39362107
A New Formalism for Relational Algebra
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.
34233329
Search Trees with Relaxed Balance and Near-Optimal Height
We introduce the relaxed k-tree, a search tree with relaxed balance and a height bound, when in balance, of (1 + Ɛ) log2 n + 1, for any Ɛ > 0. The rebalancing work is amortized O(1/Ɛ) per update. This is the first binary search tree with relaxed balance having a height bound better than c ċ log2 n for a fixed constant c. In all previous proposals, the constant is at least 1/ log2 Φ > 1.44, where Φ is the golden ratio. 
 
As a consequence, we can also define a standard (non-relaxed) k-tree with amortized constant rebalancing per update, which is an improvement over the original definition. 
 
Search engines based on main-memory databases with strongly fluctuating workloads are possible applications for this line of work.
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.
19914316
Extending the Accommodating Function
The applicability of the accommodating function, a relatively new measure for the quality of on-line algorithms, is extended. If a limited amount n of some resource is available, the accommodating function A(?) is the competitive ratio when input sequences are restricted to those for which the amount ?n of resources suffices for an optimal off-line algorithm. The accommodating function was originally used only for ? ? 1. We focus on ? < 1, observe that the function now appears interesting for a greater variety of problems, and use it to make new distinctions between known algorithms and to find new ones.
6986183
Efficient Simplification of Bisimulation Formulas
The problem of checking or optimally simplifying bisimulation formulas is likely to be computationally very hard. We take a different view at the problem: we set out to define a very fast algorithm, and then see what we can obtain. Sometimes our algorithm can simplify a formula perfectly, sometimes it cannot. However, the algorithm is extremely fast and can, therefore, be added to formula-based bisimulation model checkers at practically no cost. When the formula can be simplified by our algorithm, this can have a dramatic positive effect on the better, but also more time consuming, theorem provers which will finish the job.
5706272
The Power of Reachability Testing for Timed Automata
In this paper we provide a complete characterization of the class of properties of (networks of) timed automata for which model checking can be reduced to reachability checking in the context of testing automata.
194948
Diagnostic Model-Checking for Real-Time Systems
Uppaal is a new tool suit for automatic verification of networks of timed automata. In this paper we describe the diagnostic model-checking feature of Uppaal and illustrates its usefulness through the debugging of (a version of) the Philips Audio-Control Protocol. Together with a graphical interface of Uppaal this diagnostic feature allows for a number of errors to be more easily detected and corrected.
13462666
Timed Modal Specification - Theory and Tools
In this paper we present the theory of Timed Modal Specifications (TMS) together with its implementation, the tool Epsilon. TMS and Epsilon are timed extensions of respectively Modal Specifications [7, 9] and the Tav system [6, 4]. Also, the theory of TMS is an extension of real-timed process calculi with the specific aim of allowing loose or partial specifications. This allows us to define a notion of refinement, generalizing in a natural way the classical notion of bisimulation.
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.
8766873
Synthesis of Optimal Strategies Using HyTech
Priced timed (game) automata extend timed (game) automata with costs on both locations and transitions. The problem of synthesizing an optimal winning strategy for a priced timed game under some hypotheses has been shown decidable in P. Bouyer, F. Cassez, E. Fleury, and K.G. Larsen. Optimal strategies in priced timed game automata. Research Report BRICS RS-04-4, Denmark, Feb. 2004. Available at http://www.brics.dk/RS/04/4/]. In this paper, we present an algorithm for computing the optimal cost and for synthesizing an optimal strategy in case there exists one. We also describe the implementation of this algorithm with the tool HyTech and present an example.