This paper addresses questions regarding the decidability of
hybrid automata that may be built hierarchically as is the case in many
exemplar systems, be it natural or engineered. Parallel composition can
be considered a fundamental tool in such constructions. Somewhat surprisingly,
this operation does not always preserve the decidability of reachability
problem i.e., even if we prove the decidability of reachability over
component automata, we cannot guarantee the decidability over their
parallel composition. Despite these limitations, this paper provides a reduction
for the reachability problem over parallel composition of first-order
constant reset automata (FOCoRe) to the satisfiability of a particular
linear Diophantine system. Moreover, since such satisfiability problem
have been proved decidable for systems with semi-algebraic coe cients,
this paper presents an interesting class of hybrid automata for which the
reachability problem of parallel composition is decidable. The resulting
hybrid automata appear in systems biological modeling, and hence could
be applied when one is interested in understanding a complex biological
system composed of many smaller self-organizing systems.
