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Formal Analysis of Reachability, Infection and Propagation Conditions in Mutation Testing

Seyed-Hassan Mirian-Hosseinabadi

TL;DR

A formal approach to calculate RIP conditions is proposed using the Dijkestra's weakest precondition predicate transformer (wp(_,_)) to calculate infection and propagation conditions.

Abstract

Finding test cases to kill the alive mutants in Mutation testing needs to calculate the Reachability, Infection and Propagation(RIP) conditions and full test specification. In this paper, a formal approach to calculate RIP conditions is proposed. The Dijkestra's weakest precondition predicate transformer (wp(_,_)) is used to calculate infection and propagation conditions. The rc(_) function is defined to calculate the reachability conditions generated by each statement. Four programs and their mutants are examined as running examples and as case studies to show the applicability of the method.

Formal Analysis of Reachability, Infection and Propagation Conditions in Mutation Testing

TL;DR

A formal approach to calculate RIP conditions is proposed using the Dijkestra's weakest precondition predicate transformer (wp(_,_)) to calculate infection and propagation conditions.

Abstract

Finding test cases to kill the alive mutants in Mutation testing needs to calculate the Reachability, Infection and Propagation(RIP) conditions and full test specification. In this paper, a formal approach to calculate RIP conditions is proposed. The Dijkestra's weakest precondition predicate transformer (wp(_,_)) is used to calculate infection and propagation conditions. The rc(_) function is defined to calculate the reachability conditions generated by each statement. Four programs and their mutants are examined as running examples and as case studies to show the applicability of the method.

Paper Structure

This paper contains 32 sections, 77 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Mutation Testing and RIPR Analysis
  3. Dijkestra Guarded Commands
  4. Dijkestra Weakest Precondition Predicate Transformer
  5. Weakest Preconditions of Primitive Programming Statements
  6. Weakest Preconditions of $\DO$ Statement
  7. Literature Survey
  8. The proposed method
  9. Reachability Condition Generator Function
  10. Categorizing Program Modifications
  11. Reachability, Infection, and Propagation Conditions Calculations
  12. Case studies
  13. Min Program: Killing Mutant Strongly and Weakly
  14. Definitions
  15. RIP Calculations
  16. ...and 17 more sections

Figures (3)

  • Figure 1: BNF description of Dijkestra Guarded Commands syntax
  • Figure 2: Karno Map for $abd+ a\bar{b}c+ ad+ \bar{a}bc+\bar{a}c+bd+ \bar{b}c$
  • Figure 3: Karno Map for $a\bar{b}d + ad + \bar{a}d + \bar{a}\bar{b}c +\bar{a}b d + bd+ \bar{b}d$