Abstract
In this column, Sylvain Schmitz summarizes two recent advances on the complexity of the reachability problem for vector addition systems with states. This is one of the most celebrated decidable problems in theoretical computer science, and until now, there was absolutely no upper bound on the complexity. It was only known that the algorithms run in finite time. The first advance described in this column, by Leroux and Schmitz, is a computable upper bound on the running time of the (original) algorithm for the problem. Admittedly, the upper bound puts the Ackermann function to shame -- read the great column to see what it is --- but it's an upper bound. The second advance, by Blondin, Finkel, Göller, Haase and McKenzie, is finding the exact complexity, namely PSPACE complete, of the two dimensional case, something that has also been open for several decades.
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