Multiply-recursive upper bounds with Higman's Lemma
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Model checking coverability graphs of vector addition systems
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Complexity analysis of the backward coverability algorithm for VASS
RP'11 Proceedings of the 5th international conference on Reachability problems
The Ordinal-Recursive Complexity of Timed-arc Petri Nets, Data Nets, and Other Enriched Nets
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
The theory of WSTS: the case of complete WSTS
PETRI NETS'12 Proceedings of the 33rd international conference on Application and Theory of Petri Nets
Ordinal theory for expressiveness of well-structured transition systems
Information and Computation
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
The power of well-structured systems
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
Computable fixpoints in well-structured symbolic model checking
Formal Methods in System Design
Presburger Vector Addition Systems
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Dickson's Lemma is a simple yet powerful tool widely used in decidability proofs, especially when dealing with counters or related data structures in algorithmics, verification and model-checking, constraint solving, logic, etc. While Dickson's Lemma is well-known, most computer scientists are not aware of the complexity upper bounds that are entailed by its use. This is mainly because, on this issue, the existing literature is not very accessible. We propose a new analysis of the length of bad sequences over $(\mathbb{N}^k,\leq)$, improving on earlier results and providing upper bounds that are essentially tight. This analysis is complemented by a ``user guide'' explaining through practical examples how to easily derive complexity upper bounds from Dickson's Lemma.