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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.
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
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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