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.
27033090
Exponentially Decreasing Number of Operations in Balanced Trees
While many tree-like structures have been proven to support amortized constant number of operations after updates, considerably fewer structures have been proven to support the more general exponentially decreasing number of operations with respect to distance from the update. In addition, all existing proofs of exponentially decreasing operations are tailor-made for specific structures. We provide the first formalization of conditions under which amortized constant number of operations imply exponentially decreasing number of operations. Since our proof is constructive, we obtain the constants involved immediately. Moreover, we develop a number of techniques to improve these constants.
32290696
Efficient Rebalancing of Chromatic Search Trees
In PODS'91, Nurmi and Soisalon-Soininen presented a new type of binary search tree for databases, which they call a chromatic tree. 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.
3019314
Amortized constant relaxed rebalancing using standard rotations
Abstract. The idea of relaxed balance is to uncouple the rebalancing in search trees from the updating in order to speed up request processing in main-memory databases. This paper defines the first relaxed binary search tree with amortized constant rebalancing using only standard single or double rotations.
2802730
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 and WWW search engines. 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.
Our results also demonstrate that a binary tree scheme with the same complexities can be designed. This is an improvement over the existing results in the most interesting cases.
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.
7626010
Online Testing of Real-time Systems Using Uppaal
We present the development of T-UPPAAL — a new tool for online black-box testing of real-time embedded systems from non-deterministic timed automata specifica- tions. It is based on a sound and complete randomized online testing algorithm and is im- plemented using symbolic state representation and manipulation techniques. We propose the notion of relativized timed input/output conformance as the formal implementation relation. A novelty of this relation and our testing algorithm is that they explicitly take environment assumptions into account, generate, execute and verify the result online using the UPPAAL on-the-fly model-checking tool engine. This paper introduces the principles behind the tool, describes the present implementation status, and future work directions.
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.
406624
Model Checking Timed Automata with Priorities Using DBM Subtraction
In this paper we describe an extension of timed automata with priorities, and efficient algorithms to compute subtraction on DBMs (difference bounded matrices), needed in symbolic model-checking of timed automata with priorities. The subtraction is one of the few operations on DBMs that result in a non-convex set needing sets of DBMs for representation. Our subtraction algorithms are efficient in the sense that the number of generated DBMs is significantly reduced compared to a naive algorithm. The overhead in time is compensated by the gain from reducing the number of resulting DBMs since this number affects the performance of symbolic model-checking. The uses of the DBM subtraction operation extend beyond timed automata with priorities. It is also useful for allowing guards on transitions with urgent actions, deadlock checking, and timed games.
15710999
Synthesizing Distinguishing Formulae for Real Time Systems
This paper describes a technique for generating diagnostic information for the timed bisimulation equivalence and the timed simulation preorder. More precisely, given two (parallel) networks of regular real-time processes, the technique will provide a logical formula that differentiates them in case they are not timed (bi)similar. Our method may be seen as an extension of the algorithm by Cerans for deciding timed bisimilarity in that information of time-quantities has been added sufficient for generating distinguishing formulae.
20940088
Verification of Large State/Event Systems Using Compositionality and Dependency Analysis
A state/event model is a concurrent version of Mealy machines used for describing embedded reactive systems. This paper introduces a technique that uses compositionality and dependency analysis to significantly improve the efficiency of symbolic model checking of state/event models. This technique makes possible automated verification of large industrial designs with the use of only modest resources (less than one hour on a standard PC for a model with 1421 concurrent machines). The results of the paper are being implemented in the next version of the commercial tool visualSTATEℳ.