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.
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.
3252817
Optimal Strategies in Priced Timed Game Automata
Priced timed (game) automata extend timed (game) automata with costs on both locations and transitions. In this paper we focus on reachability priced timed game automata and prove that the optimal cost for winning such a game is computable under conditions concerning the non-zenoness of cost. Under stronger conditions (strictness of constraints) we prove that in case an optimal strategy exists, we can compute a state-based winning optimal strategy.
6242554
Guided Synthesis of Control Programs Using UPPAAL
In this paper we address the problem of scheduling and synthesizing distributed control programs for a batch production plant. We use a timed automata model of the batch plant and the verification tool UPPAAL to solve the scheduling problem.In modeling the plant, we aim at a level of abstraction which is sufficiently accurate in order that synthesis of control programs from generated timed traces is possible. Consequently, the models quickly become too detailed and complicated for immediate automatic synthesis. In fact, only models of plants producing two batches can be analyzed directly! To overcome this problem, we present a general method allowing the user to guide the model-checker according to heuristically chosen strategies. The guidance is specified by augmenting the model with additional guidance variables and by decorating transitions with extra guards on these. Applying this method have made synthesis of control programs feasible for a plant producing as many as 60 batches.The synthesized control programs have been executed in a physical plant. Besides proving useful in validating the plant model and in finding some modeling errors, we view this final step as the ultimate litmus test of our methodology's ability to generate executable (and executing) code from basic plant models.
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.
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.
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.
80794
Efficient Rebalancing of Chromatic Search Trees
Chromatic trees were defined by Nurmi and Soisalon-Soininen, as a new type of binary search tree for databases. 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. The advantages of the proposal of Nurmi and Soisalon-Soininen are quite significant, but there are definite problems with it. First, they give no explicit upper bound on the complexity of their algorithm. Second, some of their rebalancing operations can be applied many more times than necessary. Third, some of their operations, when removing one problem, create another. We define a new set of rebalancing operations which we prove give rise to at most @?log"2(N+1)@?-1 rebalancing operations per insertion and at most @?log"2(N+1)@?-2 rebalancing operations per deletion, where N is the maximum size the tree could ever have, given its initial size and the number of insertions performed. Most of these rebalancing operations, in fact, do no restructuring; they simply move weights around. The number of operations which actually change the structure of the tree is at most one per update.
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.
2737251
Better Bounds on the Accommodating Ratio for the Seat Reservation Problem
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. Passengers may attempt to make reservations at any point before they get on the train, and reservations can be made going from any station to any later station. All algorithms under consideration must be "fair", i.e., they are not allowed to reject a request for a reservation which could be made at the time. The "accommodating ratio" compares the performance of an on-line algorithm to that of the optimal off-line algorithm, under the assumption that the only sequences of requests allowed are sequences for which the optimal off-line algorithm could accommodate all requests. The train has a fixed number of seats, and we first consider the case in which all tickets have the same cost, and the seat reservation system attempts to maximize income. We prove improved upper bounds on the performance of First-Fit and Best-Fit, showing that in the worst case, neither algorithm does significantly better than any fair deterministic algorithm would. We also improve the upper bounds on the possible performance of any "fair" deterministic or randomized algorithm. A specific randomized algorithm is also considered. Finally, we consider the case in which the cost of a ticket is proportional to the distance traveled.
20582368
AVL trees with relaxed balance
AVL trees with relaxed balance (G.M. Adel'son-Vel'skii et al., 1962) were introduced with the aim of improving runtime performance by allowing a greater degree of concurrency. This is obtained by uncoupling updating from rebalancing. We define a new collection of rebalancing operations which allows for a significantly greater degree of concurrency than the original proposal. Additionally, in contrast to the original proposal, we prove the complexity of the rebalancing. If N is the maximum size the tree could ever have, we prove that each insertion gives rise to at most /spl lsqb/log/sub /spl phi(N+3/2)+log/sub /spl phi(/spl radic/(5))/spl minus/3/spl rsqb/ rebalancing operations and that each deletion gives rise to at most /spl lsqb/log/sub /spl phi(N+3/2)+log/sub /spl phi(/spl radic/(5))/spl minus/4/spl rsqb/ rebalancing operations, where /spl phi/ is the golden ratio.<<ETX>>