This note will simplify the concepts in the book and explain them in an easy-to-understand way.
Table of contents
Multiple Unique True Point Coverage
Corresponding Unique True Point and Near False Point Pair Coverage
basic knowledge
Literal: A clause or the negation of a clause.
Term: A group of words connected by logical AND.
Disjunctive Normal Form - Disjunctive Normal Form referred to as DNF
A DNF predicate is a set of terms connected by logical OR, such as ( a ^ c ) V ( b ^ c )
Implicant: A term in a DNF predicate. If a single term is true, it means that the predicate is true.
Minimal DNF: Every implicant is a main implicant, and no implicant is redundant (can be obtained by drawing a Karnaugh map)
Implicant Coverage
Given a DNF expression with predicates f and not f, for each implicant in f and not f, TR (test requirement) requires that the value of the implicant is true.
Unique True Point Coverage
The unique truth point (UTP) of the i-th implicant refers to the assignment of values to all clauses such that only the i-th implicant is true and the rest are false.
Unique truth point coverage (UTPC) requires analyzing each implication of the minimal DNF expression of f and non-f separately to find the unique truth point of each implication.
Near False Point Coverage
For each implicant's unique truth point, there is a corresponding false value point for each word. The approximate false point (NFP) of a clause c refers to assigning values to all clauses such that the predicate f is false, but if c is negated, the values of other clauses remain unchanged, and the implicant is true (f also is true).
eg: For the predicate f(a,b,c,d) = ab + cd
The UTP of the implicant ab is: {TTFF, TTFT, TTTF}
The UTP of the implicant cd is: { FTTT, TFTT, FFTT }
For the implicant ab:
The NFP of clause a is { FTFF, FTFT, FTTF }
The NFP of clause b is { TFFF, TFFT, TFTF }
For the implicant cd:
The NFP of clause c is { FTFT, TFFT, FFFT }
The NFP of clause d is { FTTF, TFTF, FFTF }
Multiple Unique True Point Coverage
Given a minimal DNF expression of a predicate f, for each implicant i in f, choose a unique truth point (UTP) such that the values of clauses not in i include both true and false.
eg: Still in the above example, for the implicant ab, if the only truth value points UTP we choose are FTFT and FTTF, then it is satisfied that clauses c and d not in ab are true or false.
Similarly, for the implication cd, the UTP we choose is FTTT, TFTT.
Therefore, for the predicate ab+cd, the test case set that satisfies MUTPC is { FTFT, FTTF, FTTT, TFTT }
Corresponding Unique True Point and Near False Point Pair Coverage
Given a minimal DNF expression of a predicate f, for each clause c in each implicant i, TR includes a unique truth point for i and an approximate falsity point for c in i, and these two The only difference between points is the value of c.
eg: Still the above example!
Predicate f(a,b,c,d) = ab + cd
The UTP of the implicant ab is: {TTFF, TTFT, TTTF} ——[1]
The UTP of the implicant cd is: { FTTT, TFTT, FFTT }
For the implicant ab:
The NFP of clause a is { FTFF, FTFT, FTTF } ——[2]
The NFP of clause b is { TFFF, TFFT, TFTF }
For the implicant cd:
The NFP of clause c is { FTFT, TFFT, FFFT }
The NFP of clause d is { FTTF, TFTF, FFTF }
This is the result of our first step. For clause a in the implication ab, we choose one of [1], and then correspondingly choose one of [2]. The only difference between the two is clause a. So we choose TTFF and FTFF.
Similarly, for clause b, we choose TTFF and TFFF, for clause c, we choose FTTT and FTFT, and for clause d, we choose FTTT and FTTF.
The final test set that satisfies CUTPNFP is {TTFF, FTFF, TFFF, FTTT, FTFT, FTTF}.