Predicate Complete Testing*

Thomas Ball

* Thomas Ball, A Theory of Predicate-Complete Test Coverage and Generation, Technical Report MSR-TR-2004-

28, Microsoft Research

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

setComplete

Some notion that the test set is “exhaustive”

Theoretical Goals

Control Flow metrics Statement, branch, multiple condition,

predicate, path, linear code sequence and jumpPredicate 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?

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 (<= m*2^n)Some BP states are observableSome BP states are reachable

Boolean Program

Reachable States

Reachability Graph

Formalizing the state abstraction

Boolean Program II

Upper and Lower bounds for R

R – set of reachable statesU – upper bound for R via may-transitionsLp – 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

Algorithm

Using algorithms for computing L and U, |L|==|U| => the abstraction accurately encodes all the paths of R.

Generate all paths for L in the graph

Test Generation

Discussion