Characterising Petri Net Solvable Binary Words

Bounded choice-free Petri net synthesis: algorithmic issues

“…Indeed, TS 8 survives all of the above pre-synthesis tests, since all properties are satisfied. It will not survive proper synthesis, however; for its non-solvability, the reader is referred to a more general analysis of 2-label lts (e.g., [8]). Fig.…”

“…In the first loop, a spanning tree is constructed, and for every state s, the Parikh vector ∆ s of a small path from ı to s is saved. 8 The second loop scans all edges which are not in the spanning tree. By these edges, a cycle is created back to some state s which has already been seen before.…”

“…It may be observed that, for each x ∈ T , the definition of the set mXNX (x) is essentially computational, since it is based on arithmetic formulas about the distances. But any set M with mXNX (x) ⊆ M ⊆ XNX (x) may be used instead in formula (8) to guarantee that no existing x-labelled arc is prevented.…”

“…It is not known how this could be avoided completely, but better solvability conditions are known in special cases [8,29].…”

“…Weak backward determinism might also be assumed. However, this is not essential for the rest of the algorithm, and it will be guaranteed by the rest of the checks by Theorem 5; but checking this property beforehand is easy, may speed up the pre-synthesis, and allows to produce a more specific error message in case of failure 8. It would have been possible to incorporate the tests for determinism and persistence in this loop, instead of doing them beforehand; but doing these tests separately is cheap, so that the gain seems negligible.…”