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MSO Decidability of Multi-Pushdown Systems via Split-Width

Abstract : Multi-threaded programs with recursion are naturally modeled as multi-pushdown systems. The behaviors are represented as multiply nested words (MNWs), which are words enriched with additional binary relations for each stack matching a push operation with the corresponding pop operation. Any MNW can be decomposed by two basic and natural operations: shuffle of two sequences of factors and merge of consecutive factors of a sequence. We say that the split-width of a MNW is k if it admits a decomposition where the number of factors in each sequence is at most k. The MSO theory of MNWs with split-width k is decidable. We introduce two very general classes of MNWs that strictly generalize known decidable classes and prove their MSO decidability via their split-width and obtain comparable or better bounds of tree-width of known classes.
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https://hal.inria.fr/hal-00776596
Contributor : Benedikt Bollig <>
Submitted on : Tuesday, January 15, 2013 - 5:34:54 PM
Last modification on : Monday, February 15, 2021 - 10:50:13 AM

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Aiswarya Cyriac, Paul Gastin, K. Narayan Kumar. MSO Decidability of Multi-Pushdown Systems via Split-Width. Proceedings of the 23rd International Conference on Concurrency Theory (CONCUR'12), 2012, Newcastle, United Kingdom. pp.547-561, ⟨10.1007/978-3-642-32940-1_38⟩. ⟨hal-00776596⟩

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