On Selective Unboundedness of VASS

Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using Rackoffʹs proof or its variants, combined with Savitchʹs theorem. However, the question is still open for many others, e.g., reversal-boundedness. In the paper, we introduce the class of generalized unboundedness properties that can be verified in exponential space by extending Rackoffʹs technique, sometimes in an unorthodox way. We obtain new optimal upper bounds, for example for place boundedness problem, reversal-boundedness detection (several variants exist), strong promptness detection problem and regularity detection. Our analysis is sufficiently refined so as we also obtain a polynomial-space bound when the dimension is fixed.