Predicate Complete Testing * Thomas Ball * Thomas Ball, A Theory of Predicate-Complete Test Coverage and Generation, Technical Report MSR-TR , 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 set Complete  Some notion that the test set is “exhaustive”

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?

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 observable Some 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 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

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