Lecture Notes in Computer Science 3472

576 Therese Berg and Harald Raffelt
19.4 Learning Finite State Machines
Techniques such as model checking and model-based test-generation are a convenient
way to automatically improve a system’s reliability as a system conforming
to its specification. The problem is that in many cases a model of the system
does not exist or if it does, it is outdated. If the model is to be constructed by
hand this may be time-consuming and it is very much dependent on how familiar
the test engineer is with the system under test (SUT). A way to facilitate
the test engineer’s work and derive a more reliable model, is to automate the
generation of a model of the SUT. A proposed procedure to attain this is to
apply a technique called model learning, sometimes also called model inference.
This section will explain how a so called learning algorithm builds a model
of a system under test. The SUT considered is a black box, i.e., we have no
information about its internal structure. We do make the assumption that the
SUT can be modeled as a deterministic finite state automaton (DFA). We also
assume that we know which actions the SUT is able to perform, here called the
alphabet Σ. The minimal model of the SUT is the DFA denoted M. Theregular
language accepted by the finite state automaton is denoted L (M), also referred
to as U.
The basic set-up for all of the variants of the learning algorithm explained
in this section is presented in Figure 19.7. The Learner represents the algorithm
which is trying to estimate U. The Learner estimates U iteratively through
gathering enough pieces of information about U until it is able to construct a
hypothesis, also called conjecture or approximation of U. The hypothesis is a
DFA A with the language L (A). If the conjecture is incorrect the learner will
continue to collect information until it can construct a “better” conjecture. The
Learner iterates in this fashion until the hypothesis is correct.
Machine M
Teacher
mq
+/-
eq
Learner
Oracle correct/
c.ex.
Fig. 19.7. Learning an Automaton.
More specifically, the Learner is able to query the Teacher whether a string
is accepted by M or not and the answers will be yes (+) or no (−), seen in
Figure 19.7. A query to the Teacher is called membership query (mq). The
name refers to the question whether a string is a member of L (M) ornot.
Furthermore the Learner can ask an equivalence query (eq) to an Oracle
whether the approximation A is correct or not. If the Oracle deems that the
conjecture is equivalent to M it confirms the correctness of the hypothesis,