Dang Van Hung

Checking Linear Duration Invariants by Linear Programming

In this paper, the problem of verifying a timed automaton for a Duration Calculus formula in the form of linear duration invariants

Prefix and Projection onto State in Duration Calculus

Abstract We study a new operator of projection onto state and the prefix operator in the extension μHDC of DC by quantifiers over state and a polyadic least fixed point operator. We give axioms and rules to enable deduction in the extension of μHDC by the new operators. Our axioms can be used to eliminate the new operators from formulas in a practically significant fragment of μHDC. This entails the decidability of certain subfragments of this fragment is preserved in the presence of the new operators.

Checking Hybrid Automata for Linear Duration Invariants

In this paper, we consider the problem of checking hybrid systems modelled by hybrid automata for a class of real-time properties represented by linear duration invariants, which are constructed from linear inequalities of integrated durations of system states. Based on linear programming, an algorithm is developed for solving the problem for a class of hybrid automata.

Completeness and Decidability of a Fragment of Duration Calculus with Iteration

Duration Calculus with Iteration (DC*) has been used as an interface between original Duration Calculus and Timed Automata, but has not been studied rigorously. In this paper, we study a subset of DC* formulas consisting of so-called simple ones which corresponds precisely with the class of Timed Automata. We give a complete proof system and the decidability results for the subset.

Checking temporal duration properties of timed automata

In this paper, the problem of checking a timed automaton for a Duration Calculus formula of the form Temporal Duration Property is addressed. It is shown that Temporal Duration Properties are in the class of discretisable real-time properties of Timed Automata, and an algorithm is given to solve the problem based on linear programming techniques and the depth-first search method in the integral region graph of the automaton. The complexity of the algorithm is in the same class as that of the solution of the reachability problem of timed automata.

On the completeness and decidability of duration calculus with iteration

The 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.

A Relatively Complete Axiomatisation of Projection onto State in the Duration Calculus

We present a complete axiomatisation of the operator of projection onto state in the Duration Calculus (DC) relative to validity in DC without extending constructs. Projection onto state was introduced and studied extensively in our earlier works. We first establish the completeness of a system of axioms and proof rules for the operator relative to validity in the extension of DC by neighbourhood formulas, which express the neighbourhood values of boolean DC state expressions. By establishing a relatively complete axiomatisation for the neighbourhood formulas in DC, we then achieve completeness of our system relative to basic DC.

Checking timed automata for linear duration properties

It is proved in this paper that checking a timed automaton ℳ with respect to a linear duration property ⊅ can be done by investigating only the integral timed states of ℳ. An equivalence relation is introduced in this paper to divide the infinite number of integral timed states into finite number of equivalence classes. Based on this, a method is proposed for checking whether ℳ satisfies ⊅. In some cases, the number of equivalence classes is too large for a computer to manipulate. A technique for reducing the search-space for checking linear duration property is also described. This technique is more, suitable for the case in this paper than those in the literature because most of those techniques are designed for reachability analysis.

Reasoning about QoS Contracts in the Probabilistic Duration Calculus

The notion of contract was introduced to component-based software development in order to facilitate the semantically correct composition of components. We extend the form of this notion which is based on designs to capture probabilistic requirements on execution time. We show how reasoning about such requirements can be done in an infinite-interval-based system of probabilistic duration calculus.

Formal Analysis of Streaming Downloading Protocol for System Upgrading

For a PC-mobile download system which is embedded with streaming download protocol, there are problems that the data cannot be transmitted correctly from the PC to the mobile, or the transmission is unacceptably slow. To solve these problems, we carry out a formal analysis for the protocol with some timing parameters and a given probability of message loss and unordered data using a probabilistic model checking tool PRISM. We introduce a technique to reduce the state space of the system modeling the protocol which is a network of probabilistic timed automata. The experimental results in PRISM give us a clear explanation to the problems, and are helpful in identifying the optimal parameter settings to meet industrial requirements.