Implementing Sequential and Parallel Programs for the Homing Sequence Problem

Homing sequences play an important role in the testing of finite state systems and have been used in a number of applications such as hardware fault-detection [7], protocol verification [4], and learning algorithms [11, 3, 1] etc. Here we present a parallel program implementation that finds a homing sequence for an input DFA. Our program can handle randomly generated instances with millions of states, and all DFA's with thousands of states. In addition to the design, analysis and implementation of the algorithm, we also discuss what constitute good test cases to test programs that deal with finite automata. 1 Introduction In most applications involving finite automata, the underlying DFA is a black-box whose internal states are not accessible. Testing problem involves determining if the DFA has a certain property using experiments. An experiment consists of applying an input and observing the output. Before performing a test, the DFA should be brought to a known state. An input seque..