In this paper we carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the Test Cover problem we are given a set [n] = {1,. .. , n} of items together with a collection, T , of distinct subsets of these items called tests. We assume that T is a test cover, i.e., for each pair of items there is a test...

In a combinatorial search problem with binary tests, we are given a set of elements (vertices) and a hypergraph of possible tests (hyperedges), and the goal is to find an unknown target element using a minimum number of tests. We explore the expected test number of randomized strategies. Our main results are that the ratio of the randomized and deterministic test numbers can be logarithmic in t...

Abstract Property-based testing uses randomly generated inputs to validate high-level program specifications. It can be shockingly effective at finding bugs, but it often requires generating a very large number of do so. In this paper, we apply ideas from combinatorial , powerful and widely studied methodology, modify the distributions our random generators so as find bugs with fewer tests. The...

We answer a question of Jockusch by showing that the measure of the Turing degrees which satisfy the cupping property is 0. In fact, every 2-random degree has a strong minimal cover, and so fails to satisfy the cupping

Effective testing can develop quality software with higher productivity at a lower cost. As the software is modified and new test cases are added to the test suite, the size of the test suite grows and the cost of testing is also increases. In order to reduce the cost of testing researcher have investigated the use of test suite reduction technique. Redundancy in test suite increases the execut...