Vector addition tree automata

Rewriting Systems for Reachability in Vector Addition Systems with Pairs

“…Indeed, in both cases, promenades are positive. It turns out that RP VASP implies RP BVASS , which is equivalent to the decidability of MELL provability [2].…”

“…the VASP in Fig. 1(b) is not a B-path from {1} because the only path connecting 3 to 1 contains the cycle (2,4,3). However the cycle (4,5,4) in Fig.…”

“…Branching Extension of VASS (BVASS also called VATA [2]) for which KarpMiller trees were designed [18] are by the way a particular restriction of VASP, where arcs in a pair do only share their target. A motivating result about BVASS was given by [2]: the reachability decision problem for BVASS is equivalent to the open decision problem of the provability in Multiplicative and Exponential Linear Logic (MELL [8]).…”

“…A motivating result about BVASS was given by [2]: the reachability decision problem for BVASS is equivalent to the open decision problem of the provability in Multiplicative and Exponential Linear Logic (MELL [8]). The VASP operational semantic we consider is restricted, so we have not full generalization of BVASS but an essential intersection.…”

“…In fact we allow to traverse pairs only under a condition called division of values, that preserves the sign component-wise. However our condition is implicit for reachability problems with positive values, like in the proof given by [2] to establish their equivalence result.…”