, l = y - 1;
while (k >= 0 && l >= 0)
lts.Transitions.Add(new LTSTransition(thisCell, string.Format("to({0},{1})", k, l), board[k--, l--]));
}
}
return lts;
}
public static LTS Parse(string file) {
// parse aldebran format
var ret = new LTS();
var sr = new StreamReader(file, Encoding.Default);
var lineRE = new Regex(@"\((\w+)\s*,\s*""([^\""]+?)""\s*,\s*(\w+)\s*\)");
string initial = string.Empty;
while (!sr.EndOfStream) {
var line = sr.ReadLine();
if (line.StartsWith("des")) {
var m = Regex.Match(line, @"des\s*\((\w+?),(\w+?),(\w+?)\)");
if (m.Success) {
initial = m.Groups[1].Captures[0].Value;
}
continue;
}
var match = lineRE.Match(line);
if (match.Success) {
string start = match.Groups[1].Captures[0].Value;
string label = match.Groups[2].Captures[0].Value;
string end = match.Groups[3].Captures[0].Value;
LTSState startState = GetState(start, ret);
LTSState endState = GetState(end, ret);
LTSTransition trans = new LTSTransition(startState, label, endState);
ret.Actions.Add(label);
ret.Transitions.Add(trans);
startState.AddOutTransition(trans);
//endState.AddInTransition(trans);
}
else {
int i = 0;
}
}
ret.InitialState = GetState(initial, ret);
return ret;
}
static void Main(string[] args)
{
var p = new MuCalculusParser();
p.Setup();
bool b = p.Parse(new StringReader("nu X.((mu Y . [b]Y) && nu Z.((<b> X) && (<a>(Z && <a> X))))\r\n"));
string ltsPath = args[0];
string formulasPath = args[1];
Log("LTS: {0}", ltsPath);
var parser = new MuCalculusParser();
parser.Setup();
var fileStream = new FileStream(formulasPath, FileMode.Open, FileAccess.ReadWrite, FileShare.ReadWrite);
bool parseResult = parser.Parse(new StreamReader(fileStream, Encoding.Default));
fileStream.Close();
if (!parseResult)
{
Log("Failed to parse!");
}
LTS lts = LTS.Parse(ltsPath);
foreach (MuFormula f in parser.formulas)
{
Log("----------------------------------");
OutputResult(f, lts);
}
Log();
Log();
logWriter.Flush();
logWriter.Close();
Console.ReadKey();
}
public static HashSet <LTSState> Solve(MuFormula formula, LTS lts, Environment env)
{
if (formula is Proposition)
{
var prop = formula as Proposition;
return(bool.Parse(prop.Value) ? lts.States : new HashSet <LTSState>());
}
else if (formula is Variable)
{
return(env.GetVariable(formula as Variable));
}
else if (formula is Negation)
{
var neg = formula as Negation;
return(new HashSet <LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env))));
}
else if (formula is Conjunction)
{
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env);
var rightStates = Solve(conj.Right, lts, env);
return(new HashSet <LTSState>(leftStates.Intersect(rightStates)));
}
else if (formula is Disjunction)
{
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env);
var rightStates = Solve(disj.Right, lts, env);
return(new HashSet <LTSState>(leftStates.Union(rightStates)));
}
else if (formula is Box)
{
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env);
return(new HashSet <LTSState>(lts.States.Where(
// states where, for all outtransitions with action a, the Formula holds in the direct successor
state => state.GetOutTransitions(box.RegularFormula).All(tr => fe.Contains(tr.Right))
)));
}
else if (formula is Diamond)
{
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return(Solve(shorthand, lts, env));
}
else if (formula is Mu)
{
var mu = formula as Mu;
env[mu.Variable] = new HashSet <LTSState>();
return(FixedPoint.LFP(delegate(Tuple <HashSet <LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(mu.Formula, lts, env);
env[mu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env));
}
else if (formula is Nu)
{
var nu = formula as Nu;
env[nu.Variable] = lts.States;
return(FixedPoint.GFP(delegate(Tuple <HashSet <LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(nu.Formula, lts, env);
env[nu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env));
}
throw new InvalidDataException("not a valid formula in our grammar");
}
public LTSState(string name, LTS lts)
{
Name = name;
LTS = lts;
}
public static HashSet <LTSState> Solve(MuFormula formula, LTS lts, Environment env, bool init = true)
{
if (init)
{
