We investigate a class of parametric timed automata, called lower bound/upper bound (L/U) automata, where each parameter occurs in the timing constraints either as a lower bound or as an upper bound. For such automata, we show that basic decision problems, such as emptiness, finiteness and universality of the set of parameter valuations for which there is a corresponding infinite accepting run of the automaton, is PSPACE-complete. We extend these results by allowing the specification of constraints on parameters as a linear system. We show that the considered decision problems are still PSPACE-complete, if the lower bound parameters are not compared with the upper bound parameters in the linear system, and are undecidable in general. Finally, we consider a parametric extension of MITL 0,∞ , and prove that the related satisfiability and model checking (w.r.t. L/U automata) problems are PSPACE-complete.

In this paper we present refinement modal logic. A refinement is like a bisimulation, except that from the three relational requirements only 'atoms' and 'back' need to be satisfied. Our logic contains a new operator ∀ in addition to the standard modalities for each agent. The operator ∀ acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier ∀ can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal µ-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness.

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Abstract. We consider the control problem for timed automata against specifications given as MTL formulas. The logic MTL is a linear-time timed temporal logic which extends LTL with timing constraints on modalities, and recently, its model-checking has been proved decidable in several cases. We investigate these decidable fragments of MTL (full MTL when interpreted over finite timed words, and Safety-MTL when interpreted over infinite timed words), and prove two kinds of results.(1) We first prove that, contrary to model-checking, the control problem is undecidable. Roughly, the computation of a lossy channel system could be encoded as a model-checking problem, and we prove here that a perfect channel system can be encoded as a control problem. (2) We then prove that if we fix the resources of the controller (by resources we mean clocks and constants that the controller can use), the control problem becomes decidable. This decidability result relies on properties of well (and better) quasi-orderings.