@inproceedings{663, abstract = {In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u→, x→) = 0, parametric in u→, which can yield an infinite number of concrete invariants by assigning different values to u→ so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u→, x→), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u→, x→) divided by g(u→, x→) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient. }, author = {Kong, Hui and Bogomolov, Sergiy and Schilling, Christian and Jiang, Yu and Henzinger, Thomas A}, booktitle = {Proceedings of the 20th International Conference on Hybrid Systems}, isbn = {978-145034590-3}, location = {Pittsburgh, PA, United States}, pages = {163 -- 172}, publisher = {ACM}, title = {{Safety verification of nonlinear hybrid systems based on invariant clusters}}, doi = {10.1145/3049797.3049814}, year = {2017}, } @inproceedings{711, abstract = {Nested weighted automata (NWA) present a robust and convenient automata-theoretic formalism for quantitative specifications. Previous works have considered NWA that processed input words only in the forward direction. It is natural to allow the automata to process input words backwards as well, for example, to measure the maximal or average time between a response and the preceding request. We therefore introduce and study bidirectional NWA that can process input words in both directions. First, we show that bidirectional NWA can express interesting quantitative properties that are not expressible by forward-only NWA. Second, for the fundamental decision problems of emptiness and universality, we establish decidability and complexity results for the new framework which match the best-known results for the special case of forward-only NWA. Thus, for NWA, the increased expressiveness of bidirectionality is achieved at no additional computational complexity. This is in stark contrast to the unweighted case, where bidirectional finite automata are no more expressive but exponentially more succinct than their forward-only counterparts.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, issn = {18688969}, location = {Berlin, Germany}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Bidirectional nested weighted automata}}, doi = {10.4230/LIPIcs.CONCUR.2017.5}, volume = {85}, year = {2017}, } @inproceedings{963, abstract = {Network games are widely used as a model for selfish resource-allocation problems. In the classical model, each player selects a path connecting her source and target vertex. The cost of traversing an edge depends on the number of players that traverse it. Thus, it abstracts the fact that different users may use a resource at different times and for different durations, which plays an important role in defining the costs of the users in reality. For example, when transmitting packets in a communication network, routing traffic in a road network, or processing a task in a production system, the traversal of the network involves an inherent delay, and so sharing and congestion of resources crucially depends on time. We study timed network games , which add a time component to network games. Each vertex v in the network is associated with a cost function, mapping the load on v to the price that a player pays for staying in v for one time unit with this load. In addition, each edge has a guard, describing time intervals in which the edge can be traversed, forcing the players to spend time on vertices. Unlike earlier work that add a time component to network games, the time in our model is continuous and cannot be discretized. In particular, players have uncountably many strategies, and a game may have uncountably many pure Nash equilibria. We study properties of timed network games with cost-sharing or congestion cost functions: their stability, equilibrium inefficiency, and complexity. In particular, we show that the answer to the question whether we can restrict attention to boundary strategies, namely ones in which edges are traversed only at the boundaries of guards, is mixed. }, author = {Avni, Guy and Guha, Shibashis and Kupferman, Orna}, issn = {18688969}, location = {Aalborg, Denmark}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Timed network games with clocks}}, doi = {10.4230/LIPIcs.MFCS.2017.37}, volume = {83}, year = {2017}, } @inproceedings{941, abstract = {Recently there has been a proliferation of automated program repair (APR) techniques, targeting various programming languages. Such techniques can be generally classified into two families: syntactic- and semantics-based. Semantics-based APR, on which we focus, typically uses symbolic execution to infer semantic constraints and then program synthesis to construct repairs conforming to them. While syntactic-based APR techniques have been shown successful on bugs in real-world programs written in both C and Java, semantics-based APR techniques mostly target C programs. This leaves empirical comparisons of the APR families not fully explored, and developers without a Java-based semantics APR technique. We present JFix, a semantics-based APR framework that targets Java, and an associated Eclipse plugin. JFix is implemented atop Symbolic PathFinder, a well-known symbolic execution engine for Java programs. It extends one particular APR technique (Angelix), and is designed to be sufficiently generic to support a variety of such techniques. We demonstrate that semantics-based APR can indeed efficiently and effectively repair a variety of classes of bugs in large real-world Java programs. This supports our claim that the framework can both support developers seeking semantics-based repair of bugs in Java programs, as well as enable larger scale empirical studies comparing syntactic- and semantics-based APR targeting Java. The demonstration of our tool is available via the project website at: https://xuanbachle.github.io/semanticsrepair/ }, author = {Le, Xuan and Chu, Duc Hiep and Lo, David and Le Goues, Claire and Visser, Willem}, booktitle = {Proceedings of the 26th ACM SIGSOFT International Symposium on Software Testing and Analysis}, location = {Santa Barbara, CA, United States}, pages = {376 -- 379 }, publisher = {ACM}, title = {{JFIX: Semantics-based repair of Java programs via symbolic PathFinder}}, doi = {10.1145/3092703.3098225}, year = {2017}, } @inproceedings{950, abstract = {Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. Both players have separate budgets, which sum up to $1$. In each turn, a bidding takes place. Both players submit bids simultaneously, and a bid is legal if it does not exceed the available budget. The winner of the bidding pays his bid to the other player and moves the token. For reachability objectives, repeated bidding games have been studied and are called Richman games. There, a central question is the existence and computation of threshold budgets; namely, a value t\in [0,1] such that if\PO's budget exceeds $t$, he can win the game, and if\PT's budget exceeds 1-t, he can win the game. We focus on parity games and mean-payoff games. We show the existence of threshold budgets in these games, and reduce the problem of finding them to Richman games. We also determine the strategy-complexity of an optimal strategy. Our most interesting result shows that memoryless strategies suffice for mean-payoff bidding games. }, author = {Avni, Guy and Henzinger, Thomas A and Chonev, Ventsislav K}, issn = {1868-8969}, location = {Berlin, Germany}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Infinite-duration bidding games}}, doi = {10.4230/LIPIcs.CONCUR.2017.21}, volume = {85}, year = {2017}, }