A generalised mathematical theory of structured programming

Fenton, Norman; Whitty, Robin; Kaposi, Agnes

doi:10.1016/0304-3975(85)90040-4

Cited by 24 publications

(11 citation statements)

References 10 publications

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“…A flow graph is constructed from the UCM using the approach described for software in [Fenton85]. A weight is given for each node representing its visit count, with a visit count of 1 for the starting node (and the remainder being unknown), and a label on each edge representing the probability of taking the successor path along that edge.…”

Section: F Ig U R E 5-7 T H E E X T E N D E D F L O W G R a P Hmentioning

confidence: 99%

Extending layered queueing network with hybrid sub-models representing exceptions and decision making

Wu¹

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Section: F Ig U R E 5-7 T H E E X T E N D E D F L O W G R a P Hmentioning

confidence: 99%

Extending layered queueing network with hybrid sub-models representing exceptions and decision making

Wu¹

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“…If P is a nontrivial path in G such that every edge is mapped by 7 to the same element of GF (2), then the image PT of P under 7 is defined to be this element.…”

Section: Predicate Functionsmentioning

confidence: 99%

“…. , x~-~, such that xJ lies in tf 2 1 of the members of R , 0 5 j 5 m -1. We shall construct a series of graphs G' = (V', E') with associated families of subsets R' = {R:…”

Section: Simplifying the Conjecturementioning

confidence: 99%

“…In this section we shall investigate B-vertex-linkings for the case k = 2. In order conveniently to manipulate these linkings we shall borrow a concept from computer science, whereby the vertices of outdegree 2 in binary graphs represent program tests or predicates, having a True and a False outcome represented by the two edges leaving the vertex (see [ 2 ] , for example). Each edge is accordingly labeled with a 1 or a 0, these values being treated arithmetically modulo 2.…”

Section: Predicate Functionsmentioning

confidence: 99%

“…An efficient algorithmic proof of Edmonds' Theorem has been given by Tong and Lawler [8]. In fact, for edge-linkings, Conjecture 1.1 (2) is trivially equivalent to the existence of any family of k arbitrary edge-disjoint R,-branchings in G . For vertex-linkings this is false, as may be seen in Figure 1 by exchanging the edges (x, r , ) and (x, r3) between the first and second branchings, and by ascertaining that the family {x,x,x} is no longer B-vertex-linked onto R .…”

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confidence: 99%

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Vertex‐disjoint paths and edge‐disjoint branchings in directed graphs

Whitty

1987

Journal of Graph Theory

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A theorem of J. Edmonds states that a directed graph has k edge-disjoint branchings rooted at a vertex r if and only if every vertex has k edge-disjoint paths to r . We conjecture an extension of this theorem to vertex-disjoint paths and give a constructive proof of the conjecture in the case k = 2. THE CONJECTURELet G = ( V , E ) be a finite directed graph with vertex set V and edge set E . Multiple edges are allowed, but self loops are excluded. An edge directed from x to y will be denoted by (x,y) (we do not distinguish between multiple edges from x to y), and we refer to x as the tail and y as the head of this edge. If P is a directed path from x to y , we refer to x and y as the tail and head of P , respectively, and say that P is trivial if x and y are the same vertex. If x' and y ' are the tail and head of a subpath of P , we write P :x' + y ' for the restriction of P to this path. Two paths are called edge-disjoint if they have no common edge and vertex-disjoint if they have no common vertices except possibly a common head or tail (the trivial path x is vertex-disjoint from precisely those paths with head or tail x). For a subset R of V , an R-branching in G is a spanning forest B of G in which all vertices of V -R have outdegree precisely 1. When R just consists of a single vertex r, we refer to B as an r-branching.Let I = (1, . . . , k}, where 1 5 k 5 IVI. Let R = { R, 1 i E I } be a family of subsets of V, and let B = {B, I i E I } be a family of edge-disjoint branchings in G such that B, is an R,-branching. Let X = {x, I i E I } be a family of (possibly

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Iconic control graph representation

Robillard¹,

Simoneau²

1993

Softw Pract Exp

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This paper presents a new representation of control flow graphs which is readable and concise, keeping all pertinent information as it appears in the source code. The iconic control graph provides an exact transformation of the source code. It is a basis for control flow visualization, unstructuredness identification, path crossing and path computation. The representation is programming‐language independent. The iconic control flow construction is automated.

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A generalised mathematical theory of structured programming

Cited by 24 publications

References 10 publications

Extending layered queueing network with hybrid sub-models representing exceptions and decision making

Extending layered queueing network with hybrid sub-models representing exceptions and decision making

Vertex‐disjoint paths and edge‐disjoint branchings in directed graphs

Iconic control graph representation

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