ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

Decidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata

Abstract: We define a new class of hybrid automata for which reachability is decidable--a proper superclass of the initialized rectangular hybrid automata--by taking parallel compositions of simple components. Attempting to generalize, we encounter timed automata with algebraic constants. We show that reachability is undecidable for these algebraic timed automata by simulating two-counter Minsky machines. Modifying the construction to apply to parametric timed automata, we reprove the undecidability of the emptiness problem, and then distinguish the dense and discrete-time cases with a new result. The algorithmic complexity-- both classical and parametric--of one-clock parametric timed automata is also examined. We finish with a table of computability-theoretic complexity results, including that the existence of a Zeno run is Σ11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.

Constructing Büchi automata from linear temporal logic using simulation relations for alternating Büchi automata

Abstract: We present a new procedure for the translation of propositional linear-time temporal logic (LTL) formulas to equivalent nondeterministic Buchi automata. Our procedure is based on simulation relations for alternating Buchi automata. Whereas most of the procedures that have been described in the past compute simulation relations in the last step of the translation (after a nondeterministic Buchi automaton has already been constructed), our procedure computes simulation relations for alternating Buchi automata in an early stage and uses them in an on the-fly fashion. This decreases the time and space consumption without sacrificing the potential of simulation relations. We present experimental results that demonstrate the advantages of our approach: Our procedure is faster than TMP but produces, on the average, automata of about the same size; LTL2BA is faster than our procedure but produces larger automata.

Use of Stochastic Automata for Parameter Self-Optimization with Multimodal Performance Criteria

Abstract: The application of stochastic automata to adaptive parameter optimization problems is considered. The fundamental problem is that of relating the concepts of automata theory and mathematical psychology learning theory to the usual notion of a performance index in a control system. Consideration is given to a number of possible automata structures, linear and nonlinear. One particular linear model is derived with optimal rather than expedient properties of convergence. A basic feature of this model is that it is based on a system response set of rewards and inactions, the latter being substituted for the more common penalty responses. This choice of response set is directly related to the achievement of the desired behavior. Simulations are described for the maximization of multimodal performance functions intentionally constructed to demonstrate the use of the method in situations where relative extrema occur. An example is also given of the automaton as a direct adaptive controller for a third order control system.

On Logics, Tilings, and Automata

Abstract: We relate the logical and the automata theoretic approach to define sets of words, trees, and graphs. For this purpose a notion of “graph acceptor” is introduced which can specify monadic second-order properties and allows to treat known types of finite automata in a common framework. In the final part of the paper, we discuss infinite graphs that have a decidable monadic second-order theory.