New complexity results for some linear counting problems using minimal solutions to linear diophantine equations

Authors:
Gaoyan Xie;Cheng Li;Zhe Dang
Affiliations:
School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA;School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA;School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA
Venue:
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Year:
2003

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Abstract

The linear reachability problem 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 results on minimal solutions (in nonnegative integers) for linear Diophantine systems, we obtain new complexity results for the problem, as well as for other linear counting problems of finite state transition systems and timed automata. In contrast to previously known results, the complexity bounds obtained in this paper are polynomial in the size of the transition system in consideration, when the linear constraint is fixed.