var allVariables = new List <Variable>();
if (formula is Variable)
{
allVariables.Add((Variable)formula);
}
allVariables.AddRange(formula.AllSubFormulas.OfType <Variable>());
allVariables.AddRange(formula.AllSubFormulas.OfType <Mu>().Select(mu => mu.Variable));
allVariables.AddRange(formula.AllSubFormulas.OfType <Nu>().Select(nu => nu.Variable));
Init(allVariables.Distinct(), lts, env);
}
if (formula is Proposition)
{
var prop = formula as Proposition;
return(bool.Parse(prop.Value) ? lts.States : new HashSet <LTSState>());
}
else if (formula is Variable)
{
return(env.GetVariable(formula as Variable));
}
else if (formula is Negation)
{
var neg = formula as Negation;
return(new HashSet <LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env, false))));
}
else if (formula is Conjunction)
{
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env, false);
var rightStates = Solve(conj.Right, lts, env, false);
return(new HashSet <LTSState>(leftStates.Intersect(rightStates)));
}
else if (formula is Disjunction)
{
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env, false);
var rightStates = Solve(disj.Right, lts, env, false);
return(new HashSet <LTSState>(leftStates.Union(rightStates)));
}
else if (formula is Box)
{
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env, false);
var hashSet = new HashSet <LTSState>();
foreach (var state in lts.States)
{
var outTransitions = state.GetOutTransitions(box.RegularFormula);
if (outTransitions.All(tr => fe.Contains(tr.Right)))
{
hashSet.Add(state);
}
}
return(hashSet);
}
else if (formula is Diamond)
{
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return(Solve(shorthand, lts, env, false));
}
else if (formula is Mu)
{
var mu = formula as Mu;
if (mu.Parent is Nu)
{
// surrounding binder is nu
// reset open subformulae of form mu Xk.g set env[k]=false
foreach (var innerMu in formula.AllSubFormulas.OfType <Mu>().Where(m => m.FreeVariables.Count > 0))
{
env[innerMu.Variable] = new HashSet <LTSState>();
}
}
HashSet <LTSState> Xold;
do
{
Xold = env.GetVariable(mu.Variable);
env[mu.Variable] = Solve(mu.Formula, lts, env, false);
} while (Xold.Count != env[mu.Variable].Count);
return(env[mu.Variable]);
}
else if (formula is Nu)
{
var nu = formula as Nu;
if (nu.Parent is Mu)
{
// surrounding binder is mu
// reset open subformulae of form nu Xk.g set env[k]=true
foreach (var innerNu in formula.AllSubFormulas.OfType <Nu>().Where(m => m.FreeVariables.Count > 0))
{
env[innerNu.Variable] = lts.States;
}
}
HashSet <LTSState> Xold;
do
{
Xold = env.GetVariable(nu.Variable);
env[nu.Variable] = Solve(nu.Formula, lts, env, false);
} while (Xold.Count != env[nu.Variable].Count);
return(env[nu.Variable]);
}
throw new InvalidDataException("formula not valid in our grammar");
}
private static void Init(IEnumerable<Variable> variables, LTS lts, Environment env)
{
foreach (var v in variables) {
if (v.Binder is Mu)
env[v] = new HashSet<LTSState>();
else if (v.Binder is Nu)
env[v] = lts.States;
}
}
public LTSState(string name, LTS lts)
{
Name = name;
LTS = lts;
}
private static void OutputResult(MuFormula f, LTS lts)
{
Log("Formula {0}", f);
Log("\t ND: {0}, AD: {1}, DAD: {2}", f.NestingDepth, f.AlternationDepth, f.DependentAlternationDepth);
var naiveSol = NaiveSolver.Solve(f, lts, new Environment());
Log("\tNAIVE: {0}", naiveSol.Contains(lts.InitialState));
var emersonLeiSol = EmersonLei.Solve(f, lts, new Environment());
Log("\tEMLEI: {0}", emersonLeiSol.Contains(lts.InitialState));
}
public static HashSet<LTSState> Solve(MuFormula formula, LTS lts, Environment env, bool init = true)
{
if (init) {
var allVariables = new List<Variable>();
if (formula is Variable) allVariables.Add((Variable)formula);
allVariables.AddRange(formula.AllSubFormulas.OfType<Variable>());
allVariables.AddRange(formula.AllSubFormulas.OfType<Mu>().Select(mu => mu.Variable));
allVariables.AddRange(formula.AllSubFormulas.OfType<Nu>().Select(nu => nu.Variable));
Init(allVariables.Distinct(), lts, env);
}
if (formula is Proposition) {
var prop = formula as Proposition;
return bool.Parse(prop.Value) ? lts.States : new HashSet<LTSState>();
}
