Parameter Synthesis Problems for one parametric clock Timed Automata

Abstract

In this paper, we study the parameter synthesis problem for a class of parametric timed automata. The problem asks to construct the set of valuations of the parameters in the parametric timed automaton, referred to as the feasible region, under which the resulting timed automaton satisfies certain properties. We show that the parameter synthesis problem of parametric timed automata with only one parametric clock (unlimited concretely constrained clock) and arbitrarily many parameters is solvable when all the expressions are linear expressions. And it is moreover the synthesis problem is solvable when the form of constraints are parameter polynomial inequality not just simple constraint and parameter domain is nonnegative real number.