An Optimal State Identification Method Using a Dynamic-Programming-Based Approach for Protocol Testing

Abstract

The Unique Input/Output (UIO) sequence has been regarded as an efficient technique for state identification for protocol testing. Unfortunately, it has been shown that some states in a protocol may possess no UIO sequences. Another input/output sequence called a signature can be generated as a substitute for a state without a UIO sequence. The existing signature technique performs state identification by distinguishing a given state from another single state at a time. The limitation is that it cannot assure a minimum-length signature. Moreover, a recently-proposed method, called the Partial UIO (PUIO) sequence, distinguishes a state from a nonempty proper subset of states at a time. The goal of the paper is to construct a minimum-length signature by selecting appropriate PUIO sequences from the set of all PUIO sequences. This paper first transforms the problem into a Minimum-Cost Pattern Covering Problem (MCPCP), where the pattern is the set of the remaining states from which the state under consideration is to be distinguished. To solve the MCPCP, the paper presents a dynamic-programming-based algorithm with three reduction rules and three termination rules. The reduction rules are used to reduce the original problem to simpler subproblems, and the termination rules are used to terminate the reduction process. The paper also discusses the time complexity of the algorithm. Consequently, an optimal-length signature can be efficiently constructed.