Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Algorithms for the Multi-constrained Routing Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Automata For Modeling Real-Time Systems
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Kronos: A Model-Checking Tool for Real-Time Systems
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Better is Better than Well: On Efficient Verification of Infinite-State Systems
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Optimal reachability for multi-priced timed automata
Theoretical Computer Science
Beyond liveness: efficient parameter synthesis for time bounded liveness
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Optimal reachability for multi-priced timed automata
Theoretical Computer Science
Concavely-Priced Probabilistic Timed Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Revisiting Decidability and Optimum Reachability for Multi-Priced Timed Automata
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
On the Supports of Recognizable Timed Series
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
How to Tackle Integer Weighted Automata Positivity
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Quantitative analysis of real-time systems using priced timed automata
Communications of the ACM
Verification, performance analysis and controller synthesis for real-time systems
FSEN'09 Proceedings of the Third IPM international conference on Fundamentals of Software Engineering
Checking correctness of services modeled as priced timed automata
ISoLA'12 Proceedings of the 5th international conference on Leveraging Applications of Formal Methods, Verification and Validation: applications and case studies - Volume Part II
| Hi-index | 5.24 |
In this paper, we prove the decidability of the minimal and maximal reachability problems for multi-priced timed automata, an extension of timed automata with multiple cost variables evolving according to given rates for each location. More precisely, we consider the problems of synthesizing the minimal and maximal costs of reaching a given target location. These problems generalize conditional optimal reachability, i.e., the problem of minimizing one primary cost under individual upper bound constraints on the remaining, secondary, costs, and the problem of maximizing the primary cost under individual lower bound constraints on the secondary costs. Furthermore, under the liveness constraint that all traces eventually reach the goal location, we can synthesize all costs combinations that can reach the goal. The decidability of the minimal reachability problem is proven by constructing a zone-based algorithm that always terminates while synthesizing the optimal cost tuples. For the corresponding maximization problem, we construct two zone-based algorithms, one with and one without the above liveness constraint. All algorithms are presented in the setting of two cost variables and then lifted to an arbitrary number of cost variables.