Path Products in Software Testing Methodologies

The name of a path that consists of two consecutive path segments which is expressed by the concatenation or path product of the segment names

Example:

If X and Y are defined as X = abcde, Y = fghij, then the path corresponding to X followed by Y is denoted by,

YX = abcdefghij

similarly,

YX = fghijabcde

aX = aabcde

Xa = abcdea

XaX = abcdeaabcde

If X and Y represent set of path expressions, then their product alsi represents the set of paths which can be obtained by following every element of X by any element of Y in all achievable ways

Example:

X = abc + def +ghi

Y = uvw + z

Then,

XY = abcuvw + defuvw + ghiuvw + abcz +defz + ghiz

If a link or segment name is repeated, then that fact is identified by an exponent. The exponent's value indicates the number of repetitions as shown below:

a¹ = a

a² = aa

a³ = aaa

aⁿ = aaa----- n times

similarly,

if X = abcde

then

X¹ = abcde

X² = abcdeabcde = (abcde)2

The path product is not commutative (i.e., XY! = YX)

The path product is associative

RULE 1: A (BC) = AB (C) =ABC

where A, B, C can be path names, set of path names or path expressions

The O^th power of a link name, path product or path expression is also needed for fullness which is denoted by the numeral '1' and if the path does not have any links then it is denoted by zero

a⁰ = 1

x⁰ = 1

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About Data Sciences by Venu

Hi, My name is Venugopala Chary and I'm Currently working as Associate Professor in Reputed Engineerng College, Hyderabad. I have B.Tech and M.tech in regular from JNTU Hyderabad. I have 11 Years of Teaching Experience for both B.Tech and M.Tech Courses.