/// <summary>
/// Performs the entire ARMC verification algorithm.
/// </summary>
/// <returns>Verification result, i.e. whether property holds.</returns>
/// <param name="counterexample">Counterexample (if encountered, i.e. <code>false</code> returned).</param>
/// <remarks>Termination not guaranteed, consider setting timeout in configuration.</remarks>
public bool Verify(out Counterexample <SYMBOL> counterexample)
{
stopwatch.Reset();
while (true)
{
bool?result = VerifyStep(out counterexample);
if (result.HasValue)
{
return((bool)result);
}
if (timeout > 0 && stopwatch.ElapsedTicks > timeout)
{
throw ARMCException.Timeout();
}
loops++;
}
}
/// <summary>
/// Print the counterexample (SSAs).
/// </summary>
/// <param name="counterexample">Counterexample.</param>
/// <param name="directory">Output directory path.</param>
public void PrintCounterexample(Counterexample <SYMBOL> counterexample, string directory)
{
int i = 0;
foreach (var pair in counterexample.Ms)
{
SSA <SYMBOL> m = pair.Item1;
SSA <SYMBOL> mAlpha = pair.Item2;
PrintAutomaton(m, directory, "M" + i.ToString());
if (mAlpha != null)
{
PrintAutomaton(mAlpha, directory, "M" + i.ToString() + "+");
}
i++;
}
i = 0;
foreach (SSA <SYMBOL> x in counterexample.Xs)
{
PrintAutomaton(x, directory, "X" + i.ToString());
i++;
}
}
/// <summary>
/// Performs one step (inner loop) of ARMC.
/// </summary>
/// <returns>Verification result, or <code>null</code> if undecided.</returns>
/// <param name="counterexample">Counterexample (if encountered, i.e. <code>false</code> returned).</param>
public bool?VerifyStep(out Counterexample <SYMBOL> counterexample)
{
var ssas = new Stack <Tuple <SSA <SYMBOL>, SSA <SYMBOL> > >();
SSA <SYMBOL> m;
SSA <SYMBOL> ml;
SSA <SYMBOL> mAlpha = null;
SSA <SYMBOL> x;
var xs = new Stack <SSA <SYMBOL> >();
int i = 0;
int l = 0;
string ext = "." + format.ToString().ToLower();
string dir = Path.Combine(outputDir, "armc-loop-" + loops.ToString());
stopwatch.Start();
if (printAutomata)
{
Directory.CreateDirectory(dir);
abstr.Print(dir, this);
}
counterexample = null;
m = init;
if (printAutomata)
{
PrintAutomaton(m, dir, "M0");
}
while (true)
{
if (verbose)
{
Log("\r" + loops.ToString() + "." + i.ToString());
}
if (i > 0 && !SSA <SYMBOL> .ProductIsEmpty(m, bad))
{
if (verbose)
{
LogLine(": counterexample encountered");
}
l = i;
x = m & bad;
x.Name = "<i>X</i><sub>" + l.ToString() + "</sub>";
if (printAutomata)
{
PrintAutomaton(x, dir, "X" + l.ToString());
}
ml = m;
xs.Push(x);
break;
}
mAlpha = abstr.Collapse(m).Determinize().Minimize();
mAlpha.Name = "<i>M</i><sub>" + i.ToString() + "</sub><sup>α</sup>";
if (printAutomata)
{
PrintAutomaton(mAlpha, dir, "M" + i.ToString() + "+");
}
if (i > 0 && mAlpha == ssas.Peek().Item2)
{
stopwatch.Stop();
if (verbose)
{
LogLine(": fixpoint reached");
LogLine("time = " + stopwatch.Elapsed.ToString());
}
return(true);
}
if (timeout > 0 && stopwatch.ElapsedTicks > timeout)
{
stopwatch.Stop();
if (verbose)
{
LogLine(": timeout (" + stopwatch.Elapsed.ToString() + ")");
}
throw ARMCException.Timeout();
}
ssas.Push(Tuple.Create(m, mAlpha));
i++;
m = tau.Apply(mAlpha).Determinize().Minimize();
m.Name = "<i>M</i><sub>" + i.ToString() + "</sub>";
if (printAutomata)
{
PrintAutomaton(m, dir, "M" + i.ToString());
}
}
bool spurious = false;
foreach (var pair in ssas)
{
m = pair.Item1;
mAlpha = pair.Item2;
i--;
if (verbose)
{
Log("\r" + loops.ToString() + "." + l.ToString() + "-" + i.ToString());
}
x = (tauInv.Apply(x) & mAlpha).Determinize().Minimize();
x.Name = "<i>X</i><sub>" + i.ToString() + "</sub>";
xs.Push(x);
if (printAutomata)
{
PrintAutomaton(x, dir, "X" + i.ToString());
}
if (SSA <SYMBOL> .ProductIsEmpty(x, m))
{
spurious = true;
break;
}
}
stopwatch.Stop();
if (spurious)
{
if (verbose)
{
LogLine(": counterexample is spurious");
}
abstr.Refine(m, x);
return(null);
}
else
{
if (verbose)
{
LogLine(": counterexample is real");
LogLine("time = " + stopwatch.Elapsed.ToString());
}
List <Tuple <SSA <SYMBOL>, SSA <SYMBOL> > > ms = ssas.ToList();
ms.Reverse();
ms.Add(new Tuple <SSA <SYMBOL>, SSA <SYMBOL> >(ml, null));
counterexample = new Counterexample <SYMBOL> {
Ms = ms,
Xs = xs.ToList()
};
return(false);
}
}