39576178
Resource-Efficient Scheduling for Real Time Systems
For embedded systems efficient utilization of resources is an acute problem arising from the increasing computational demands in all sorts of applications. The consumers constantly demand better functionality and flexibility of embedded products which imply an increase in the resources needed for their realization. In several areas – e.g. portable devices such as PDAs, mobile phones and laptops as well as mission critical systems such as space applications – the ability to design resource efficient solutions is crucial.
1457644
Time-Optimal Test Cases for Real-Time Systems
Testing is the primary software validation technique used by industry today, but remains ad hoc, error prone, and very expensive. A promising improvement is to automatically generate test cases from formal models of the system under test.
4574615
As Cheap as Possible: Efficient Cost-Optimal Reachability for Priced Timed Automata
In this paper we present an algorithm for efficiently computing optimal cost of reaching a goal state in the model of Linearly Priced Timed Automata (LPTA). The central contribution of this paper is a priced extension of so-called zones. This, together with a notion of facets of a zone, allows the entire machinery for symbolic reachability for timed automata in terms of zones to be lifted to cost-optimal reachability using priced zones. We report on experiments with a cost-optimizing extension of Uppaal on a number of examples.
12983032
Practical verification of embedded software
Using a new verification algorithm called the compositional backward technique, the authors demonstrate that they can exhaustively verify even the largest industrial applications-comprising more than 1,000 components-in a few minutes on a standard PC.
8987497
Efficient Timed Reachability Analysis Using Clock Difference Diagrams
One of the major problems in applying automatic verification tools to industrial-size systems is the excessive amount of memory required during the state-space exploration of a model. In the setting of real-time, this problem of state-explosion requires extra attention as information must be kept not only on the discrete control structure but also on the values of continuous clock variables. 
 
In this paper, we exploit Clock Difference Diagrams, CDD's, a BDD-like data-structure for representing and effectively manipulating certain nonconvex subsets of the Euclidean space, notably those encountered during verification of timed automata. 
 
A version of the real-time verification tool Uppaal using CDD's as a compact data-structure for storing explored symbolic states has been implemented. Our experimental results demonstrate significant spacesavings: for eight industrial examples, the savings are in average 42% with moderate increase in runtime. 
 
We further report on how the symbolic state-space exploration itself may be carried out using CDD's.
14315022
Scaling up Uppaal Automatic Verification of Real-Time Systems Using Compositionality and Abstraction
To combat the state-explosion problem in automatic verification, we present a method for scaling up the real-time verification tool UPPAAL by complementing it with methods for abstraction and compositionality. We identify a notion of timed ready simulation which we show is a sound condition for preservation of safety properties between real-time systems, and in addition is a precongruence with respect to parallel composition. Thus, it supports both abstraction and compositionality. We furthermore present a method for automatically testing for the existence of a timed ready simulation between real-time systems using the UPPAAL tool.
28434166
Relaxed Balance Using Standard Rotations

AbstractAbstract. In search trees with relaxed balance, rebalancing transformations need not be connected with updates, but may be delayed. For standard AVL tree rebalancing, we prove that even though the rebalancing operations are uncoupled from updates, their total number is bounded by O(M log (M+N)) , where M is the number of updates to an AVL tree of initial size N . Hence, relaxed balancing of AVL trees comes at no extra cost asymptotically. Furthermore, our scheme differs from most other relaxed balancing schemes in an important aspect: No rebalancing transformation can be done in the wrong direction, i.e., no performed rotation can make the tree less balanced. Moreover, each performed rotation indeed corresponds to a real imbalance situation in the tree. Finally, and perhaps most importantly, our structure is capable of forgetting registered imbalance if later updates happen to improve the situation. Our results are of theoretical interest and have possible sequential and parallel applications.

80794
Efficient Rebalancing of Chromatic Search Trees
Chromatic trees were defined by Nurmi and Soisalon-Soininen, as a new type of binary search tree for databases. The aim is to improve runtime performance by allowing a greater degree of concurrency, which, in turn, is obtained by uncoupling updating from rebalancing. This also allows rebalancing to be postponed completely or partially until after peak working hours. The advantages of the proposal of Nurmi and Soisalon-Soininen are quite significant, but there are definite problems with it. First, they give no explicit upper bound on the complexity of their algorithm. Second, some of their rebalancing operations can be applied many more times than necessary. Third, some of their operations, when removing one problem, create another. We define a new set of rebalancing operations which we prove give rise to at most @?log"2(N+1)@?-1 rebalancing operations per insertion and at most @?log"2(N+1)@?-2 rebalancing operations per deletion, where N is the maximum size the tree could ever have, given its initial size and the number of insertions performed. Most of these rebalancing operations, in fact, do no restructuring; they simply move weights around. The number of operations which actually change the structure of the tree is at most one per update.
30882911
Complexity of Layered Binary Search Trees with Relaxed Balance
When search trees are made relaxed, balance constraints are weakened such that updates can be made without immediate rebalancing. This can lead to a speed-up in some circumstances. However, the weakened balance constraints also make it more challenging to prove complexity results for relaxed structures.In our opinion, one of the simplest and most intuitive presentations of balanced search trees has been given via layered trees. We show that relaxed layered trees are among the best of the relaxed structures. More precisely, rebalancing is worst-case logarithmic and amortized constant per update, and restructuring is worst-case constant per update.
17731673
Relaxed Balance through Standard Rotations
We consider binary search trees, where rebalancing transformations need not be connected with updates but may be delayed. For standard AVL tree rebalancing, we prove that even though the rebalancing operations are uncoupled from updates, their total number is bounded by O(M log(M+N)), where M is the number of updates to an AVL tree of initial size N. Hence, relaxed balancing of AVL trees comes at no extra cost asymptotically. Furthermore, our scheme differs from most other relaxed balancing schemes in an important aspect: No rebalancing transformation can be done in the wrong direction, i.e., no performed rotation can make the tree less balanced. Moreover, each performed rotation indeed corresponds to a real imbalance situation in the tree. Our results are important in designing efficient concurrency control strategies for main-memory databases. Main-memory search structures have gained new applications in large embedded systems, such as switching systems for mobile telephones.
125126786
Relaxed multi-way trees with group updates
Data structures with relaxed balance differ from standard structures in that rebalancing can be delayed and interspersed with updates. This gives extra flexibility in both sequential and parallel, applications. We study the version of multi-way trees called (a, b)-trees (which includes B-trees) with the operations insertion, deletion, and group insertion. The latter has applications in for instance document databases, WWW search engines, and differential indexing. We prove that we obtain the optimal asymptotic rebalancing complexities of amortized constant time for insertion and deletion and amortized logarithmic time in the size of the group for group insertion. These results hold even for the relaxed version. This is an improvement over the existing results in the most interesting cases.