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The Complexity of the Finite Containment Problem for Petri Nets
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Algorithmic analysis of programs with well quasi-ordered domains
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Well-structured transition systems everywhere!
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Post embedding problem is not primitive recursive, with applications to channel systems
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MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
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ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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Well-structured systems, aka WSTS, are computational models where the set of possible configurations is equipped with a well-quasi-ordering which is compatible with the transition relation between configurations. This structure supports generic decidability results that are important in verification and several other fields. This paper recalls the basic theory underlying well-structured systems and shows how two classic decision algorithms can be formulated as an exhaustive search for some "bad" sequences. This lets us describe new powerful techniques for the complexity analysis of WSTS algorithms. Recently, these techniques have been successful in precisely characterizing the power, in a complexity-theoretical sense, of several important WSTS models like unreliable channel systems, monotonic counter machines, or networks of timed systems.