On the possibilities of FSM description of parallel composition of timed finite state machines

Конечные автоматы широко используются для анализа и синтеза дискретных систем. При описании систем, поведение которых зависит от времени, конечный автомат расширяется введением временных аспектов и вводится понятие временного автомата. В настоящей статье рассматривается проблема построения параллельной композиции для двух моделей временных автоматов, а именно, для автоматов с таймаутами и автоматов с временными ограничениями. Две эти формы временных автоматов не являются взаимозаменяемыми и являются более частными случаями общей модели временного автомата, содержащего как таймауты, так и временные ограничения. Мы также считаем, что все выше упомянутые модели временных автоматов имеют целочисленные выходные задержки (выходные таймауты). Автоматы-компоненты работают в режиме диалога, по завершении которого композиция выдаёт внешний выходной символ. При решении задач анализа для системы взаимодействующих конечных автоматов с использованием классических методов такая композиция обычно описывается единственным автоматом. В работе показывается, что в общем случае, в отличие от случая классических конечных автоматов, наличия «медленной внешней среды» и отсутствия осцилляций недостаточно для описания поведения композиции детерминированным автоматом с одной временной переменной, если входные символы могут поступать не только в целочисленные, но и рациональные моменты времени. Тем не менее, определяется класс систем, в которых каждое внешнее входное воздействие инициирует диалог между компонентами, что позволяет описать поведение такой композиции детерминированным автоматом с одной временной переменной. В частности, рассматривается последовательная композиция временных автоматов, которая удовлетворяет такому ограничению. Другое ограничение продиктовано наличием таймаутов, значение которого в каждом из состояний должно превышать величину выходной задержки при обработке любого перехода в этом состоянии

Bounded Determinization of Timed Automata with Silent Transitions

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. The approach is implemented in a prototype tool and evaluated on several examples. To our best knowledge, this is the first implementation of this type of procedure for timed automata.Comment: 25 page

Reducing Clocks in Timed Automata while Preserving Bisimulation

Model checking timed automata becomes increasingly complex with the increase in the number of clocks. Hence it is desirable that one constructs an automaton with the minimum number of clocks possible. The problem of checking whether there exists a timed automaton with a smaller number of clocks such that the timed language accepted by the original automaton is preserved is known to be undecidable. In this paper, we give a construction, which for any given timed automaton produces a timed bisimilar automaton with the least number of clocks. Further, we show that such an automaton with the minimum possible number of clocks can be constructed in time that is doubly exponential in the number of clocks of the original automaton.Comment: 28 pages including reference, 8 figures, full version of paper accepted in CONCUR 201

Compositional schedulability analysis of real-time actor-based systems

We present an extension of the actor model with real-time, including deadlines associated with messages, and explicit application-level scheduling policies, e.g.,"earliest deadline first" which can be associated with individual actors. Schedulability analysis in this setting amounts to checking whether, given a scheduling policy for each actor, every task is processed within its designated deadline. To check schedulability, we introduce a compositional automata-theoretic approach, based on maximal use of model checking combined with testing. Behavioral interfaces define what an actor expects from the environment, and the deadlines for messages given these assumptions. We use model checking to verify that actors match their behavioral interfaces. We extend timed automata refinement with the notion of deadlines and use it to define compatibility of actor environments with the behavioral interfaces. Model checking of compatibility is computationally hard, so we propose a special testing process. We show that the analyses are decidable and automate the process using the Uppaal model checke

Determinisability of register and timed automata

The deterministic membership problem for timed automata asks whether the timed language given by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. An analogous problem can be stated in the setting of register automata. We draw the complete decidability/complexity landscape of the deterministic membership problem, in the setting of both register and timed automata. For register automata, we prove that the deterministic membership problem is decidable when the input automaton is a nondeterministic one-register automaton (possibly with epsilon transitions) and the number of registers of the output deterministic register automaton is fixed. This is optimal: We show that in all the other cases the problem is undecidable, i.e., when either 1) the input nondeterministic automaton has two registers or more (even without epsilon transitions), or 2) it uses guessing, or 3) the number of registers of the output deterministic automaton is not fixed. The landscape for timed automata follows a similar pattern. We show that the problem is decidable when the input automaton is a one-clock nondeterministic timed automaton without epsilon transitions and the number of clocks of the output deterministic timed automaton is fixed. Again, this is optimal: We show that the problem in all the other cases is undecidable, i.e., when either 1) the input nondeterministic timed automaton has two clocks or more, or 2) it uses epsilon transitions, or 3) the number of clocks of the output deterministic automaton is not fixed.Comment: journal version of a CONCUR'20 paper. arXiv admin note: substantial text overlap with arXiv:2007.0934

Utilization of timed automata as a verification tool for real-time security protocols

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2010Includes bibliographical references (leaves: 85-92)Text in English; Abstract: Turkish and Englishxi, 92 leavesTimed Automata is an extension to the automata-theoretic approach to the modeling of real time systems that introduces time into the classical automata. Since it has been first proposed by Alur and Dill in the early nineties, it has become an important research area and been widely studied in both the context of formal languages and modeling and verification of real time systems. Timed automata use dense time modeling, allowing efficient model checking of time-sensitive systems whose correct functioning depend on the timing properties. One of these application areas is the verification of security protocols. This thesis aims to study the timed automata model and utilize it as a verification tool for security protocols. As a case study, the Neuman-Stubblebine Repeated Authentication Protocol is modeled and verified employing the time-sensitive properties in the model. The flaws of the protocol are analyzed and it is commented on the benefits and challenges of the model