  The well-known problem of state space explosion in model checking is even
more critical when applying this technique to programming languages, mainly due
to the presence of complex data structures. One recent and promising approach
to deal with this problem is the construction of an abstract and correct
representation of the global program state allowing to match visited states
during program model exploration. In particular, one powerful method to
implement abstract matching is to fill the state vector with a minimal amount
of relevant variables for each program point. In this paper, we combine the
on-the-fly model-checking approach (incremental construction of the program
state space) and the static analysis method called influence analysis
(extraction of significant variables for each program point) in order to
automatically construct an abstract matching function. Firstly, we describe the
problem as an alternation-free value-based mu-calculus formula, whose validity
can be checked on the program model expressed as a labeled transition system
(LTS). Secondly, we translate the analysis into the local resolution of a
parameterised boolean equation system (PBES), whose representation enables a
more efficient construction of the resulting abstract matching function.
Finally, we show how our proposal may be elegantly integrated into CADP, a
generic framework for both the design and analysis of distributed systems and
the development of verification tools.
