Safety analysis of timing properties in real-time systems

Abstract

A~stract-Two important characteristics of time-critical systems are: the requirement to satisfy stringent timing constraints, and the need to guard against an, imperfect execution environment. In this paper, we formalize the safety analysis of timing properties in real-time syste~s. Our analysis is based on a formal logic: RTL (Real-Time Logic) which is especially suitable for reasoning about the timing behavior of systems. Given the for~al specification of a~ystem a~d a safety assertion to be analyzed, our goal is to relate the safety assertion to the systems specification. There are three distinct eases: 1) the safety assertion is, a theorem derivable from the systems specification, 2) the safety assertion is,~nsatisfia~le with respect to the systems specification, or 3) the negation of the safety assertion is satisfiable under certain conditions. A systematic method for performing safety analysis will be presented.'

Specification and verification of reactive system behaviour: The Railroad Crossing example

“…Real Time Logic [8], [7] is a formal logic for reasoning about the timing behaviour of real-time systems. It deals with time quantitatively, and so has no modal operators.…”

“…We use Proofpower HOL [6], though any prover in which RTL can be axiomatised is suitable. By using RTL we have adopted the event-action model of computation as proposed by [8].…”

Yeast: A case study for a practical use of formal methods

“…And since time in Yeast applications can be considered discrete, we model time explicitly in the operational semantics. Thus, time events axe ordered, and for each pair e, e I of time events such that e ~ is a immediate successor of e in the (total) timing ordering, a rule of the form S, E (9 e ct~ S, E (9 e I is considered 9 Some actions are identified to be external, i.e. actions that a user or an external agent may perform.…”

“…We use this result here in order to derive a Petri net representation for Yeast specifications. As has been pointed out earlier, Petri nets provide a natural representation, since the properties we want to check involve causal dependencies among events and require a clear distinction between nondeterminism and concurrency 9 Masty proposals have been made for Real-time Petri nets (see for example [2]). Timed Petri nets are more complex than the model we are proposing 9 Here, the clock is considered a process that updates the events associated with time.…”

“…In fact, no "dead places" (i.e. places with no outgoing transitions) are taken into account 9 We first show how to specialize the meta-rule given in the previous section to a particular set of Yeast specifications.…”