A Semantically Meaningful Characterization of Reducible Flowchart Schemes

Calvin C. Elgot and John C. Shepherdson
Additional contact information
Calvin C. Elgot: IBM Thomas J. Watson Research Center, Mathematical Sciences Department
John C. Shepherdson: University of Bristol, School of Mathematics

A chapter in Selected Papers, 1982, pp 327-359 from Springer

Abstract: 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.

Keywords: Isomorphism Class; Back Edge; Separate Pairing; Scalar Iteration; Common Extension (search for similar items in EconPapers)
Date: 1982
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-8177-8_11

Ordering information: This item can be ordered from
http://www.springer.com/9781461381778

DOI: 10.1007/978-1-4613-8177-8_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().