The theory of reachability in trace-pushdown systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911643620868096 |
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| author | Kuske, Dietrich |
| author_facet | Kuske, Dietrich |
| contents | We consider pushdown systems that store, instead of a single word, a Mazurkiewicz trace on its stack. These systems are special cases of valence automata over graph monoids and subsume multi-stack systems. We identify a class of such systems that allow to decide the first-order theory of their configuration graph with reachability.
This result complements results by D'Osualdo, Meyer, and Zetzsche (namely the decidability for arbitrary pushdown systems under a severe restriction on the dependence alphabet). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The theory of reachability in trace-pushdown systems Kuske, Dietrich Formal Languages and Automata Theory We consider pushdown systems that store, instead of a single word, a Mazurkiewicz trace on its stack. These systems are special cases of valence automata over graph monoids and subsume multi-stack systems. We identify a class of such systems that allow to decide the first-order theory of their configuration graph with reachability. This result complements results by D'Osualdo, Meyer, and Zetzsche (namely the decidability for arbitrary pushdown systems under a severe restriction on the dependence alphabet). |
| title | The theory of reachability in trace-pushdown systems |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2507.15733 |