{"paper":{"title":"An Efficient Algorithm for the Equation Tree Automaton via the $k$-C-Continuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Djelloul Ziadi, Ludovic Mignot, Nadia Ouali Sebti","submitted_at":"2014-01-23T12:11:52Z","abstract_excerpt":"Champarnaud and Ziadi, and Khorsi et al. show how to compute the equation automaton of word regular expression $E$ via the $k$-C-Continuations.\n  Kuske and Meinecke extend the computation of the equation automaton to a regular tree expression $E$ over a ranked alphabet $\\Sigma$ and produce a $O(R\\cdot|E|^2)$ time and space complexity algorithm, where $R$ is the maximal rank of a symbol occurring in $\\Sigma$ and $|E|$ is the size of $E$. In this paper, we give a full description of the algorithm based on the acyclic minimization of Revuz. Our algorithm, which is performed in an $O(|Q|\\cdot|E|)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5951","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}