Complexity of node coverage games

Modern software systems may exhibit a nondeterministic behavior due to many unpredictable factors. In this work, we propose the node coverage game, a two-player turn-based game played on a finite game graph, as a formalization of the problem to test such systems. Each node in the graph represents a functional equivalence class of the software under test (SUT). One player, the tester, wants to maximize the node coverage, measured by the number of nodes visited when exploring the game graphs, while his opponent, the SUT, wants to minimize it. An optimal test would maximize the cover, and it is an interesting problem to find the maximal number of nodes that the tester can guarantee to visit, irrespective of the responses of the SUT. We show that the decision problem of whether the guarantee is less than a given number is NP-complete. We also discuss two extensions of our result and present a testing procedure based on our result when the SUT is not so hostile.

Authors

• Farn Wang
• Sven Schewe
• Jung-Hsuan Wu

Keywords

• Testing
• Nondeterminism
• Coverage
• Game
• Strategy
• Complexity