Real-Time: Theory in Practice

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2001

[lo], TILCO [5], Temporal logics are typically used for the specification Logic-based languages for modeling temporal constraints can be based on time points, or on time in-Of systems since they are capable Of describing tempora1 constraints among events and actions: tervals. For a review, please see [Ill. Interval logic formulE have typically a higher level of abstraction, properties of invariance, precedence, periodicity, re-These logics usually have specific operators to express peated occurrences, liveness and safety conditions, etc. the between intervals (meet, before, This paper describes an Of the Tempora1 Int e r) , operators to combine intervals (e.g,, the chop operator), or operator? that specify the interval that con-terval Logic called TILCO. TILCO is based on time inwith time In this paper, TILCO-X extension logics are typically concise than point-based tern-tervals and can express tempora1 constraints stitutes the context of temporal formulE [123. Interval Of 's presented' proposes two new poral logics for the specification of real-time systems. operators that strongly increase conciseness and readability of specifications to allow describing (i) the ternporal ordering of events without distinction between According to [5i 1 where logic (Ternwith ComPositional Operators) Poral Interva1 past and future, and (ii) predicates depending on the has been presented by the authors, it has been shown number of Occurrences of events in intervals, TILCO-that none of the temporal logics presented in the past is capable to describe specifications by using a lower number of quantifications and of nesting levels betweed temporal This paper also presents the semantics of TILCO-X and related examples showing the few years is completely satisfactory for real-time system specification. In fact, most of them have no metric for time, thus allowing only specification of qualitative temporal requirementse.g., [2], [13], [4]. In the litpower of the model proposed in terms of conciseness, erature, only a few examples of quantitative temporal Index formal specification language, first or-logics exist. In these cases, an operator expressing the der logic, temporal interval logic, verification and validation, real-time systems, temporal operators. distance between time points is usually defined. Those first-order temporal logics that provide a metric for time usually allow quantification over the temporal domaine.g., RTL, MTL, T R I O [ll]-whereas a prohibition of this kind of quantification has been shown F~~ the specification of system behavior many to be a necessary condition for the existence of feasifactors have to be considered, ~~~i~~l l~, their specifi-ble automated verification mechanisms [14]. All these cation includes the definition of a set of relationships temporal logics are based on time points and provide a expressing the temporal constraints among events and sharp distinction between past and future. In that conactions [I] : properties of invariance, precedence among ditions, when a simple constraints imposes its validity events, periodicity, liveness and safety conditions, etc. always it has to be specified by using three different T~ this end, many temporal logics for temporal rea-pieces: one for the past, one for the current evaluation soning have been proposed; e.g., [a], [SI. [4], [5], [GI, time instant and one for the future. TILCO does not allow the quantification over time and present unique Several different temporal logics with different de-Operators to Specify the events and action from past to grees of expressiveness have been proposed. Some of future. them are based on propositional logice.g., PTL [a], The authors defined TILCO temporal logic in order T P T L [7], RTTL, ITLand adopt the 0 and op-to cover the above-mentioned problems, with a special erators. Other logics are based on first or higher order emphasis on temporal logic expressiveness and conlogice.g., TRIO [8], MTL [9], interval temporal logic ciseness for the specification of real-time systems 151.

TENCON '91. Region 10 International Conference on EC3-Energy, Computer, Communication and Control Systems

Temporal logic is widely acclaimed to be a highly successful tool for analyzing non-real-time properties of programs. However, a few fundamental problems arise while designing temporal logic-based techniques to verify real-time properties of programs. In this context, we formulateamodallogiccalleddishibufed Iogic (DL) byusingideas from both the interleaving and partial ordering approach. This logic uses spatial modal operators in addition to temporal operators for representing real-timed concurrency. In additikn to the syntax and semantics of the logic, a programming model, and a formal proof technique based on the logic are also presented. FmaUy, use of the proof method is illustrated through the analysis of the real-time properties of a generic multiprocess producer/consumer program.

Real-Time Systems, 1992

A substantially large class of programs operate in distributed and real-time environments, and an integral part of their correctness specification requires the expression of time-critical properties that relate the occurrence of events of the system. We focus on the formal specification and reasoning about the correctness of such programs. We propose a system of temporal logic, RTCI'L (Real-Time Computation Tree Logic), that allows the melding of qualitative temporal assertions together with real-time constraints to permit specification and reasoning at the twin levels of abstraction: qualitative and quantitative. We argue that many practically useful correctness properties of temporal systems, which need to express timing as an essential part of their functionality requirements, can be expressed in RTCTL. We develop a model-checking algorithm for RTCTL whose complexity is linear in the size of the RTCTL specification formula and in the size of the structure. We also present an essentially optimal, exponential time tableau-based decision procedure for the satisfiability of RTCTL formulae. Finally, we consider several variants and extensions of RTCTL for real-time reasoning.

Science of Computer Programming, 1993

Embedding time granularity in a logical specification language for synchronous real-time systems, Science of Computer Programming 20 (1993) 141-171. Formal methods have proved to be highly beneficial in the requirements specification phase of software production and are particularly valuable in the development of real-time applications (the most critical software systems). Unfortunately, most common specification languages are inadequate for real-time applications because they lack a quantitative representation of time. In this paper, we define a logical language to specify the temporal constraints of the wide-ranging class of real-time systems whose components have dynamic behaviours regulated by very different time constants. We motivate the need for allowing the consistent treatment of different time scales in formal specifications of these systems with the purpose of enhancing the naturalness and practical usability of the notation. The logical specification language is based on a revised version of the specification language TRIO. We first present the features of the basic logical language; then, we semantically and axiomatically define its granularity extension in a topological logic framework. Finally, we show some examples of its application.