# Cut-elimination and the decidability of reachability in alternating pushdown systems

Abstract : We propose a new approach to formalize alternating pushdown systems as natural-deduction style inference systems. In this approach, the decidability of reachability can be proved as a simple consequence of a cut-elimination theorem for the corresponding inference system. Then, we show how this result can be used to extend an alternating pushdown system into a complete system where, for every configuration $A$, either $A$ or $\neg A$ is provable. The key idea is that cut-elimination permits to build a system where a proposition of the form $\neg A$ has a co-inductive (hence possibly infinite) proof if and only if it has an inductive (hence finite) proof.
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Preprints, Working Papers, ...

Cited literature [11 references]

https://hal.inria.fr/hal-01101835
Contributor : Gilles Dowek <>
Submitted on : Friday, January 30, 2015 - 12:05:31 PM
Last modification on : Friday, May 25, 2018 - 12:02:06 PM
Long-term archiving on: : Friday, September 11, 2015 - 6:27:51 AM

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reachability.pdf
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• HAL Id : hal-01101835, version 1

### Citation

Gilles Dowek, Ying Jiang. Cut-elimination and the decidability of reachability in alternating pushdown systems. 2015. ⟨hal-01101835⟩

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