With advanced computer technology, systems are getting larger to fulfill more complicated tasks: however, they are also becoming less reliable. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. This motivates the study of testing finite stare machines to ensure the correct functioning of systems and to discover aspects of their behavior. A finite state machine contains a finite number of states and produces outputs on state transitions after receiving inputs. Finite state machines are widely used to model systems in diverse areas, including sequential circuits, certain types of programs, and, more recently, communication protocols. In a testing problem we have a machine about which we lack some information; we would like to deduce this information by providing a sequence of inputs to the machine and observing the outputs produced. Because of its practical importance and theoretical interest, the problem of testing finite state machines has been studied in different areas and at various times. The earliest published literature on this topic dates back to the 1950's. Activities in the 1960's mid early 1970's were motivated mainly by automata theory and sequential circuit testing. The area seemed to have mostly died down until a few years ago when the testing problem was resurrected and is now being studied anew due to its applications to conformance testing of communication protocols. While some old problems which had been open for decades were resolved recently, new concepts and more intriguing problems from new applications emerge. We review the fundamental problems in testing finite state machines and techniques for solving these problems, tracing progress in the area from its inception to the present and the stare of the art. In addition, we discuss extensions of finite state machines and some other topics related to testing.

Principles and methods of testing finite state machines-a survey

A Protocol Test Generation Procedure.

https://ris.utwente.nl/ws/files/5157948/00000006.pdf

Testing timed automata

We study the complexity of two fundamental problems in the testing of finite-state machines. 1) Distinguishing sequences (state identification). We show that it is PSPACE-complete to determine whether a finite-state machine has a preset distinguishing sequence. There are machines that have distinguishing sequences, but only of exponential length. We give a polynomial time algorithm that determines whether a finite-state machine has an adaptive distinguishing sequence. (The previous classical algorithms take exponential time.) Furthermore, if there is an adaptive distinguishing sequence, then we give an efficient algorithm that constructs such a sequence of length at most n(n/spl minus/1)/2 (which is the best possible), where n is the number of states. 2) Unique input output sequences (state verification). It is PSPACE-complete to determine whether a state of a machine has a unique input output sequence. There are machines whose states have unique input output sequences but only of exponential length. >

Testing finite-state machines: state identification and verification

We study the problem of uniquely identifying the initial state of a given finite-state machine from among a set of possible choices, based on the input-output behavior. Equivalently, given a set of machines, the problem is to design a test that distinguishes among them. We consider nondeterministic machines as well as probabilistic machines. In both cases, we show that it is PsPAcE-complete to decide whether there is a preset distinguishing strategy (i.e. a sequence of inputs fixed in advance), and it is ExPTIME-complete to decide whether there is an adaptive distinguishing strategy (i.e. when the next input can be chosen based on the outputs observed so far). The probabilistic testing is closely related to probabilistic games, or Markov Decision Processes, with incomplete information. We also provide optimal bounds for deciding whether such games have strategies winning with probability 1.

Distinguishing tests for nondeterministic and probabilistic machines

This paper shows the Unique Input/Output, UIO, approach and the Distinguishing Sequence, DS, approach for the conformance testing of protocol implementations do not always produce identical fault converges, contrary to a previous claim. In the UIO approach, when UIO sequences and signatures are not unique in an implementation, they may not be able to detect erroneous states in the implementation. The UIO approach is revised here with the addition of a verification procedure to ensure that the UIO sequences are all unique in an implementation. Since signatures are generally not unique, this revision requires substituting the use of a signature for a state, S, with a set of input/output sequences, IO(S,K)s, unique to S, each of which distinguishes S from at least one other state, K. Verification is then applied to the IO(S,K)s. Fault coverage in the revised UIO, UIOv, approach is better than that in the original approach. A uniqueness criterion is discussed here to capture a desirable fault coverage for finite-state machine, FSM, test sequences. This criterion ensures the detection of any faulty FSM implementation provided that its set of states does not exceed that in the specified FSM. It is shown that test sequences generated by the UIOv approach and the DS approach always satisfy the uniqueness criterion. In fact, the DS approach is a special case of the UIOv approach; however, the UIOv approach has wider applicability and is generally applicable to k-distinguishable FSMs.

C. T. Vuong

Papers

An improved protocol test generation procedure based on UIOS