Lecture Notes in Computer Science 3472

Generating FSMs out of ASMs
14 Tools for Test Case Generation 413
In the following we will try to sketch the extraction process which generates an
FSM out of a given ASM specification. This is the crucial step because it highly
depends on user-defined and domain-specific conditions to guide the extraction.
The quality of these conditions determines whether the resulting FSM is an
appropriate abstraction of the ASM and if the extraction algorithm terminates
at all.
If one is not familiar with ASMs just think of it as a simple programming
language with variables, functions/methods, some control structure like
an if-then-else, loops, etc. Now every action of the SUT is specified as follows:
if g1 then R1
...
if gk then Rk
where the gi are boolean guards and the Ri are further instructions which are
not allowed to make use of the if-then-else construct anymore (this is a kind
of normal form, one can be less strict when specifying). As expected the initial
values of the variables determine the initial state of a program run. When an
action a is executed the program moves to a next state, which can be seen as a
transition with label a between two program states.
The main problem is that such an ASM has usually an infinite number of
reachable states (unless all possible runs terminate). Hence it is necessary to reduce
the number of states by grouping them according to a suitable equivalence
relation. To get a satisfying result this relation must guarantee that firstly the
number of resulting equivalence classes (also called hyperstates) is finite, otherwise
the algorithm does not terminate. Secondly the number should not be too
small, i.e. the result does not reflect a meaningful test purpose anymore. In fact
you can consider the definition of the equivalence relation as a kind of very general
test purpose definition, respectively test selection. The resulting hyperstates
basically become the states of the generated FSM.
The equivalence relation is based on a set of boolean conditions {b1,...,bn}.
Two states of the ASM lay in the same class iff none of the bi distinguishes them.
Therefore at most 2 n hyperstates are possibly reachable. For example take the
gi of the action specifications as mentioned above as a base for the condition-set.
Using them one can define that states differ (represent different hyperstates) iff
their sets of executable actions differ. Other obvious selections are conceivable.
Beside the potentially exponential number of resulting hyperstates the problem
of computing the so called true-FSM, whichcoversallreachablehyperstates,is
undecidable (and in a bounded version still NP-hard).
The extracting algorithm which computes the FSM does a kind of graph
reachability analysis. A pragmatic solution to the stated problems is to additionally
define a so called relevance condition which tells the extraction algorithm if
the actually encountered ASM-state is worth being taken into account for fur-