Abstract not found

Abstract. We study schedulability problems of timed systems with nonuniformly recurring computation tasks. Assume a set of real time tasks whose best and worst execution times, and deadlines are known. We use timed automata to describe the arrival patterns (and release times) of tasks. From the literature, it is known that the schedulability problem for a large class of such systems is decidable and can be checked efficiently. In this paper, we provide a summary on what is decidable and what is undecidable in schedulability analysis using timed automata. Our main technical contribution is that the schedulability problem will be undecidable if these two conditions hold: (1) the execution times of tasks are intervals and (2) a task is allowed to reset clocks. We show that if one of the above two conditions is dropped, the problem will be decidable again. Thus our result can be used as an indication in identifying classes of timed systems that can be analysed efficiently. 1

Abstract not found

proefschrift ter verkrijging van de graad van Doctor aan de Universiteit Leiden, op gezag van de Rector Magnificus Dr. D.D. Breimer, hoogleraar in de faculteit der Wiskunde en Natuurwetenschappen en die der Geneeskunde, volgens besluit van het College voor Promoties te verdedigen op woensdag 14 september 2005 klokke 15.15 uur door

We illustrate the application of the hybrid I/O automata framework of Lynch, Segala & Vaandrager by using it to model and analyze the behavior of a simple Lego car with caterpillar treads. We derive constraints on the values of the parameters that occur in our hybrid model that guarantee that the car will always move forward along a black tape, and will never get off the tape or move backward. In order to simplify the correctness proof, we introduce a transition systems that abstracts from the hybrid automaton in a rather drastic manner, but still preserves validity of the correctness properties in which we are interested. Even though our original model does not involve any disturbances, the general parametric analysis of the system allows us to exend our results in a trivial manner to a hybrid model in which several disturbances are allowed (mistakes in measurements of lengths, drift and jitter of the hardware clock, velocity, and distance between the two caterpillar treads).

voor het integratie- en testplanningsprobleem. In deze analogie wordt het leggen van de verschillende puzzelstukjes, gezien als het integreren van een systeem. Op de achterkant van dit proefschrift wordt deze analogie uitgelegd voor ieder afzonderlijk hoofdstuk. De foto opdevoorkantlaateendeelvaneenlithografischemachinevanASMLzien. Dezesystemen zijngebruiktalsvoorbeeldstudiesvoorde gepresenteerde methodieken. Cover: The cover of this thesis shows a puzzle that is used as analogy of the integration and test planning problem. In this analogy, laying the different puzzle pieces is seen as the integration of a system. On the back of this thesis, we explain for each individual chapter the related analogy. The photograph on the cover shows a part of a lithographic machineofASML.Thesesystemshavebeenusedascasestudiesforthemethodspresented.

ter verkrijging van de graad van doctor aan de

We illustrate the application of the hybrid I/O automata framework of Lynch, Segala & Vaandrager by using it to model and analyze the behavior of a simple Lego car with caterpillar treads. We derive constraints on the values of the parameters that occur in our hybrid model that guarantee that the car will always move forward along a black tape, and will never get off the tape or move backward. In order to simplify the correctness proof, we introduce a transition systems that abstracts from the hybrid automaton in a rather drastic manner, but still preserves validity of the correctness properties in which we are interested. Even though our original model does not involve any disturbances, the general parametric analysis of the system allows us to exend our results in a trivial manner to a hybrid model in which several disturbances are allowed (mistakes in measurements of lengths, drift and jitter of the hardware clock, velocity, and distance between the two caterpillar treads).

syntax . . . . . . . . . . . . . . . . . . . . . 92 5.4.2 Step 2: Abstract Syntax embedding . . . . . . . . . . . . . . 93 5.4.3 Step 3: Type embedding . . . . . . . . . . . . . . . . . . . . . 94 5.5 Relational algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.5.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.5.2 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.5.3 Relational expressions . . . . . . . . . . . . . . . . . . . . . . 97 5.5.4 Restriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.5.5 Union,Di#erence and Cartesian product . . . . . . . . . . . . 99 5.6 Embedding queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.6.1 Step 1: Abstract syntax . . . . . . . . . . . . . . . . . . . . . 99 5.6.2 Step 2: Abstract syntax embedding . . . . . . . . . . . . . . 103 5.6.3 Step 3: Type embedding . . . . . . . . . . . . . . . . . . . . . 110 5.7 Exam marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.7.1 Visual Basic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.7.2 Haskell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.8 Status and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6 The Lazy Virtual Machine 121 Contents vii 6.2 An overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3 The abstract machine . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.3.1 Basic instructions . . . . . . . . . . . . . . . . . . . . . . . . 128 6.3.2 Local definitions . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.3.3 Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.3.4 Recursive values . . . . . . . . . . . . . . . . . . . . . . . . . 13...

ter verkrijging van de graad Doctor aan