Specifying real-time properties in autonomic systems

Increasingly, computer software must adapt dynamically to changing conditions. The correctness of adaptation cannot be rigorously addressed without precisely specifying the requirements for adaptation. In many situations, these requirements involve absolute time, in addition to a logical ordering of events. This paper introduces an approach to formally specifying such timing requirements for adaptive software. We introduce TA-LTL, a timed adaptation-based extension to linear temporal logic, and use this logic to specify three timing properties associated with the adaptation process: safety, liveness, and stability. A dynamic adaptation scenario involving interactive audio streaming software is used to illustrate the timed temporal logic. A number of related papers and technical reports of the Software Engineering and Network Systems Laboratory can be found at the following URL: http://www.cse.msu.edu/sens.     

Timer formulas and decidable metric temporal logic

We define a quantitative temporal logic that is based on a simple modality within the framework of monadic predicate logic. Its canonical model is the real line (and not an ω-sequence of some type). It can be interpreted either by behaviors with finite variability or by unrestricted behaviors. For finite variability models it is as expressive as any logic suggested in the literature. For unrestricted behaviors our treatment is new. In both cases we prove decidability and complexity bounds using general theorems from logic (and not from automata theory). The technical proof uses a sublanguage of the metric monadic logic of order, the language of timer normal form formulas. Metric formulas are reduced to timer normal form and timer normal form formulas allow elimination of the metric.     

Specifying coalgebras with modal logic

We propose to use modal logic as a logic for coalgebras and discuss it in view of the work done on coalgebras as a semantics of object-oriented programming. Two approaches are taken: First, standard concepts of modal logic are applied to coalgebras. For a certain kind of functor it is shown that the logic exactly captures the notion of bisimulation and a complete calculus is given. Examples of verifications of object properties are given. Second, we discuss the relationship of this approach with the coalgebraic logic of Moss (Coalgebraic logic, Ann Pure Appl. Logic 96 (1999) 277–317.).     

Specifying safety-critical systems with a decidable duration logic

Punctual timing constraints are important in formal modelling of safety-critical real-time systems. But they are very expensive to express in dense time. In most cases, punctuality and dense-time lead to undecidability. Efforts have been successful to obtain decidability; but the results are either non-primitive recursive or nonelementary. In this paper we propose a duration logic which can express quantitative temporal constraints and punctuality timing constraints over continuous intervals and has a reasonable complexity. Our logic allows most specifications that are interesting in practice, and retains punctuality. It can capture the semantics of both events and states, and incorporates the notions duration and accumulation. We call this logic ESDL (the acronym stands for Event- and State-based Duration Logic). We show that the satisfiability problem is decidable, and the complexity of the satisfiability problem is NEXPTIME. ESDL is one of a few decidable interval temporal logics with metric operators. Through some case studies, we also show that ESDL can specify many safety-critical real-time system properties which were previously specified by undecidable interval logics or their decidable reductions based on some abstractions.     

Specifying a real-time kernel

The application of formal methods to a safety-critical system is illustrated. The objective of the study was to improve the existing documentation of a diagnostic X-ray machine to serve later reimplementations. The separation of the kernel from applications helped identify a design flaw in the kernel that could have caused damage by the X-ray application. The case study which shows that mathematical techniques have an important role to play in documenting systems and avoiding design flaws, is a good example of the use of the Z (pronounced `Zed') notation and its methods for modeling systems. The limitations of this specification are delineated, showing that there is a need for other specification techniques to tackle the remaining properties, like real-time performance, for completeness and comparison     

对称逻辑度量次范整子空间及其性质

在经典逻辑度量空间中定义了加法和数乘运算,利用公式的距离引入了经典逻辑度量空间中的范数的概念,从而证明了经典逻辑度量空间作成线性次范整空间。引入了次范整线性子空间的概念。证明了n元逻辑公式之集中的对称逻辑公式子集构成了次范整线性子空间,并讨论了该子空间的简单性质。     

Formal testing of timed graph transformation systems using metric temporal graph logic

Embedded real-time systems generate state sequences where time elapses between state changes. Ensuring that such systems adhere to a provided specification of admissible or desired behavior is essential. Formal model-based testing is often a suitable cost-effective approach. We introduce an extended version of the formalism of symbolic graphs, which encompasses types as well as attributes, for representing states of dynamic systems. Relying on this extension of symbolic graphs, we present a novel formalism of timed graph transformation systems (TGTSs) that supports the model-based development of dynamic real-time systems at an abstract level where possible state changes and delays are specified by graph transformation rules. We then introduce an extended form of the metric temporal graph logic (MTGL) with increased expressiveness to improve the applicability of MTGL for the specification of timed graph sequences generated by a TGTS. Based on the metric temporal operators of MTGL and its built-in graph binding mechanics, we express properties on the structure and attributes of graphs as well as on the occurrence of graphs over time that are related by their inner structure. We provide formal support for checking whether a single generated timed graph sequence adheres to a provided MTGL specification. Relying on this logical foundation, we develop a testing framework for TGTSs that are specified using MTGL. Lastly, we apply this testing framework to a running example by using our prototypical implementation in the tool AutoGraph.

     

Specifying and detecting temporal patterns with shape expressions

International Journal on Software Tools for Technology Transfer - Modern cyber-physical systems (CPS) and the Internet of things (IoT) are data factories generating, measuring and recording huge...     