else if (formula is Variable) {
return env.GetVariable(formula as Variable);
}
else if (formula is Negation) {
var neg = formula as Negation;
return new HashSet<LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env, false)));
}
else if (formula is Conjunction) {
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env, false);
var rightStates = Solve(conj.Right, lts, env, false);
return new HashSet<LTSState>(leftStates.Intersect(rightStates));
}
else if (formula is Disjunction) {
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env, false);
var rightStates = Solve(disj.Right, lts, env, false);
return new HashSet<LTSState>(leftStates.Union(rightStates));
}
else if (formula is Box) {
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env, false);
var hashSet = new HashSet<LTSState>();
foreach (var state in lts.States) {
var outTransitions = state.GetOutTransitions(box.RegularFormula);
if (outTransitions.All(tr => fe.Contains(tr.Right)))
hashSet.Add(state);
}
return hashSet;
}
else if (formula is Diamond) {
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return Solve(shorthand, lts, env, false);
}
else if (formula is Mu) {
var mu = formula as Mu;
if (mu.Parent is Nu) {
// surrounding binder is nu
// reset open subformulae of form mu Xk.g set env[k]=false
foreach (var innerMu in formula.AllSubFormulas.OfType<Mu>().Where(m => m.FreeVariables.Count > 0))
env[innerMu.Variable] = new HashSet<LTSState>();
}
HashSet<LTSState> Xold;
do {
Xold = env.GetVariable(mu.Variable);
env[mu.Variable] = Solve(mu.Formula, lts, env, false);
} while (Xold.Count != env[mu.Variable].Count);
return env[mu.Variable];
}
else if (formula is Nu) {
var nu = formula as Nu;
if (nu.Parent is Mu) {
// surrounding binder is mu
// reset open subformulae of form nu Xk.g set env[k]=true
foreach (var innerNu in formula.AllSubFormulas.OfType<Nu>().Where(m => m.FreeVariables.Count > 0))
env[innerNu.Variable] = lts.States;
}
HashSet<LTSState> Xold;
do {
Xold = env.GetVariable(nu.Variable);
env[nu.Variable] = Solve(nu.Formula, lts, env, false);
} while (Xold.Count != env[nu.Variable].Count);
return env[nu.Variable];
}
throw new InvalidDataException("formula not valid in our grammar");
}
public static HashSet<LTSState> Solve(MuFormula formula, LTS lts, Environment env)
{
if (formula is Proposition) {
var prop = formula as Proposition;
return bool.Parse(prop.Value) ? lts.States : new HashSet<LTSState>();
}
else if (formula is Variable) {
return env.GetVariable(formula as Variable);
}
else if (formula is Negation) {
var neg = formula as Negation;
return new HashSet<LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env)));
}
else if (formula is Conjunction) {
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env);
var rightStates = Solve(conj.Right, lts, env);
return new HashSet<LTSState>(leftStates.Intersect(rightStates));
}
else if (formula is Disjunction) {
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env);
var rightStates = Solve(disj.Right, lts, env);
return new HashSet<LTSState>(leftStates.Union(rightStates));
}
else if (formula is Box) {
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env);
return new HashSet<LTSState>(lts.States.Where(
// states where, for all outtransitions with action a, the Formula holds in the direct successor
state => state.GetOutTransitions(box.RegularFormula).All(tr => fe.Contains(tr.Right))
));
}
else if (formula is Diamond) {
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return Solve(shorthand, lts, env);
}
else if (formula is Mu) {
var mu = formula as Mu;
env[mu.Variable] = new HashSet<LTSState>();
return FixedPoint.LFP(delegate(Tuple<HashSet<LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(mu.Formula, lts, env);
env[mu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env);
}
else if (formula is Nu) {
var nu = formula as Nu;
env[nu.Variable] = lts.States;
return FixedPoint.GFP(delegate(Tuple<HashSet<LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(nu.Formula, lts, env);
env[nu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env);
}
throw new InvalidDataException("not a valid formula in our grammar");
}