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Box-Reachability in Vector Addition Systems
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DOI：10.1007/978-3-032-09524-4_9.png)
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Abstract
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We consider a variant of reachability in Vector Addition Systems (VAS) dubbed box reachability, whereby a vector nu is an element of N-d is box-reachable from 0 in a VAS v if v admits a path from 0 to nu that not only stays in the positive orthant (as in the standard VAS semantics), but also stays below nu, i.e., within the box whose opposite corners are 0 and nu. Our main result is that for two-dimensional VAS, the set of box-reachable vertices almost coincides with the standard reachability set: the two sets coincide for all vectors whose coordinates are both above some threshold W. We also study properties of box-reachability, exploring the differences and similarities with standard reachability.
Keywords:
Vector Addition Systems
Box Reachability
Reachability Set
Two-Dimensional VAS
Threshold Properties
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