Predicate Complete Testing*

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Predicate Complete Testing

• Thomas Ball
• Thomas Ball, A Theory of Predicate-Complete
  Test Coverage and Generation, Technical Report
  MSR-TR-2004-28, Microsoft Research

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Testing Definitions

• Statement
• Every statement is executed by the test set
• Path
• Every control path is executed by the test set
• Predicate
• Every logical predicate is executed by the test
  set
• Complete
• Some notion that the test set is exhaustive

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Theoretical Goals

• Control Flow metrics
• Statement, branch, multiple condition, predicate,
  path, linear code sequence and jump
• Predicate Complete Testing
• Cover all reachable observable states
• Bound the number tests
• Know when to stop (when do we have a complete
  test set)
• Does PCT actually produce tests?

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Using Boolean Programs

• Recall that BP transforms the original program
  into a program of its Boolean predicates
• A BP state is some Boolean assignment of all
  predicates
• The BP state space is finite (lt m2n)
• Some BP states are observable
• Some BP states are reachable

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Boolean Program
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Reachable States
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Reachability Graph
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Formalizing the state abstraction
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Boolean Program II
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Upper and Lower bounds for R

• R set of reachable states
• U upper bound for R via may-transitions
• Lp pessimistic lower bound for R via must
  transitions, a may transition, and must-
  transitions
• Lo optimistic lower bound for R, with the
  assumption that the program does not diverge

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Algorithm

• Using algorithms for computing L and U, LU
  gt the abstraction accurately encodes all the
  paths of R.
• Generate all paths for L in the graph

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Test Generation
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Discussion