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Completeness and decidability of a fragment of duration calculus with iteration
 Presented at International Conference on Mathematical Foundation of Informatics, Hanoi
, 1999
"... Abstract. Duration Calculus with Iteration (DC ∗ ) has been used as an interface between original Duration Calculus and Timed Automata, but has not been studied rigorously. In this paper, we study a subset of DC ∗ formulas consisting of socalled simple ones which corresponds precisely with the clas ..."
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Cited by 14 (10 self)
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Abstract. Duration Calculus with Iteration (DC ∗ ) has been used as an interface between original Duration Calculus and Timed Automata, but has not been studied rigorously. In this paper, we study a subset of DC ∗ formulas consisting of socalled simple ones which corresponds precisely with the class of Timed Automata. We give a complete proof system and the decidability results for the subset. Keywords: RealTime system, formal methods, Duration Calculus, completeness, decidability.
A Duration Calculus with Infinite Intervals
 In Fundamentals of Computation Theory, Horst Reichel (Ed.), pages 1641. LNCS 965
, 1995
"... Abstract. This paper introduces infinite intervals into the Duration Calculus [32]. The extended calculus defines a state duration over an infinite interval by a property which specifies the limit of the state duration over finite intervals, and excludes the description operator. Thus the calculus c ..."
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Cited by 13 (2 self)
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Abstract. This paper introduces infinite intervals into the Duration Calculus [32]. The extended calculus defines a state duration over an infinite interval by a property which specifies the limit of the state duration over finite intervals, and excludes the description operator. Thus the calculus can be established without involvement of unpleasant calculation of infinity. With limits of state durations, one can treat conventional liveness and fairness, and can also measure liveness and fairness through properties of limits. Including both finite and infinite intervals, the calculus can, in a simple manner, distinguish between terminating behaviour and nonterminating behaviour, and therefore directly specify and reason about sequentiality. 1
Duration Calculus Specification of Scheduling for Tasks with Shared Resources
 LNCS 1023, SpringerVerlag
, 1995
"... This paper presents a formalization in the duration calculus (DC) of scheduling policies for tasks with shared resources. Two frameworks are presented for specifying classes of schedulers. With these specifications, some properties of these schedulers were proved using the formal deduction of DC. Th ..."
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Cited by 6 (4 self)
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This paper presents a formalization in the duration calculus (DC) of scheduling policies for tasks with shared resources. Two frameworks are presented for specifying classes of schedulers. With these specifications, some properties of these schedulers were proved using the formal deduction of DC. This paper aims to encourage other researchers to formally treat realtime aspects of operating systems which in the past were conventionally a piece of ad hoc territory in computer science. Philip Chan is a Fellow of UNU/IIST, on leave from the Department of Software Technology, College of Computer Studies, De La Salle University, Manila, Philippines, where he is an assistant professor. His current research interests include operating systems, distributed operating systems, and Duration Calculus. His email address at UNU/IIST is pc@iist.unu.edu and at De La Salle University is ccspc@linux1.dlsu.edu.ph Dang Van Hung is from the Institute of Information Technology of National Center for Natu...
A MachineChecked Proof of the Optimality of a RealTime Scheduling Policy
 In ComputerAided Verification – CAV’98
, 1998
"... . We describe a mechanicallychecked proof of the optimality of earliestdeadlinefirst (EDF) schedulers on periodic tasks accomplished using the Nqthm theorem prover. We present a formalization of the theorem and discuss why the machinechecked proof is both more complex and more reliable than a co ..."
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Cited by 5 (0 self)
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. We describe a mechanicallychecked proof of the optimality of earliestdeadlinefirst (EDF) schedulers on periodic tasks accomplished using the Nqthm theorem prover. We present a formalization of the theorem and discuss why the machinechecked proof is both more complex and more reliable than a corresponding informal proof. 1 Introduction Realtime applications often have several required functions with different timing constraints. In a seminal paper for building realtime systems, Liu and Layland introduce abstractions that facilitate realtime application development [4]. Using a simple computation model, they exhibit different realtime scheduling policies that choose which of an application's various tasks to assign a processor and argue that these policies have certain useful properties. One scheduling policy is earliestdeadlinefirst (EDF), which assigns the processor to a task that has earliest deadline among the tasks that are currently running. An EDF scheduler is optimal...
Formalizing Realtime Scheduling as Program Refinement
 Proceedings of TransformationBased Reactive Systems Development, ARTS'97, Lecture Notes in Computer Science 1231
, 1997
"... This paper shows how the feasibility of scheduling a realtime program consisting of a number of parallel processes (tasks) can be proved as a step in the refinement of the program from its specification. Verification of this step of refinement makes formal use of methods and results from realtime ..."
