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.
30176003
Lower and Upper Bounds in Zone Based Abstractions of Timed Automata
Timed automata have an infinite semantics. For verification purposes, one usually uses zone based abstractions w.r.t. the maximal constants to which clocks of the timed automaton are compared. We show that by distinguishing maximal lower and upper bounds, significantly coarser abstractions can be obtained. We show soundness and completeness of the new abstractions w.r.t. reachability. We demonstrate how information about lower and upper bounds can be used to optimise the algorithm for bringing a difference bound matrix into normal form. Finally, we experimentally demonstrate that the new techniques dramatically increases the scalability of the real-time model checker Uppaal.
16545835
UPPAAL Implementation Secrets
In this paper we present the continuous and on-going development of datastructures and algorithms underlying the verification engine of the tool UPPAAL. In particular, we review the datastructures of Difference Bounded Matrices, Minimal Constraint Representation and Clock Difference Diagrams used in symbolic state-space representation and -analysis for real-time systems.In addition we report on distributed versions of the tool, and outline the design and experimental results for new internal datastructures to be used in the next generation of UPPAAL.Finally, we mention work on complementing methods involving acceleration, abstraction and compositionality.
18794799
Model-Checking for 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. 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.
8797594
UPPAAL - Now, Next, and Future
UPPAAL is a tool for modeling, simulation and verification of real-time systems, developed jointly by BRICS at Aalborg University and the Department of Computer Systems at Uppsala University. The tool is appropriate for systems that can be modeled as a collection of non-deterministic processes with finite control structure and real-valued clocks, communicating through channels or shared variables. Typical application areas include real-time controllers and communication protocols, in particular those where timing aspects are critical. 
 
This paper reports on the currently available version and summarizes developments during the last two years. We report on new directions that extends UPPAAL with cost-optimal exploration, parametric modeling, stop-watches, probablistic modeling, hierachical modeling, executable timed automata, and a hybrid automata animator. We also report on recent work to improve the efficiency of the tool. In particular, we outline Clock Difference Diagrams (CDDs), new compact representations of states, a distributed version of the tool, and application of dynamic partitioning. 
 
UPPAAL has been applied in a number of academic and industrial case studies. We describe a selection of the recent case studies.
12303667
Formal Verification of a Power Controller Using the Real-Time Model Checker UPPAAL
A real-time system for power-down control in audio/video components is modeled and verified using the real-time model checker UPPAAL. The system is supposed to reside in an audio/video component and control (read from and write to) links to neighbor audio/video components such as TV, VCR and remote-control. In particular, the system is responsible for the powering up and down of the component in between the arrival of data, and in order to do so in a safe way without loss of data, it is essential that no link interrupts are lost. Hence, a component system is a multitasking system with hard real-time requirements, and we present techniques for modeling time consumption in such a multitasked, prioritized system. The work has been carried out in a collaboration between Aalborg University and the audio/video company B&O. By modeling the system, 3 design errors were identified and corrected, and the following verification confirmed the validity of the design but also revealed the necessity for an upper limit of the interrupt frequency. The resulting design has been implemented and it is going to be incorporated as part of a new product line.
36519093
Fair versus Unrestricted Bin Packing
We consider the Unrestricted Bin Packing problem where we have bins of equal size and a sequence of items. The goal is to maximize the number of items that are packed in the bins by an on-line algorithm. We investigate the power of performing admission control on the items, i.e., rejecting items while there is enough space to pack them, versus behaving fairly, i.e., rejecting an item only when there is not enough space to pack it. We show that by performing admission control on the items, we get better performance for various measures compared with the performance achieved on the fair version of the problem. Our main result shows that we can pack 2/3 of the items for sequences in which the optimal can pack all the items.
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.
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.
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.
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.