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A Counting Logic for Structure Transition Systems Kaiser, Lukasz Leßenich, Simon Logic in Computer Science Quantitative Logics Model Checking Quantitative questions such as "what is the maximum number of tokens in a place of a Petri net?" or "what is the maximal reachable height of the stack of a pushdown automaton?" play a significant role in understanding models of computation. To study such problems in a systematic way, we introduce structure transition systems on which one can define logics that mix temporal expressions (e.g. reachability) with properties of a state (e.g. the height of the stack). We propose a counting logic Qmu[#MSO] which allows to express questions like the ones above, and also many boundedness problems studied so far. We show that Qmu[#MSO] has good algorithmic properties, in particular we generalize two standard methods in model checking, decomposition on trees and model checking through parity games, to this quantitative logic. These properties are used to prove decidability of Qmu[#MSO] on tree-producing pushdown systems, a generalization of both pushdown systems and regular tree grammars. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Lukasz Kaiser and Simon Leßenich 2012 Is Part Of LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2012.366 urn:nbn:de:0030-drops-36848 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.366 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode