Abstract. We propose and evaluate a new algorithm for checking the universality of nondeterministic finite automata. In contrast to the standard algorithm, which uses the subset construction to explicitly determinize the automaton, we keep the determinization step implicit. Our algorithm computes the least fixed point of a monotone function on the lattice of antichains of state sets. We evaluate the performance of our algorithm experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, the antichain algorithm outperforms the standard one by several orders of magnitude. We also show how variations of the antichain method can be used for solving the language-inclusion problem for nondeterministic finite automata, and the emptiness problem for alternating finite automata.
Abstract. In this paper, we introduce a parametric semantics for timed controllers called the Almost ASAP semantics. This semantics is a relaxation of the usual ASAP semantics (also called the maximal progress semantics) which is a mathematical idealization that can not be implemented by any physical device no matter how fast it is. On the contrary, any correct Almost ASAP controller can be implemented by a program on a hardware if this hardware is fast enough. We study the properties of this semantics, show how it can be analyzed using the tool HyTech, and illustrate its practical use on examples.
Abstract. In this paper, we propose a fixed point theory to solve games of imperfect information. The fixed point theory is defined on the lattice of antichains of sets of states. Contrary to the classical solution proposed by Reif [Rei84], our new solution does not involve determinization. As a consequence, it is readily applicable to classes of systems that do not admit determinization. Notable examples of such systems are timed and hybrid automata. As an application, we show that the discrete control problem for games of imperfect information defined by rectangular automata is decidable. This result extends a result by Henzinger and Kopke in [HK99].
The linear temporal logic (LTL) was introduced by Pnueli as a logic to express properties over the computations of reactive systems. Since this seminal work, there have been a large number of papers that have studied deductive systems and algorithmic methods to reason about the correctness of reactive programs with regard to LTL properties. In this paper, we propose new efficient algorithms for LTL satisfiability and model-checking. Our algorithms do not construct nondeterministic automata from LTL formulas but work directly with alternating automata using efficient exploration techniques based on antichains.
Abstract. In this paper, we introduce a parametric semantics for timed controllers called the Almost ASAP semantics. This semantics is a relaxation of the usual ASAP semantics (also called the maximal progress semantics) which is a mathematical idealization that can not be implemented by any physical device no matter how fast it is. On the contrary, any correct Almost ASAP controller can be implemented by a program on a hardware if this hardware is fast enough. We study the properties of this semantics, show how it can be analyzed using the tool HyTech, and illustrate its practical use on examples.
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