Clock Allocation in Timed Automata and Graph Colouring

Abstract

We consider the problem of optimal clock allocation for a fairly general class of timed automata, TAS, under the safe assumption that all locations are reachable. Techniques similar to those used in compiler technology allow us to construct an interference graph: the problem of clock allocation for timed automata in TAS can be reduced to that of colouring this graph. We then describe a class of timed automata, TADS ⊊ TAS, for which optimal clock allocation can be computed in polynomial time, because the corresponding interference graphs are perfect. Finally, we discuss some of the difficulties in applying similar techniques to timed automata outside TAS.