8200399
Compositional and symbolic model-checking of real-time systems
Efficient automatic model-checking algorithms for real-time systems have been obtained in recent years based on the state-region graph technique of Alur, Courcoubetis and Dill (1990). However, these algorithms are faced with two potential types of explosion arising from parallel composition: explosion in the space of control nodes, and explosion in the region space over clock-variables. In this paper we attack these explosion problems by developing and combining compositional and symbolic model-checking techniques. The presented techniques provide the foundation for a new automatic verification tool UPPAAL. Experimental results indicate that UPPAAL performs time- and space-wise favorably compared with other real-time verification tools.
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.
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.
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.
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.
43259181
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.
5220058
The Seat Reservation Problem
Abstract. We investigate the problem of giving seat reservations on-line. We assume that a train travels from a start station to an end station, stopping at k stations, including the first and last. Reservations can be made for any trip going from any station to any later station. The train has a fixed number of seats. The seat reservation system attempts to maximize income. We consider the case in which all tickets have the same price and the case in which the price of a ticket is proportional to the length of the trip. For both cases we prove upper and lower bounds of Θ(1/k) on the competitive ratio of any ``fair'' deterministic algorithm. We also define the accommodating ratio which is similar to the competitive ratio except that the only sequences of requests allowed are sequences for which the optimal off-line algorithm could accommodate all requests. We prove upper and lower bounds of Θ(1) on the accommodating ratio of any ``fair'' deterministic algorithm, in the case in which all tickets have the same price, but Θ(1/k) in the case in which the ticket price is proportional to the length of the trip. The most surprising of these results is that all ``fair'' algorithms are at least 1/2 -accommodating when all tickets have the same price. We prove similar results bounding the performance of any ``fair'' randomized algorithm against an adaptive on-line adversary. We also consider concrete algorithms; more specifically, First-Fit and Best-Fit.
15364808
The relative worst order ratio applied to paging
The relative worst order ratio, a new measure for the quality of on-line algorithms, was recently defined and applied to two bin packing problems. Here, we apply it to the paging problem and obtain the following results: We devise a new deterministic paging algorithm, Retrospective-LRU, and show that it performs better than LRU. This is supported by experimental results, but contrasts with the competitive ratio. All deterministic marking algorithms have the same competitive ratio, but here we find that LRU is better than FWF. According to the relative worst order ratio, no deterministic marking algorithm can be significantly better than LRU, but the randomized algorithm MARK is better than LRU. Finally, look-ahead is shown to be a significant advantage, in contrast to the competitive ratio, which does not reflect that look-ahead can be helpful.
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.
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.