A closed-form evaluation for Datalog queries with integer (gap)-order constraints
ICDT Selected papers of the 4th international conference on Database theory
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Mixed real-integer linear quantifier elimination
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Timed Automata and the Theory of Real Numbers
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
An Improved Reachability Analysis Method for Strongly Linear Hybrid Systems (Extended Abstract)
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Multiple Counters Automata, Safety Analysis and Presburger Arithmetic
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
Diagonal constraints in timed automata: forward analysis of timed systems
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Convex Hull of Arithmetic Automata
SAS '08 Proceedings of the 15th international symposium on Static Analysis
T(O)RMC: A Tool for (ω)-Regular Model Checking
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Computing Convex Hulls by Automata Iteration
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Don't care words with an application to the automata-based approach for real addition
Formal Methods in System Design
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
On (Omega-)regular model checking
ACM Transactions on Computational Logic (TOCL)
Transitive closures of affine integer tuple relations and their overapproximations
SAS'11 Proceedings of the 18th international conference on Static analysis
Applying abstract acceleration to (co-)reachability analysis of reactive programs
Journal of Symbolic Computation
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This paper addresses the problem of computing symbolically the set of reachable configurations of a linear hybrid automaton. A solution proposed in earlier work consists in exploring the reachable configurations using an acceleration operator for computing the iterated effect of selected control cycles. Unfortunately, this method imposes a periodicity requirement on the data transformations labeling these cycles, that is not always satisfied in practice. This happens in particular with the important subclass of timed automata, even though it is known that the paths of such automata have a periodic behavior. The goal of this paper is to broaden substantially the applicability of hybrid acceleration. This is done by introducing powerful reduction rules, aimed at translating hybrid data transformations into equivalent ones that satisfy the periodicity criterion. In particular, we show that these rules always succeed in the case of timed automata. This makes it possible to compute an exact symbolic representation of the set of reachable configurations of a linear hybrid automaton, with a guarantee of termination over the subclass of timed automata. Compared to other known solutions to this problem, our method is simpler, and applicable to a much larger class of systems.