{"paper":{"title":"A walk on max-plus algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Akiko Fukuda, Etsuo Segawa, Iwao Sato, Sennosuke Watanabe","submitted_at":"2019-08-23T23:57:30Z","abstract_excerpt":"Max-plus algebra is a kind of idempotent semiring over $\\mathbb{R}_{\\max}:=\\mathbb{R}\\cup\\{-\\infty\\}$ with two operations $\\oplus := \\max$ and $\\otimes := +$.In this paper, we introduce a new model of a walk on one dimensional lattice on $\\mathbb{Z}$, as an analogue of the quantum walk, over the max-plus algebra and we call it max-plus walk. In the conventional quantum walk, the summation of the $\\ell^2$-norm of the states over all the positions is a conserved quantity. In contrast, the summation of eigenvalues of state decision matrices is a conserved quantity in the max-plus walk.Moreover, s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09051","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/1908.09051/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"}