@article{blondin_finkel_goubault-larrecq_2018, 
  title={Forward Analysis for WSTS, Part III: Karp-Miller Trees}, 
  DOI={10.23638/lmcs-16(2:13)2020}, 
  abstractNote={This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and "Forward Analysis for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward reachability analyses of WSTS, using finite representations of downward-closed sets. We further develop this framework to obtain a generic Karp-Miller algorithm for the new class of very-WSTS. This allows us to show that coverability sets of very-WSTS can be computed as their finite ideal decompositions. Under natural effectiveness assumptions, we also show that LTL model checking for very-WSTS is decidable. The termination of our procedure rests on a new notion of acceleration levels, which we study. We characterize those domains that allow for only finitely many accelerations, based on ordinal ranks.}, 
  publisher={episciences.org}, 
  author={Blondin, Michael and Finkel, Alain and Goubault-Larrecq, Jean}, 
  year={2018}, 
  month={Nov}
  }