Cut-elimination and the decidability of reachability in alternating pushdown systems
Résumé
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.
Domaines
Logique en informatique [cs.LO]Origine | Fichiers produits par l'(les) auteur(s) |
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