Automated logical verification based on trace abstractions
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We delimit the boundary between decidability versus undecidability of the weak monadic second-order logic of one successor (WS1S) extended with linear cardinality constraints of the form |X1|+...+|Xr| Y1|+...+|Ys|, where the Xis and Yjs range over finite subsets of natural numbers. Our decidability and undecidability results are based on an extension of the classic logic-automata connection using a novel automaton model based on Parikh maps.