Conformance Testing of Boolean Programs with Multiple Faults

Conformance testing is the problem of constructing a complete test suite of inputs based on a specification S such that any implementation I (of size less than a given bound) that is not equivalent to S gives a different output on the test suite than S. Typically I and S are assumed to be some type of finite automata. In this paper we consider the problem of constructing test suites for boolean programs (or more precisely modular visibly pushdown automata) that are guaranteed to catch all erroneous implementations that have at least R faults, and pass all correct implementations; if the incorrect implementation has fewer than R faults then the test suite may or may not detect it. We present a randomized algorithm for the construction of such test suites, and prove the near optimality of our test suites by proving lower bounds on the size of test suites.