Proving linearizability with temporal logic

Linearizability is a global correctness criterion for concurrent systems. One technique to prove linearizability is applying a composition theorem which reduces the proof of a property of the overall system to sufficient rely-guarantee conditions for single processes. In this paper, we describe how the temporal logic framework implemented in the KIV interactive theorem prover can be used to model concurrent systems and to prove such a composition theorem. Finally, we show how this generic theorem can be instantiated to prove linearizability of two classic lock-free implementations: a Treiber-like stack and a slightly improved version of Michael and Scott’s queue.     

Extending statecharts with temporal logic

The task of designing large real-time reactive systems, which interact continuously with their environment and exhibit concurrency properties, is a challenging one. The authors explore the utility of a combination of behavior and function specification languages in specifying such systems and verifying their properties. An existing specification language, statecharts, is used to specify the behavior of real-time reactive systems, while a new logic-based language called FNLOG (based on first-order predicate calculus and temporal logic) is designed to express the system functions over real time. Two types of system properties, intrinsic and structural, are proposed. It is shown that both types of system properties are expressible in FNLOG and may be verified by logical deduction, and also hold for the corresponding behavior specification     

Specifying and verifying requirements of real-time systems

An approach to specification of requirements and verification of design for real-time systems is presented. A system is defined by a conventional mathematical model for a dynamic system where application specific states denote functions of real time. Specifications are formulas in duration calculus, a real-time interval logic, where predicates define durations of states. Requirements define safety and functionality constraints on the system or a component. A top-level design is given by a control law: a predicate that defines an automation controlling the transition between phases of operation. Each phase maintains certain relations among the system states; this is analogous to the control functions known from conventional control theory. The top-level design is decomposed into an architecture for a distributed system with specifications for sensor, actuator, and program components. Programs control the distributed computation through synchronous events. Sensors and actuators relate events with system states. Verification is a deduction showing that a design implies requirements     

Querying datalog programs with temporal logic

Temporal logic queries on Datalog and negated Datalog programs are studied, and their relationship to Datalog queries on these programs is explored. It is shown that, in general, temporal logic queries have more expressive power than Datalog queries on Datalog and negated Datalog programs. It is also shown that anexistential domain-independent fragment of temporal logic queries has the same expressive power as Datalog queries on negated Datalog programs with inflationary semantics. This means that for finite structures this class of queries has the power of the fixpoint logic.     

Specifying causality in action theories: a default logic approach

Recent research on reasoning about action has shown that the traditional logic form of domain constraints is problematic to represent ramifications of actions that are related to causality of domains. To handle this problem properly, as proposed by some researchers, it is necessary to describe causal relations of domains explicitly in action theories. In this paper, we address this problem from a new point of view. Specifically, unlike other researchers viewing causal relations as some kind of inference rules, we distinguish causal relations between defeasible and non-defeasible cases. It turns out that a causal theory in our formalism can be specified by using Reiter's default logic. Based on this idea, we propose a causality-based minimal change approach for representing effects of actions, and argue that our approach provides more plausible solutions for the ramification and qualification problems compared with other related work. We also describe a logic programming approximation to compute causal theories of actions which provides an implementational basis for our approach.     

Fuzzy branching temporal logic

Intelligent systems require a systematic way to represent and handle temporal information containing uncertainty. In particular, a logical framework is needed that can represent uncertain temporal information and its relationships with logical formulae. Fuzzy linear temporal logic (FLTL), a generalization of propositional linear temporal logic (PLTL) with fuzzy temporal events and fuzzy temporal states defined on a linear time model, was previously proposed for this purpose. However, many systems are best represented by branching time models in which each state can have more than one possible future path. In this paper, fuzzy branching temporal logic (FBTL) is proposed to address this problem. FBTL adopts and generalizes concurrent tree logic (CTL*), which is a classical branching temporal logic. The temporal model of FBTL is capable of representing fuzzy temporal events and fuzzy temporal states, and the order relation among them is represented as a directed graph. The utility of FBTL is demonstrated using a fuzzy job shop scheduling problem as an example.     

Mining parametric temporal logic properties in model-based design for cyber-physical systems

International Journal on Software Tools for Technology Transfer - One of the advantages of adopting a model-based development process is that it enables testing and verification at early stages of...     

Extending hoare logic to real-time

Classical Hoare triples are modified to specify and design distributed real-time systems. The assertion language is extended with primitives to express the timing of observable actions. Further the interpretation of triples is adapted such that both terminating and nonterminating computations can be specified. To verify that a concurrent program, with message passing along asynchronous channels, satisfies a real-time specification, we formulate a compositional proof system for our extended Hoare logic. The use of compositionality during top-down design is illustrated by a process control example of a chemical batch processing system.     

Extending hoare logic to real-time

Classical Hoare triples are modified to specify and design distributed real-time systems. The assertion language is extended with primitives to express the timing of observable actions. Further the interpretation of triples is adapted such that both terminating and nonterminating computations can be specified. To verify that a concurrent program, with message passing along asynchronous channels, satisfies a real-time specification, we formulate a compositional proof system for our extended Hoare logic. The use of compositionality during top-down design is illustrated by a process control example of a chemical batch processing system.