Weak Alternating Timed Automata

Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for MITL, the characterisation remains the same even if no punctual constraints are allowed

Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems

The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem for the system of probabilistic ITL with respect to an abstract semantics and a relative completeness theorem for the system of probabilistic DC with respect to real-time semantics. The proposed systems subsume probabilistic real-time DC as known from the literature. A correspondence between the proposed systems and a system of probabilistic interval temporal logic with finite intervals and expanding modalities is established too.Comment: 43 page

On the completeness and decidability of duration calculus with iteration

AbstractThe extension of the duration calculus (DC) by iteration, which is also known as Kleene star, enables the straightforward specification of repetitive behaviour in DC and facilitates the translation of design descriptions between DC, timed regular expressions and timed automata. In this paper we present axioms and a proof rule about iteration in DC. We consider abstract-time DC and its extension by a state-variable binding existential quantifier known as higher-order DC (HDC). We show that the ω-complete proof systems for DC and HDC known from our earlier work can be extended by our axioms and rule in various ways in order to axiomatise iteration completely. The additions we propose include either the proof rule or an induction axiom. We also present results on the decidability of a subset of the extension DC* of DC by iteration

State Estimation of Timed Discrete Event Systems and Its Applications

Many industrial control systems can be described as discrete event systems (DES), whose state space is a discrete set where event occurrences cause transitions from one state to another. Timing introduces an additional dimension to DES modeling and control. This dissertation provides two models of timed DES endowed with a single clock, namely timed finite automata (TFA) and generalized timed finite automata (GTFA). In addition, a timing function is defined to associate each transition with a time interval specifying at which clock values it may occur. While the clock of a TFA is reset to zero after each event occurs and the time semantics constrain the dwell time at each discrete state, there is an additional clock resetting function associated with a GTFA to denote whether the clock is reset to a value in a given closed time interval. We assume that the logical and time structure of a partially observable TFA/GTFA is known. The main results are summarized as follows. 1. The notion of a zone automaton is introduced as a finite automaton providing a purely discrete event description of the behaviour of a TFA/GTFA of interest. Each state of a zone automaton contains a discrete state of the timed DES and a zone that is a time interval denoting a range of possible clock values. We investigate the dynamics of a zone automaton and show that one can reduce the problem of investigating the reachability of a given timed DES to the reachability analysis of a zone automaton. 2. We present a formal approach that allows one to construct offline an observer for TFA/GTFA, i.e., a finite structure that describes the state estimation for all possible evolutions. During the online phase to estimate the current discrete state according to each measurement of an observable event, one can determine which is the state of the observer reached by the current observation and check to which interval (among a finite number of time intervals) the time elapsed since the last observed event occurrence belongs. We prove that the discrete states consistent with a timed observation and the range of clock values associated with each estimated discrete state can be inferred following a certain number of runs in the zone automaton. In particular, the state estimation of timed DES under multiple clocks can be investigated in the framework of GTFA. We model such a system as a GTFA with multiple clocks, which generalizes the timing function and the clock resetting function to multiple clocks. 3. As an application of the state estimation approach for TFA, we assume that a given TFA may be affected by a set of faults described using timed transitions and aim at diagnosing a fault behaviour based on a timed observation. The problem of fault diagnosis is solved by constructing a zone automaton of the TFA with faults and a fault recognizer as the parallel composition of the zone automaton and a fault monitor that recognizes the occurrence of faults. We conclude that the occurrence of faults can be analyzed by exploring runs in the fault recognizer that are consistent with a given timed observation. 4. We also study the problem of attack detection in the context of DESs, assuming that a system may be subject to multiple types of attacks, each described by its own attack dictionary. Furthermore, we distinguish between constant attacks, which corrupt observations using only one of the attack dictionaries, and switching attacks, which may use different attack dictionaries at different steps. The problem we address is detecting whether a system has been attacked and, if so, which attack dictionaries have been used. To solve it in the framework of untimed DES, we construct a new structure that describes the observations generated by a system under attack. We show that the attack detection problem can be transformed into a classical state estimation/diagnosis problem for these new structures

On the Design of Hybrid Control Systems Using Automata Models

. The paper gives a systematic way for the development of hybrid control systems, i.e. to refine specifications written in DC (Duration Calculus) into automata models. Firstly, DC formulas are extended with iteration form and a technique for deriving plant automata from DC formulas is presented. Then, a specification of control automata can be synthesized from plant automata with respect to requirements , based on a necessary and sufficient condition for a plant automaton and a requirement to have a control automaton. Water tank and Gas burner examples are demonstrated to illustrate our method. 1 Introduction In this paper, we shall deal with hybrid control systems which consist of continuous plants controlled by decision makers via controllers. Typical hybrid systems can be found widely in the areas of robots, process control, aviation and so on. Because of safety critical properties of these systems, many efforts have been involved from computing science and control theory to get a..