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A Semantically Meaningful Characterization of Reducible Flowchart Schemes

In: Selected Papers

Author

Listed:
  • Calvin C. Elgot

    (IBM Thomas J. Watson Research Center, Mathematical Sciences Department)

  • John C. Shepherdson

    (University of Bristol, School of Mathematics)

Abstract

A “scalar” flowchart scheme, i.e. one with a single begin “instruction” is reducible iff its underlying flowgraph is reducible in the sense of Cocke and Allen or Hecht and Ullman. We characterize the class of reducible scalar flowchart schemes as the smallest class containing certain members and closed under certain operations (on and to flowchart schemes). These operations are “semantically meaningful” in the sense that operations of the same form are meaningful for “the” functions (or partial functions) computed by interpreted flowchart schemes; moreover, the schemes and the functions “are related by a homomorphism.” By appropriately generalizing “flowgraph” to (possibly) several begins (i.e. entries) we obtain a class of reducible “vector” flowchart schemes which can be characterized in a manner analogous to the scalar case but involving simpler more basic operations (which are also semantically meaningful). A significant side effect of this semantic viewpoint is the treatment of multi-exit flowchart schemes on an equal footing with single exit ones.

Suggested Citation

  • Calvin C. Elgot & John C. Shepherdson, 1982. "A Semantically Meaningful Characterization of Reducible Flowchart Schemes," Springer Books, in: Stephen L. Bloom (ed.), Selected Papers, pages 327-359, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8177-8_11
    DOI: 10.1007/978-1-4613-8177-8_11
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