/// <summary>
/// Run the machine
/// </summary>
/// <param name="x">The input to run the machine on.</param>
/// <returns>True if the machine halts in the accept state.</returns>
/// <remarks>The first move the machine makes is to fill the first tape (tape 0) with the blank symbol followed by the input.</remarks>
public new bool Run(IEnumerable <char> x)
{
var tapes = Enumerable.Range(0, Tapes).Select(n => new List <char>(Alphabet.Blank)).ToList();
// Fill the first tape with the input
foreach (var c in x)
{
if (!Alphabet.Contains(c))
{
return(false);
}
if (c == Alphabet.EmptyString)
{
continue;
}
tapes[0].Add(c);
}
try {
return(Run(tapes, InitialState, Enumerable.Range(0, Tapes).Select(n => 0).ToArray()).Result);
}
catch (StackOverflowException) {
return(false); // infinite loop, reject
}
}
/// <summary>
/// Run the machine
/// </summary>
/// <param name="x">The input to run the machine on.</param>
/// <param name="o">The completed tape contents</param>
/// <returns>True if the machine halts in the accept state.</returns>
/// <remarks>The first move the machine makes is to fill the tape with the blank symbol followed by the input.</remarks>
public bool Run(IEnumerable <char> x, out char[] o)
{
var tape = new List <char>()
{
Alphabet.Blank
};
// Fill the tape with the input
foreach (var c in x)
{
if (!Alphabet.Contains(c))
{
o = new char[0];
return(false);
}
if (c == Alphabet.EmptyString)
{
continue;
}
tape.Add(c);
}
try {
var res = Run(tape, InitialState, 0).Result;
o = res.Item2;
return(res.Item1);
}
catch (StackOverflowException) {
o = new char[0];
return(false); // infinite loop, reject
}
}
/// <param name="q">The set of states</param>
/// <param name="a">The language alphabet</param>
/// <param name="g">The stack alphabet</param>
/// <param name="d">The transition function containing Transition and PushdownTransition objects</param>
/// <param name="q0">The initial state</param>
/// <param name="f">The set of accepting states</param>
/// <exception cref="ArgumentException"></exception>
public PushdownAutomaton(States q, Alphabet a, StackAlphabet g, PushdownTransitionFunction d, State q0, AcceptingStates f)
{
States = q;
Alphabet = a;
StackAlphabet = g;
Transitions = d;
InitialState = q0;
AcceptingStates = f;
if (States.Count == 0)
{
throw new ArgumentException("The set of states cannot be empty.");
}
if (!States.Contains(InitialState))
{
throw new ArgumentException("The inital state does not exist in the set of states!");
}
foreach (var s in AcceptingStates)
{
if (!States.Contains(s))
{
throw new ArgumentException($"The accepting state {s} is not in the set of states!");
}
}
foreach (var t in Transitions)
{
if (!States.Contains(t.P) || !States.Contains(t.Q) ||
(!Alphabet.Contains(t.A) && t.A != Alphabet.EmptyString) ||
(!StackAlphabet.Contains(t.Top) && t.Top != Alphabet.Wildcard && t.Top != Alphabet.EmptyString))
{
throw new ArgumentException($"Invalid transition {t}");
}
if (t.Replace.Length == 1 && ((t.Replace[0] != Alphabet.Wildcard && t.Replace[0] != Alphabet.EmptyString) && !StackAlphabet.Contains(t.Replace[0])))
{
throw new ArgumentException($"Invalid replace char for transition {t}");
}
if (t.Replace.Length > 1 && Array.Exists(t.Replace, x => !StackAlphabet.Contains(x)))
{
throw new ArgumentException($"Invalid replace char sequence for transition {t}");
}
}
}
private async Task <bool> Run(char[] x, State p, int i)
{
for (; i < x.Length; i++)
{
if (!Alphabet.Contains(x[i]))
{
return(false);
}
if (x[i] == Alphabet.EmptyString)
{
continue;
}
// get possible transitions
var q = Transitions[p, x[i]];
if (q.Length == 0) // nothing to do, stop
{
return(false);
}
if (q.Length == 1)
{
p = q[0].Q; // switch states
if (q[0].A == Alphabet.EmptyString)
{
i--; // Don't increment on null transition!
}
}
else // we have a choice
{
var tasks = new Task <bool> [q.Length];
// check each path asynchronously
for (var j = 0; j < q.Length; j++)
{
tasks[j] = Run(x, q[j].Q, q[j].A == Alphabet.EmptyString ? i : i + 1);
}
var result = false;
// check the result
foreach (var t in tasks)
{
result = result || await t;
}
return(result); // if one of them is successful, this branch accepts
}
}
// No more moves!
if (p.Accepting)
{
return(true);
}
// check for lambda transitions
var r = Transitions[p, Alphabet.EmptyString];
var lambdas = new Task <bool> [r.Length];
for (var k = 0; k < r.Length; k++)
{
lambdas[k] = Run(x, r[k].Q, i);
}
var accept = false;
foreach (var t in lambdas)
{
accept = accept || await t;
}
return(accept);
}
private async Task <bool> Run(char[] x, State p, int i, Stack <char> stack)
{
for (; i < x.Length; i++)
{
if (!Alphabet.Contains(x[i]))
{
return(false);
}
if (x[i] == Alphabet.EmptyString)
{
continue;
}
// Get possible transitions
var q = Transitions[p, x[i], stack.Peek()];
if (q.Length == 0) // nothing to do, stop
{
return(false);
}
if (q.Length == 1)
{
// try to update the stack. if we are out of bounds, reject
try { stack = updateStack(stack, q[0].Top, q[0].Replace); }
catch (Exception) { return(false); }
p = q[0].Q;
if (q[0].A == Alphabet.EmptyString)
{
i--; // Don't increment on null transition!
}
}
else
{
var tasks = new Task <bool> [q.Length];
// check each path asynchronously
for (var j = 0; j < q.Length; j++)
{
var s = new Stack <char>(stack);
try { s = updateStack(s, q[j].Top, q[j].Replace); }
catch (Exception) { continue; }
tasks[j] = Run(x, q[j].Q, q[j].A == Alphabet.EmptyString ? i : i + 1, s);
}
var result = false;
foreach (var t in tasks)
{
result = result || (t != null && await t);
}
return(result);
}
}
// No more moves!
if (p.Accepting)
{
return(true);
}
// check for lambda transitions
var r = Transitions[p, Alphabet.EmptyString, stack.Peek()];
var lambdas = new Task <bool> [r.Length];
for (var k = 0; k < r.Length; k++)
{
var s = new Stack <char>(stack);
try { s = updateStack(s, r[k].Top, r[k].Replace); }
catch (Exception) { continue; }
lambdas[k] = Run(x, r[k].Q, i, s);
}
var accept = false;
foreach (var t in lambdas)
{
accept = accept || (t != null && await t);
}
return(accept);
}