The WHILE Hierarchy of Program Schemes Is Infinite

  title={The WHILE Hierarchy of Program Schemes Is Infinite},
  author={Can Adam Albayrak and Thomas Noll},
We exhibit a sequence S n (n ≥ 0) of while program schemes, i. e., while programs without interpretation, with the property that the while nesting depth of S n is n, and prove that any while program scheme which is scheme equivalent to S n , i. e., equivalent for all interpretations over arbitrary domains, has while nesting depth at least n. This shows that the while nesting depth imposes a strict hierarchy (the while hierarchy) when programs are compared with respect to scheme equivalence and… 
3 Citations
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