{"paper":{"title":"The complexity of Presburger arithmetic with power or powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alessio Mansutti, Dmitry Chistikov, Michael Benedikt","submitted_at":"2023-05-04T17:57:16Z","abstract_excerpt":"We investigate expansions of Presburger arithmetic, i.e., the theory of the integers with addition and order, with additional structure related to exponentiation: either a function that takes a number to the power of $2$, or a predicate for the powers of $2$. The latter theory, denoted $\\mathrm{PresPower}$, was introduced by B\\\"uchi as a first attempt at characterizing the sets of tuples of numbers that can be expressed using finite automata; B\\\"uchi's method does not give an elementary upper bound, and the complexity of this theory has been open. The former theory, denoted as $\\mathrm{PresExp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.03037","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.03037/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}