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

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 present simple randomized algorithms for the fault detection problem: Given a specification in the form of a deterministic finite state machine A and an implementation machine B, determine whether B is equal to A. If A has n states and p inputs, then in randomized polynomial time we can construct with high probability a checking sequence of length O(pn4 log n), i.e., a sequence that detects all faulty machines with at most n states. Better bounds can be obtained in certain cases. The techniques generalize to partially specified finite state machines.

Testing finite state machines

This document investigates the integration of adaptive distinguishing sequences into the process of active automata learning (AAL). A novel AAL algorithm "ADT" (adaptive discrimination tree) is developed and presented. Since the submission of the original thesis, the presented algorithm has been integrated into LearnLib - an open-source library for active automata learning - and has been successfully used in related fields of research.

Active Automata Learning with Adaptive Distinguishing Sequences.

Le test d’identification d’etat d’un systeme a evenement discret (SED) a pour but d’en identifier l’etat final, lorsque son etat initial est inconnu. Une solution classique a ce probleme, en supposant que le SED n’ait pas de sorties observables, consiste a determiner une sequences de synchronisation, c.a-d., une sequence d’evenements d’entree qui conduit le SED sur un etat connu. Ce probleme a ete resolu dans les annees 60’ a l’aide des automates. L’objectif principal de cette these est d’utiliser les reseaux de Petri (RdP) pour obtenir une resolution plus optimal de ce probleme et pour une plus large classe de systemes.Initialement, nous montrons que la methode classique peut etre aisement etendue aux RdP synchronises. Pour cette classe de reseaux non-autonomes, toute transition est associee a un evenement d’entree.L’approche proposee est generale, dans la mesure ou elle s’applique a des RdP bornes arbitraires. Cependant, elle engendre le probleme d’explosion combinatoire du nombre d’etats. Pour obtenir des meilleures solutions, nous considerons une classe speciale de RdP : les graphes d’etat (GdE). Pour ces reseaux, nous considerons d’abord les GdE fortement connexes et proposons des approches pour la construction de SS, qui exploitent les proprietes structurelles du reseau en evitant ainsi une enumeration exhaustive de l’espace d’etat. Ces resultats s’etendent aux GdE non fortement connexes et a tout RdP synchronise compose de GdE. Enfin, nous considerons la classe des RdP non bornes et proposons des sequences qui synchronisent le marquage des places non bornees. Une boite a outils fournit toutes les approches decrites et est appliquee a des differents bancs d’essai.

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S. M. Gobershtein

Papers

Check words for the states of a finite automaton