5 research outputs found
Polynomial Interrupt Timed Automata
Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where
reachability and some variants of timed model checking are decidable even in
presence of parameters. They are well suited to model and analyze real-time
operating systems. Here we extend ITA with polynomial guards and updates,
leading to the class of polynomial ITA (PolITA). We prove the decidability of
the reachability and model checking of a timed version of CTL by an adaptation
of the cylindrical decomposition method for the first-order theory of reals.
Compared to previous approaches, our procedure handles parameters and clocks in
a unified way. Moreover, we show that PolITA are incomparable with stopwatch
automata. Finally additional features are introduced while preserving
decidability
Finite Bisimulations for Dynamical Systems with Overlapping Trajectories
Having a finite bisimulation is a good feature for a dynamical system, since it can lead to the decidability of the verification of reachability properties. We investigate a new class of o-minimal dynamical systems with very general flows, where the classical restrictions on trajectory intersections are partly lifted. We identify conditions, that we call Finite and Uniform Crossing: When Finite Crossing holds, the time-abstract bisimulation is computable and, under the stronger Uniform Crossing assumption, this bisimulation is finite and definable
Polynomial interrupt timed automata: Verification and expressiveness
International audienceInterrupt Timed Automata (ITA ) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (PolITA ). We prove that reachability is decidable in 2EXPTIME on PolITA, using an adaptation of the cylindrical algebraic decomposition algorithm for the first-order theory of reals. We also obtain decidability for the model checking of a timed version of CTL and for reachability in several extensions of PolITA. In particular, compared to previous approaches, our procedure handles parameters and clocks in a unified way. We also study expressiveness questions for PolITA and show that PolITA are incomparable with stopwatch automata
Revisiting Reachability in Polynomial Interrupt Timed Automata
International audiencePolynomial Interrupt Timed Automata (PolITA) are finite automata with clocks organized along hierarchical levels. These clocks are equipped with an interruption mechanism, well suited to the modeling of real-time operating systems. Moreover, transitions between states contain polynomial guards and updates. The reachability problem in this class is known to be in 2EXPTIME with a decision procedure based on the cylindrical algebraic decomposition. We improve this complexity to EXPSPACE mainly using a combinatorial argument and we include a reduction leading to a PSPACE lower bound