Checking timed automata for linear duration properties

It is proved in this paper that checking a timed automaton M with respect to a linear duration property D can be done by investigating only the integral timed states of M. An equivalence relation is introduced in this paper to divide the infinite number of integral timed states into finite number of equivalence classes. Based on this, a method is proposed for checking whether M satisfies D. In some cases, the number of equivalence classes is too large for a computer to manipulate. A technique for reducing the search-space for checking linear duration property is also described. This technique is more suitable for the case in this paper than those in the literature because most of those techniques are designed for reachability analysis.