New complexity results for some linear counting problems using minimal solutions to linear diophantine equations
Authors: 
Gaoyan Xie, Cheng Li, Zhe DangAuthors Info & Claims
Gaoyan Xie, Cheng Li, Zhe DangAuthors Info & ClaimsPages 163 - 175
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.
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- Graduat Division, University of California, Santa Barbara
- Computer Science Department, University of California, Santa Barbara
- College of Engineering, University of California, Santa Barbara
- Expertcity, Inc.
- AT&T: AT&T Labs Research
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Published: 16 July 2003
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