{"paper":{"title":"Computing degree and class degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mahsa Allahbakhshi","submitted_at":"2014-04-09T16:10:49Z","abstract_excerpt":"Let $\\pi$ be a factor code from a one dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$. If $\\pi$ is finite-to-one then the number of preimages of a typical point in $Y$ is an invariant called the degree of $\\pi$. In this paper we present an algorithm to compute this invariant. The generalized notion of the degree when $\\pi$ is not limited to finite-to-one factor codes, is called the class degree of $\\pi$. The class degree of a code is defined to be the number of transition classes over a typical point of $Y$ and is invariant under topological conjugacy. We show that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2530","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"}