{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:AV5VYWGLCU5ER6AXDKPBM75DPN","short_pith_number":"pith:AV5VYWGL","schema_version":"1.0","canonical_sha256":"057b5c58cb153a48f8171a9e167fa37b4990c9eebe2e1714928ce7f2fb53303c","source":{"kind":"arxiv","id":"1310.5242","version":1},"attestation_state":"computed","paper":{"title":"Groups and Semigroups Defined by Colorings of Synchronizing Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.CO"],"primary_cat":"math.GR","authors_text":"Daniele D'Angeli, Emanuele Rodaro","submitted_at":"2013-10-19T16:11:48Z","abstract_excerpt":"In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to finitely generated synchronizing automata and characterize finite automata groups in terms of nilpotency of the corresponding DFA. Moreover, we present a decidable sufficient condition to have free semigroups in an automaton group. A series of examples and applications is widely discussed, in particular we show a way to color the De Bruijn automata into Mealy aut"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.5242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-19T16:11:48Z","cross_cats_sorted":["cs.FL","math.CO"],"title_canon_sha256":"dc831ba9766bb3746ae9a9264bf5cc0e2bd04571b503fcb2c295a13828e91dd8","abstract_canon_sha256":"c43cb28fd09e07a6258877d049f89e8ccde7f1940eb7b383be8bb50dff146eac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:52.630325Z","signature_b64":"z0JE/5PmDXkBWOf1B8nwlVvwgykzDxymFx5Z4WGAm7mBwQxPvB3/RCZiIuf3mXrpp0LqiyWS2QxPKDyKi95QBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"057b5c58cb153a48f8171a9e167fa37b4990c9eebe2e1714928ce7f2fb53303c","last_reissued_at":"2026-05-18T02:34:52.629927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:52.629927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groups and Semigroups Defined by Colorings of Synchronizing Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.CO"],"primary_cat":"math.GR","authors_text":"Daniele D'Angeli, Emanuele Rodaro","submitted_at":"2013-10-19T16:11:48Z","abstract_excerpt":"In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to finitely generated synchronizing automata and characterize finite automata groups in terms of nilpotency of the corresponding DFA. Moreover, we present a decidable sufficient condition to have free semigroups in an automaton group. A series of examples and applications is widely discussed, in particular we show a way to color the De Bruijn automata into Mealy aut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5242","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.5242","created_at":"2026-05-18T02:34:52.629987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5242v1","created_at":"2026-05-18T02:34:52.629987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5242","created_at":"2026-05-18T02:34:52.629987+00:00"},{"alias_kind":"pith_short_12","alias_value":"AV5VYWGLCU5E","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"AV5VYWGLCU5ER6AX","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"AV5VYWGL","created_at":"2026-05-18T12:27:38.830355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN","json":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN.json","graph_json":"https://pith.science/api/pith-number/AV5VYWGLCU5ER6AXDKPBM75DPN/graph.json","events_json":"https://pith.science/api/pith-number/AV5VYWGLCU5ER6AXDKPBM75DPN/events.json","paper":"https://pith.science/paper/AV5VYWGL"},"agent_actions":{"view_html":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN","download_json":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN.json","view_paper":"https://pith.science/paper/AV5VYWGL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5242&json=true","fetch_graph":"https://pith.science/api/pith-number/AV5VYWGLCU5ER6AXDKPBM75DPN/graph.json","fetch_events":"https://pith.science/api/pith-number/AV5VYWGLCU5ER6AXDKPBM75DPN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN/action/storage_attestation","attest_author":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN/action/author_attestation","sign_citation":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN/action/citation_signature","submit_replication":"https://pith.science/pith/AV5VYWGLCU5ER6AXDKPBM75DPN/action/replication_record"}},"created_at":"2026-05-18T02:34:52.629987+00:00","updated_at":"2026-05-18T02:34:52.629987+00:00"}