{"paper":{"title":"Mathematical Informatics: Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Algorithms are defined as finite directed graphs whose edges are labelled by partial maps over an abstract data structure.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"JFLI), Thomas Seiller (CNRS","submitted_at":"2026-05-18T12:55:40Z","abstract_excerpt":"This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of computation are described as monoid actions on a configuration space, and programs as dynamical systems constrained by this action. Within this framework, we introduce a formal notion of algorithm as a finite directed graph whose edges are labelled by partial maps over an abstract data structure. This definition separates control from data, representing the forme"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce a formal notion of algorithm as a finite directed graph whose edges are labelled by partial maps over an abstract data structure. This yields a precise notion of implementation and situates algorithms as abstract partial specifications of computational behaviour.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That models of computation can be uniformly described as monoid actions on a configuration space and that programs are dynamical systems constrained by this action, allowing a correspondence between computational steps and labelled graph transitions that preserves induced transformations on data representations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Algorithms are defined as finite directed graphs with edges labelled by partial maps on abstract data structures, with programs implementing them via step correspondences that preserve data transformations in monoid-action models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Algorithms are defined as finite directed graphs whose edges are labelled by partial maps over an abstract data structure.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"28f1ab8b988ac21540e1e769a7fd5b23487cf5d18f4dec4c2dbbf03eb53e1dcb"},"source":{"id":"2605.18342","kind":"arxiv","version":1},"verdict":{"id":"f790d6d3-dacc-46c8-9f9b-dbffe4a7242b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:35:58.289370Z","strongest_claim":"We introduce a formal notion of algorithm as a finite directed graph whose edges are labelled by partial maps over an abstract data structure. This yields a precise notion of implementation and situates algorithms as abstract partial specifications of computational behaviour.","one_line_summary":"Algorithms are defined as finite directed graphs with edges labelled by partial maps on abstract data structures, with programs implementing them via step correspondences that preserve data transformations in monoid-action models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That models of computation can be uniformly described as monoid actions on a configuration space and that programs are dynamical systems constrained by this action, allowing a correspondence between computational steps and labelled graph transitions that preserves induced transformations on data representations.","pith_extraction_headline":"Algorithms are defined as finite directed graphs whose edges are labelled by partial maps over an abstract data structure."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18342/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:20.421911Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:40:58.068350Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.162306Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.826338Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ef12570b3b3c2ab1c61496d4171c26a40f2e1f5eaba5bda2b43bf78c8cb7b4c1"},"references":{"count":25,"sample":[{"doi":"","year":2022,"title":"Polity Press (2022), https://books.google.fr/books?id=sIVdzgEACAAJ","work_id":"e5984e2f-44e3-44b0-b930-ea15578a7f36","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Anh-Ton Le, H.L., Valarcher, P.: Completeness of Seiller ’s Abstract Machine (2025), https://hal.u-pec.fr/hal-05137612 , preprint","work_id":"992a24f8-0c13-4d2d-bf03-b8f4567b8518","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/bf01201998","year":1992,"title":"Computational Complexity 2 (1992), https://doi.org/10.1007/BF01201998","work_id":"a9f84e8f-5e5a-4c14-8da3-e688ef221750","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Bulletin of the European Association for Theoretical Computer Science (2003)","work_id":"1788b944-1770-48d1-86d3-75dd0097e120","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"Blass, A., Dershowitz, N., Gurevich, Y.: When are two algo rithms the same? CoRR abs/0811.0811 (2008), http://arxiv.org/abs/0811.0811","work_id":"fecd590c-0f9c-4546-831a-87ab6046ca02","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":25,"snapshot_sha256":"eda05253232013f925164c379214a7ee998cc555bbda6ea6cb835866f71d41ce","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"}