Recursion induction applied to generalized flowcharts

• Authors: Donald M. Kaplan
• Venue: ACM '69 Proceedings of the 1969 24th national conference
• Year: 1969

Recursion induction here is a rule of inference for proving flowchart programs equivalent. If a flowchart A is equivalent to another B(A), and if the so-called closed form of B, namely C, halts whenever B(A) does, then A is equivalent to C. It is shown that this rule can be extended to apply to a very general class of flowcharts. A formal theory of flowcharts is introduced that permits proofs of the premises of this extended rule to be carried out, and a derivation using recursion induction is illustrated. As a further example, two flowcharts are introduced that are each equivalent to a two-tape, one-way automaton. A derivation using recursion induction is presented that proves the flowcharts, and hence the automata as well, equivalent.