9243889
Generality in design and compositional verification usingTav
It is a well recognised fact that design errors in parallel systems are often hard to identify—due to their non-deterministic nature. It is therefore important that designs are analysedbefore the implementation phase begins. Even small parallel systems often have an intrinsic structure which is hard to fully understand, and the support of automated tools is therefore indispensable. In order to be of any practical use, the computations of such tools must be (polynomially) effective in terms of the system size, and furthermore it must be possible to reason about the system in terms of the properties of its (parallel) components—in order to avoid state-space explosion. Finally, the well-establishedstepwise refinement design strategy must be supported.The tools of theTav-system fulfil the above requirements, and in this paper we present its features by analysing a simple transmission protocol. The cornerstone of the system is the theory ofmodal transition systems, which allows for efficient decidability, stepwise refinement, and compositionality. The theory also supports a unique feature ofTav, namely the ability to provide explanations in case of design errors.
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.
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.
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.
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.
2055715
Relaxed Balance for Search Trees with Local Rebalancing
Search trees with relaxed balance were introduced with the aim of facilitating fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating, so extensive locking in connection with updates is avoided. Rebalancing is taken care of by background processes, which do only a constant amount of work at a time before they release locks. Thus, the rebalancing and the associated locks are very localized in time as well as in space. In particular, there is no exclusive locking of whole paths. This means that the amount of parallelism possible is not limited by the height of the tree. Search trees with relaxed balance have been obtained by adapting standard sequential search trees to this new paradigm; clearly using similar techniques in each case, but no general result has been obtained. We show how any search tree with local bottom-up rebalancing can be used in a relaxed variant preserving the complexity of the rebalancing from the sequential case. Additionally, we single out the one high level locking mechanism that a parallel implementation must provide in order to guarantee consistency.
39188673
Amortization Results for Chromatic Search Trees, with an Application to Priority Queues
The intention in designing data structures with relaxed balance, such as chromatic search trees, is to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, the updating and rebalancing have been uncoupled, so extensive locking in connection with updates is avoided.
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.

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.
28707658
Bounds on Certain Multiplications of Affine Combinations
Let A and B be n × n matrices the entries of which are affine combinations of the variables a1,…,am, b1,…,bm over GF(2). Suppose that, for each i, 1 ⩽ i ⩽ m, the term aibi is an element of the product matrix C = A · B. What is the maximum value that m can have as a function of n? This question arises from a recent technique for improving the communication complexity of zero-knowledge proofs. 
 
The obvious upper bound of n2 is improved to n233+ O(n). Tighter bounds are obtained for smaller values of n. The bounds for n = 2, n = 3, and n = 4 are tight.