{"paper":{"title":"On the State Complexity of the Reverse of R- and J-trivial Regular Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Galina Jir\\'askov\\'a, Tom\\'a\\v{s} Masopust","submitted_at":"2013-04-02T18:42:05Z","abstract_excerpt":"The tight upper bound on the state complexity of the reverse of R-trivial and J-trivial regular languages of the state complexity n is 2^{n-1}. The witness is ternary for R-trivial regular languages and (n-1)-ary for J-trivial regular languages. In this paper, we prove that the bound can be met neither by a binary R-trivial regular language nor by a J-trivial regular language over an (n-2)-element alphabet. We provide a characterization of tight bounds for R-trivial regular languages depending on the state complexity of the language and the size of its alphabet. We show the tight bound for J-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0733","kind":"arxiv","version":2},"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"}