The higher-dimensional modal mu-calculus is an extension of the mu-calculus
in which formulas are interpreted in tuples of states of a labeled transition
system. Every property that can be expressed in this logic can be checked in
polynomial time, and conversely every polynomial-time decidable problem that
has a bisimulation-invariant encoding into labeled transition systems can also
be defined in the higher-dimensional modal mu-calculus. We exemplify the latter
connection by giving several examples of decision problems which reduce to
model checking of the higher-dimensional modal mu-calculus for some fixed
formulas. This way generic model checking algorithms for the logic can then be
used via partial evaluation in order to obtain algorithms for theses problems
which may benefit from improvements that are well-established in the field of
program verification, namely on-the-fly and symbolic techniques. The aim of
this work is to extend such techniques to other fields as well, here
exemplarily done for process equivalences, automata theory, parsing, string
problems, and games.Comment: In Proceedings FICS 2012, arXiv:1202.317