Revisiting Reachability in Timed Automata

We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a new and simpler proof of this result, building on the well-known reachability analysis of timed automata involving difference bound matrices. Using this new proof, we give an exponential-space procedure for model checking the reachability fragment of the logic parametric TCTL. Finally we show that the latter problem is NEXPTIME-hard

Register Set Automata (Technical Report)

We present register set automata (RsAs), a register automaton model over data words where registers can contain sets of data values and the following operations are supported: adding values to registers, clearing registers, and testing (non-)membership. We show that the emptiness problem for RsAs is decidable and complete for the $F_\omega$ class. Moreover, we show that a large class of register automata can be transformed into deterministic RsAs, which can serve as a basis for (i) fast matching of a family of regular expressions with back-references and (ii) language inclusion algorithm for a sub-class of register automata. RsAs are incomparable in expressive power to other popular automata models over data words, such as alternating register automata and pebble automata

A compositional analysis of broadcasting embedded systems

This work takes as its starting point D Kendall's CANdle/bCANdle algebraic framework for formal modelling and specification of broadcasting embedded systems based on CAN networks. Checking real-time properties of such systems is beset by problems of state-space explosion and so a scheme is given for recasting systems specified in Kendall's framework as parallel compositions of timed automata; a CAN network channel is modelled as an automaton. This recasting is shown to be bi-similar to the original bCANdle model. In the recast framework,"compositionality" theorems allow one to infer that a model of a system is simulated by some abstraction of the model, and hence that properties of the model expressible in ACTL can be inferred from analogous properties of the abstraction. These theorems are reminiscent of "assume-guarantee" reasoning allowing one to build simulations component-wise although, unfortunately, components participating in a "broadcast" are required to be abstracted "atomically". Case studies are presented to show how this can be used in practice, and how systems which take impossibly long to model-check can tackled by compositional methods. The work is of broader interest also, as the models are built as UPPAAL systems and the compositionality theorems apply to any UPPAAL system in which the components do not share local variables. The method could for instance extend to systems using some network other than CAN, provided it can be modelled by timed automata. Possibilities also exist for building it into an automated tool, complementing other methods such as counterexample- guided abstraction refinement

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Sequence-Based Specification of Embedded Systems

Software has become integral to the control mechanism of modern devices. From transportation and medicine to entertainment and recreation, embedded systems integrate fundamentally with time and the physical world to impact our lives; therefore, product dependability and safety are of paramount importance. Model-based design has evolved as an effective way to prototype systems and to analyze system function through simulation. This process mitigates the problems and risks associated with embedding software into consumer and industrial products. However, the most difficult tasks remain: Getting the requirements right and reducing them to precise specifications for development, and providing compelling evidence that the product is fit for its intended use. Sequence-based specification of discrete systems, using well-chosen abstractions, has proven very effective in exposing deficiencies in requirements, and then producing precise specifications for good requirements. The process ensures completeness, consistency, and correctness by tracing each specification decision precisely to the requirements. Likewise, Markov chain based testing has proven effective in providing evidence that systems are fit for field use. Model-based designs integrate discrete and continuous behavior; models have both hybrid and switching properties. In this research, we extend sequence-based specification to explicitly include time, continuous functions, nondeterminism, and internal events for embedded real-time systems. The enumeration is transformed into an enumeration hybrid automaton that acts as the foundation for an executable model-based design and an algebraic hybrid I/O automaton with valuable theoretical properties. Enumeration is a step-wise problem solving technique that complements model-based design by converting ordinary requirements into precise specifications. The goal is a complete, consistent, and traceably correct design with a basis for automated testing