E.Asarin, O. Maler and A.Pnueli, Symbolic Controller Synthesis for Discrete and Timed Systems.
This paper presents algorithms for the symbolic
synthesis of discrete and real-time controllers. At the semantic
level the controller is synthesized by finding a winning strategy
for certain games defined by automata or by timed-automata. The
algorithms for finding such strategies need, this way or another,
to search the state-space of the system which grows exponentially
with the number of components. Symbolic methods allow such a
search to be conducted without necessarily enumerating the state-space.
This is achieved by representing sets of states using formulae (syntactic
objects) over state variables. Although in the worst case such
methods are as bad as enumerative ones, many huge practical
problems can be treated by fine-tuned symbolic methods. In this
paper the scope of these methods is extended from analysis to
synthesis and from purely discrete systems to real-time systems.
We believe that these results will pave the way for the application of program synthesis techniques to the construction of real-time embedded systems from their specifications and to a solution of other related design problems associated with real-time systems in general and asynchronous circuits in particular.[Postscript]