Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Small solution of linear Diophantine equations
Discrete Mathematics
Minimal solutions of linear diophantine systems: bounds and algorithms
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Journal of the ACM (JACM)
Theoretical Computer Science
IEEE Transactions on Software Engineering - Special issue on formal methods in software practice
Patterns in property specifications for finite-state verification
Proceedings of the 21st international conference on Software engineering
Journal of the ACM (JACM)
Symbolic Model Checking
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Binary Reachability Analysis of Discrete Pushdown Timed Automata
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Presburger liveness verification of discrete timed automata
Theoretical Computer Science
On the Verification Problem of Nonregular Properties for Nonregular Processes
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Pushdown timed automata: a binary reachability characterization and safety verification
Theoretical Computer Science
Semi-linear Parikh images of regular expressions via reduction
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
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The linear reachability problem for finite state transition systems is to decide whether there is an execution path in a given finite state transition system such that the counts of labels on the path satisfy a given linear constraint. Using some known results on minimal solutions (in nonnegative integers) for linear Diophantine equation systems, we present new time complexity bounds for the problem. In contrast to the previously known results, the bounds obtained in this paper are polynomial in the size of the transition system in consideration, when the linear constraint is fixed. The bounds are also used to establish a worst-case time complexity result for the linear reachability problem for timed automata.