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.
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.
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.
1349074
Static Guard Analysis in Timed Automata Verification
By definition Timed Automata have an infinite state-space, thus for verification purposes, an exact finite abstraction is required. We propose a location-based finite zone abstraction, which computes an abstraction based on the relevant guards for a particular state of the model (as opposed to all guards).We show that the location-based zone abstraction is sound and complete with respect to location reachability; that it generalises active-clock reduction, in the sense that an inactive clock has no relevant guards at all; that it enlarges the class of timed automata, that can be verified. We generalise the new abstraction to the case of networks of timed automata, and experimentally demonstrate a potentially exponential speedup compared to the usual abstraction.
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.
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.
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.
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.
125126786
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, WWW search engines, and differential indexing. 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. This is an improvement over the existing results in the most interesting cases.
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.
945379
Fair versus Unrestricted Bin Packing

AbstractAbstract. We consider the on-line Dual Bin Packing problem where we have nunit size bins 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 unrestrictedalgorithms that have the power of performing admission control on the items, i.e., rejecting items while there is enough space to pack them, versus fairalgorithms that reject 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 compared with the performance achieved on the fair version of the problem. Our main result shows that with an unfair variant of First-Fit, we can pack approximately two-thirds of the items for sequences for which an optimal off-line algorithm can pack all the items. This is in contrast to standard First-Fit where we show an asymptotically tight hardness result: if the number of bins can be chosen arbitrarily large, the fraction of the items packed by First-Fit comes arbitrarily close to five-eighths.
