stsys/tests/ack.js

String rewriting system (semi-Thue system)

// increase stack size through parameter --stack_size=<size>. e.g.
// node --stack_size=100000 ack 3 11
function a(n, m)
{
  if (n === 0)
    return m + 1;
  if (m === 0)
    return a(n - 1, 1);
  return a(n - 1, a(n, m - 1));
}

function a2(n, m)
{
  const stack = [n, m];
  let l = 1;
  do
  {
    if (stack[l - 1] === 0)
      stack[--l] = stack.pop() + 1;
    else if (stack[l] === 0)
    {
      stack[l - 1] -= 1;
      stack[l] = 1;
    }
    else
    {
      stack.push(stack[l] - 1);
      stack[l] = stack[l - 1];
      stack[l++ - 1] -= 1;
    }
  }
  while (l > 0);
  return stack[0];
}

function isValidInput(n, m)
{
  const regex = /^\d+$/;
  return regex.test(n) && regex.test(m);
}

if (process.argv.length < 4 || process.argv.length > 5 || !isValidInput(process.argv[2], process.argv[3]))
{
  console.log('USAGE:', process.argv0, process.argv[1], '<n>', '<m>', '[-s]');
  console.log('  where <n> and <m> are natural numbers, i.e. from the set {0, 1, 2, ...}');
  console.log('  Computes the value A(<n>,<m>) of the Ackermann function A for the given natural numbers <n> and <m>.');
  console.log('  Use option -s to invoke the standard recursive implemenation of the Ackermann function.');
}
else
{
  console.log('Computing A(' + process.argv[2] + ',' + process.argv[3] + ')');
  console.log('Result:', (process.argv.length === 5 && process.argv[4] === '-s' ? a : a2)(process.argv[2] * 1, process.argv[3] * 1));
}