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example diagram showing PLD elements,

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refs: changed howse:sd to howse:spider
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robin 2011-03-27 11:29:26 +01:00
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logic_diagram/examplepld.dia
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logic_diagram/logic_diagram.tex
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@ -128,7 +128,7 @@ All features may be labelled, and the labels must be unique within a diagram, ho
%Regions defined by contours are used to represent given conjunctive logical conditions. %Regions defined by contours are used to represent given conjunctive logical conditions.
Test~cases are marked by asterisks. The asterisk is used rather than a point, because is analogous to the constraint Test~cases are marked by asterisks. The asterisk is used rather than a point, because is analogous to the constraint
diagram universal qualifier~\cite{uconstraintd}. These are used as a visual `anchor' diagram universal qualifier~\cite{howse:spider}. These are used as a visual `anchor'
to mark a logical condition, the logical condition being defined by the contours to mark a logical condition, the logical condition being defined by the contours
that enclose the region on which the test~case has been placed. that enclose the region on which the test~case has been placed.
The contours that enclose represent conjunction. The contours that enclose represent conjunction.
@ -169,7 +169,7 @@ Definitions of concrete and abstract PLD's follow.
Well-formedness conditions for PLD's are separated from this definition, because of Well-formedness conditions for PLD's are separated from this definition, because of
practical differences between the way they are used to represent software as opposed to practical differences between the way they are used to represent software as opposed to
representing electronics and mechanical systems. representing electronics and mechanical systems.
The concrete definitions for PLD's and Spider Diagrams\cite{howse:sd} share many common features. The concrete definitions for PLD's and Spider Diagrams~\cite{howse:spider} share many common features.
\subsection{Concrete PLD Definition} \subsection{Concrete PLD Definition}
@ -178,12 +178,14 @@ A concrete {\em Propositional logic diagram} is a set of labelled {\em contours}
(closed curves) in the plane (examples of closed curves a,b,c are shown in figure \ref{fig:examplepld}). (closed curves) in the plane (examples of closed curves a,b,c are shown in figure \ref{fig:examplepld}).
The minimal regions formed by the closed curves The minimal regions formed by the closed curves
can by occupied by `test cases' (represented by asterisks). can by occupied by `test cases' (represented by asterisks).
The example diagram in figure \ref{fig:examplepld} has fournumbered test~cases, TC1, TC2, TC3 and TC4. The example diagram in figure \ref{fig:examplepld} has fournumbered test~cases, TC1, TC2, TC3, TC4 and TC4.
The `test cases' may be joined by joining lines. The example diagram (figure \ref{fig:examplepld}) shows two joining lines The `test cases' may be joined by joining lines. The example diagram (figure \ref{fig:examplepld}) shows three joining lines
R1 and R2. R1, R2 and R3.
A group of `test cases' connected by joining lines A group of `test cases' connected by joining lines
is defined as a `test case disjunction' or Spider. is defined as a `test case disjunction' or symptomatically merged group (SMG).
Spiders may be labelled. This is the analog of a `spider' in constraint diagrams~\cite{howse:spider}.
Joining lines R2 and R3 form a Spider, or symptomatically merged group (SMG).
%SMGs may be labelled.
%To differentiate these from common Euler diagram notation (normally used to represent set theory) %To differentiate these from common Euler diagram notation (normally used to represent set theory)
%the curves are drawn using dotted and dashed lines. %the curves are drawn using dotted and dashed lines.
@ -297,7 +299,7 @@ Test~cases on the concrete diagram pair-wise connected by a `joining line'
The graph formed by test~cases connected by joining lines is called an $SMG$. The graph formed by test~cases connected by joining lines is called an $SMG$.
%A collection of test cases connected by joining lines, is an Symptom Merged Group, $SMG$ %A collection of test cases connected by joining lines, is an Symptom Merged Group, $SMG$
%or `test case disjunction'. %or `test case disjunction'.
The $SMG$ is the analog of the Spider in spider/constraint diagrams\ref{howse:sd}. The $SMG$ is the analog of the Spider in spider/constraint diagrams\ref{howse:spider}.
An $SMG$ can be considered to be a collection of test~cases. An $SMG$ can be considered to be a collection of test~cases.
{ {