Graph Algorithms for Conformance Testing Using the Rural Chinese Postman Tour

Abstract

This paper presents new results and graph algorithms for the automatic testing of protocols using “unique input/output” (UIO) sequences. UIO sequences can be efficiently employed in checking conformance of protocols to their specifications by using transition testing. The optimization of the test sequence is based on finding the rural Chinese postman tour, of the state transition diagram of a finite state machine (FSM). The process of conformance test generation using a touring algorithm is valid provided that certain connectivity properties of the graph are present. This implies that a weakly connected graph must be constructed. It is possible that this connectivity condition may not be met when multiple UIO sequences are used even if the reset capability and/or the self-loop properties are present. The “weakly connected graph problem” consists of finding an edge-induced subgraph of the FSM which is still weakly connected when multiple UIO sequences are used. The “multiple UIO tour minimization problem” addresses the assignment of edges to UIO sequences for minimizing the degree of the directed UIO graph. This process may not also minimize the length of the tour. The above two problems, left open in previous papers, are solved in this paper. It is proved that by appropriately changing the original assignment graph and using network flow techniques with a new UIO generation process referred to as chaining, efficient solutions can be provided. The theoretical approaches behind the solution to these problems are fully characterized.