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Computing Downward Closures for Stacked Counter Automata Zetzsche, Georg abstraction downward closure obstruction set computability The downward closure of a language L of words is the set of all (not necessarily contiguous) subwords of members of L. It is well known that the downward closure of any language is regular. Although the downward closure seems to be a promising abstraction, there are only few language classes for which an automaton for the downward closure is known to be computable. It is shown here that for stacked counter automata, the downward closure is computable. Stacked counter automata are finite automata with a storage mechanism obtained by adding blind counters and building stacks. Hence, they generalize pushdown and blind counter automata. The class of languages accepted by these automata are precisely those in the hierarchy obtained from the context-free languages by alternating two closure operators: imposing semilinear constraints and taking the algebraic extension. The main tool for computing downward closures is the new concept of Parikh annotations. As a second application of Parikh annotations, it is shown that the hierarchy above is strict at every level. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Georg Zetzsche 2015 Is Part Of LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2015.743 urn:nbn:de:0030-drops-49554 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.743 eng https://creativecommons.org/licenses/by/3.0/legalcode