Timed automata as acceptors of languages of finite timed words form a very useful framework for the verification of safety properties of real-time systems. Many of the classical automata-theoretic decision problems are undecidable for timed automata, for instance the inclusion or the universality problem. In this paper we consider restrictions of these problems: universality for deterministic timed automata and inclusion of a nondeterministic one by a deterministic one. We then advocate the use

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... of SMT solvers for the exact incremental analysis of timed automata via these problems. We stratify these problems by considering domains of timed words of bounded length only and show that each bounded instance is in (co-)NP. We present some experimental data obtained from a prototypical implementation measuring the practical feasibility of the approach to timed automata via SMT solvers.