Reachability in Vector Addition Systems is Ackermann-complete · HackerPapers discussions

Reachability in Vector Addition Systems is Ackermann-complete — mentioned by nyrikki

Tue, 19 May 2026 17:30:06 GMT

As TLA+ uses state machines that can define infinite state spaces, checking arbitrary temporal logic formulas is undecidable in the general case. Using a TLC model checker to verify invariants or properties, finding a valid counterexample can scale non-elementarily. In fact, in some situations it can end up being Ackermann-complete[0], but even recursively enumerable problems can be Tower-complete. I would say that unless you focus on more detailed temporal logic pitfalls you may have issues. So IMHO this will stay a use case specific solution, that you choose based on context. Even a common…

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Reachability in Vector Addition Systems is Ackermann-complete — mentioned by hwayne

Thu, 17 Apr 2025 18:59:18 GMT

> Hmm.. I'd love to see a more formal statement of this, because it feels unintuitive. The problem is called "Vector Addition System Reachability", and the proof that it's Ackermann-complete is here: https://arxiv.org/pdf/2104.13866 (It's actually for "Vector Addition Systems with states, but the two are equivalent formalisms. They're also equivalent to Petri nets, which is what got me interested in this problem in the first place!) > Notably the question "given a number as input, output as many 1's as that number" is exponential in the input size. Is this problem therefore also strictly…

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Reachability in Vector Addition Systems is Ackermann-complete — mentioned by hwayne

Mon, 04 Dec 2023 20:10:40 GMT

If you're up for the challenge, the original paper proving ACK-completeness is here: https://arxiv.org/pdf/2104.13866.pdf

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