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Cited by 3 (2 self)
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This paper shows how the feasibility of scheduling a realtime program consisting of a number of parallel processes (tasks) can be proved as a step in the refinement of the program from its specification. Verification of this step of refinement makes formal use of methods and results from realtime scheduling theory. Keywords: realtime program; specification; refinement; schedulability; feasibility. 1 Introduction A typical realtime program is required to respond to external events within specified time bounds and so it must be executed on a system that is sufficiently fast. In general, external events may occur at a rate which results in more than one process of the program being simultaneously under execution; if, at any time, there are fewer processors in the system than active processes, scheduling decisions must be taken to allocate processors to processes. Schedulability is the condition under which a scheduler can execute a realtime program on a system and meet its deadlin...
Formal Analysis of the Priority Ceiling Protocol
 In IEEE RealTime Systems Symposium (RTSS’00
, 2000
"... We present a case study in formal specification and toolassisted verification of realtime schedulers, based on the priority ceiling protocol. Starting from operational specifications of the protocol, we obtain rigorous proofs of both synchronization and timing properties, and we derive a schedulabi ..."
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Cited by 3 (0 self)
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We present a case study in formal specification and toolassisted verification of realtime schedulers, based on the priority ceiling protocol. Starting from operational specifications of the protocol, we obtain rigorous proofs of both synchronization and timing properties, and we derive a schedulability result for sporadic tasks. 1. Introduction Scheduling and synchronization services are critical components of realtime operating systems that are being used in safetycritical applications. In such contexts, one must obtain strong guarantees of correctness, and rigorous development and verification methods are required. Using the priority ceiling protocol [10] as a case study, we illustrate how mechanical theorem proving can give high assurance that a scheduler ensures critical synchronization and timing properties, and that associated schedulability results are valid. Previous applications of formal methods to the priority ceiling protocol typically consider only parts of the issue...
Formalising Scheduling Theories in Duration Calculus
, 2000
"... Correctness of real time scheduling algorithms has traditionally been argued in adhoc manners using natural languages. Proofs in this way are often unreliable. Work has been done on using a formal logic, in particular Duration Calculus, a real time interval temporal logic, to specify the algorithms ..."
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Cited by 2 (0 self)
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Correctness of real time scheduling algorithms has traditionally been argued in adhoc manners using natural languages. Proofs in this way are often unreliable. Work has been done on using a formal logic, in particular Duration Calculus, a real time interval temporal logic, to specify the algorithms and verify their properties. This paper aims to improve the work on this topic and give a summary. The two fundamental real time scheduling algorithms, namely, the Rate Monotonic and the Earliest Deadline First schedulers, are specified. The classic theorems on feasibility conditions due to Liu and Layland are proven as logical theorems.
A Theory of Duration Calculus with Application
"... Abstract. In this chapter we will present selected central elements in the theory of Duration Calculus and we will give examples of applications. The chapter will cover syntax, semantics and proof system for the basic logic. Furthermore, results on decidability, undecidability and modelchecking wil ..."
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Abstract. In this chapter we will present selected central elements in the theory of Duration Calculus and we will give examples of applications. The chapter will cover syntax, semantics and proof system for the basic logic. Furthermore, results on decidability, undecidability and modelchecking will be presented. A few extensions of the basic calculus will be described, in particular, Hybrid Duration Calculus and Duration Calculus with iterations. Furthermore, a case study: the biphase mark protocol, is presented. We will not attempt to be exhaustive in our coverage of topics; but we will provide references for further study. Keywords: Realtime systems, metrictime temporal logic, duration calculus, decidability, modelchecking, application 1 Introduction to Duration Calculus In this chapter we will introduce Durations Calculus (abbreviated DC) [72], present central elements of the theory, and show examples of applications. The aim is not to make a comprehensive presentation of the logic; but rather to cover
A Formal Proof of the Rate Monotonic Scheduler
 In Proc. the Sixth International Conference on RealTime Computing Systems and Applications (RTCSA'99), part of the federated 1999 International Computer Congress, Hong Kong, 1999, IEEE Computer
, 1999
"... We formally prove Liu and Layland's classic theorem on the Rate Monotonic Scheduler in Duration Calculus, a real time interval temporal logic. We describe the assumption of the system, the scheduling policy, the requirement, i.e., service is met for the processes before their deadlines, all by Durat ..."
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Cited by 1 (1 self)
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We formally prove Liu and Layland's classic theorem on the Rate Monotonic Scheduler in Duration Calculus, a real time interval temporal logic. We describe the assumption of the system, the scheduling policy, the requirement, i.e., service is met for the processes before their deadlines, all by Duration Calculus formulae. That a feasibility condition is sufficient is formalised as logical implication. By using the proof system of Duration Calculus, we formally prove that the feasibility condition due to Liu and Layland is sufficient. Dong Shuzhen was a fellow of UNU/IIST between February 1999 and July 1999. Xu Qiwen is a Research Fellow of UNU/IIST. His research interest is in Formal Techniques of Programming, including concurrency, verification, and design calculi. Email: qxu@iist.unu.edu Zhan Naijun was a fellow of UNU/IIST between July 1998 and August 1999, on leave from Institute of Software, Chinese Academy of Sciences, where he is a PhD student. Email: znj@ox.ios.ac.cn Copyrigh...
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
 Logical Methods in Computer Science
"... Vol. 3 (3:3) 2007, pp. 1–43 ..."