Timed Transition Systems Research Articles

Conformance Tests for Real-Time Systems with Timed Automata Specifications

Abstract. A method is introduced for testing the conformance of implemented real-time systems to timed automata specifications. Uppaal timed automata are transformed into testable timed transition systems (TTTSs) using a test view. Fault hypotheses and a test generation algorithm for TTTSs are defined. Results of applying the method are presented.

Model checking on timed-event structures

We propose a new style of model checking of timed transition systems, where instead of reasoning about the timing of states with specific properties, we reason about the timings of events with specific properties. This shift in paradigm appears to be useful for verification of edge triggered control paths, where we are more interested in the timings of changes in signal values. We propose a temporal logic, event-triggered timed computation tree logic (ETCTL), which allows the specification of event properties such as posedge(signal) and negedge(signal) along with real time computation tree logic (RTCTL) properties. We show that all ETCTL properties are interval independent, that is, their truth can never change on states between successive events. By virtue of the interval independent property, reasoning about timings of events (using ETCTL) is more efficient computationally than reasoning about general timed properties. We present a labeling algorithm, and suggest extensions to automata theoretic and symbolic approaches.

Event-clock automata: a determinizable class of timed automata

We introduce event-recording automata. An event-recording automaton is a timed automaton that contains, for every event a, a clock that records the time of the last occurrence of a. The class of event-recording automata is, on one hand, expressive enough to model (finite) timed transition systems and, on the other hand, determinizable and closed under all boolean operations. As a result, the language-inclusion problem is decidable for event-recording automata. We present a translation from timed transition systems to event-recording automata, which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors. We also consider event-predicting automata, which contain clocks that predict the time of the next occurrence of an event. The class of event-clock automata, which contain both event-recording and event-predicting clocks, is a suitable specification language for real-time properties. We provide an algorithm for checking if a timed automaton meets a specification that is given as an event-clock automaton.

Bisimulation and Open Maps for Timed Transition Systems

Formal models for real-time systems have been studied intensively over the past decade. Much of the theory of untimed systems have been lifted to real-time settings. One example is the notion of bisimulation applied to timed transition systems, which is studied here within the general categorical framework of open maps. We define a category of timed transition systems, and show how to characterise standard timed bisimulation in terms of spans of open maps with a natural choice of a path category. This allows us to apply general results from the theory of open maps, e.g. the existence of canonical models and characteristic logics. Also, we obtain here an alternative proof of decidability of bisimulation for finite transition systems, and illustrate the use of open maps in finite presentations of bisimulations

Timed Bisimulation and Open Maps

Formal models for real-time systems have been studied intensively over the past decade. Much of the theory of untimed systems has been lifted to real-time settings. One example is the notion of bisimulation applied to timed transition systems, which is studied here within the general categorical framework of open maps. We define a category of timed transition systems, and show how to characterize standard timed bisimulation in terms of spans of open maps with a natural choice of a path category. This allows us to apply general results from the theory of open maps, e.g. the existence of canonical models and characteristic logics. Also, we obtain here an alternative proof of decidability of bisimulation for finite transition systems, and illustrate the use of open maps in finite presentations of bisimulations

A Formal Approach to Real-Time Object Oriented Software

The ARTS paradigm involves a friendly user plane, where object oriented designs take place, and a corresponding formal plane where user decisions are verified, and which allows for early prototyping. The approach adopted for modelling real-time aspects (timed transition systems for the object’s life-cycle specification) relies on an extension of Henzinger’s Timed Transition Systems and Chang’s Metric Temporal Logic with δ-operators in the style of Segerberg, and actions modelling methods and message passing.

Timed rewriting logic with an application to object-based specification

In this paper timed rewriting logic is presented and its application to the specification of real-time object-oriented systems is shown by an example. Time rewriting logic (TRL) is an extension of Meseguer's rewriting logic. The functional and the static properties of a system are described by algebraic specifications, whereas the behaviour of a process is described by nondeterministic term rewriting where each rewriting step is labelled by a time stamp or a time interval. Thus our approach is similar to timed transition systems and can be seen as a generalization of timed automata combined with algebraic specifications. The approach is illustrated by several examples, such as clocks, time out and timer. As the main application we present Timed Maude, an object-based specification language for real-time concurrent systems. Timed Maude is a timed variant of Meseguer's language Maude which is based on rewriting logic. The algebraic specification part and the module part of Maude are kept unchanged in Timed Maude, only concurrent rewriting is replaced by TRL.

SEMANTICS OF TIMED CONCURRENT SYSTEMS

A truly concurrent and timeless semantics is proposed for a composition of sequential, non-deterministic processes with asynchronous communication. It is shown when this semantics differs from simple interleaving. Implementation-dependent time constraints determine a subset of all computations of the timeless semantics. This set is precisely characterized for given constraints. It is shown how the same set may be generated by a timed transition system, i.e., how to simulate time-constrained and concurrent computations by sequential, non-deterministic system. The paper includes a proof of the correctness of such simulation.

Parametric Timing Analysis for Real-Time Systems

We extend a TCTL model-checking problem to a parametric timing analysis problem for real-time systems and develop new techniques for solving it. The algorithm we present here accepts timed transition system descriptions and parametric TCTL formulas with timing parameter variables of unknown sizes and can give back general linear equations of timing parameter variables whose solutions make the systems work.

Algebra of timed frames

Timed frames are introduced as objects that can form a basis of a model theory fsor discrete time process algebra. An algebraic setting for timed frames is proposed and results ;oncerning its connection with discrete time process algebra are given. The presented theory o c timed frames captures the basic algebraic properties of timed transition systems for the re1a:ive time case. Further structure on timed frames is provided by adding signal inserted states and conditional transitions, thus giving a semantic basis for discrete time process algebra with propositional signals. Time conditions are introduced to cover the absolute time case.

Metric temporal logic with durations

We present a formal framework based on metric temporal logic (MTL) for specifying and verifying real-time systems with a continuous environment. Metric temporal logic is extended to allow specification of properties about duration of system's states. We prove that every formula of the duration calculus (DC) can be translated into an equivalent MTL-∫, formula. Expressiveness of DC and MTL-∫ are compared. We formulate axioms for MTL-∫ and a sound rule for proving duration properties of timed transition systems.

Temporal Proof Methodologies for Timed Transition-Systems

We extend the specification language of temporal logic, the corresponding verification framework, and the underlying computational model to deal with real-;time properties of reactive systems. The abstract notion of timed transition systems generalizes traditional transition systems conservatively: qualitative fairness requirements are replaced (and superseded) by quantitative lower-bound and upper-bound timing constraints on transitions. This framework can model real-time systems that communicate either through shared variables or by message passing and real-time issues such as timeouts, process priorities (interrupts), and process scheduling. We exhibit two styles for the specification of real-time systems. While the first approach uses time-bounded versions of the temporal operators, the second approach allows explicit references to time through a special clock variable. Corresponding to the two styles of specification, we present and compare two different proof methodologies for the verification of timing requirements that are expressed in these styles. For the bounded - operator style, we provide a set of proof rules for establishing bounded-invariance and bounded-responce properties of timed transition systems. This approach generalizes the standard temporal proof rules for verifying invariance and response properties conservatively. For the explicit - clock style, we exploit the observation that every time-bounded property is a safety property and use the standard temporal proof rules for establishing safety properties.

An embedding of Timed Transition Systems in HOL

An embedding of Timed Transition Systems in HOL