Abstract

We consider the following decision problems. PROOFNET: given a multiplicative linear logic (MLL) proof structure, is it a proof net? ESSNET: given an essential net (of an intuitionistic MLL sequent), is it correct? The authors show that linear-time algorithms for ESSNET can be obtained by constructing the dominator tree of the input essential net. As a corollary, by showing that PROOFNET is linear-time reducible to ESSNET (by the trip translation), we obtain a linear-time algorithm for PROOFNET. We show further that these linear-time algorithms can be optimized to simple one-pass algorithms: each node of the input structure is visited at most once. As another application of dominator trees, we obtain linear time algorithms for sequentializing proof nets (i.e. given a proof net, find a derivation for the underlying MLL sequent) and essential nets.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.