{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:N56LGAHIZ7G347HQ6OLCQQ3HSW","short_pith_number":"pith:N56LGAHI","schema_version":"1.0","canonical_sha256":"6f7cb300e8cfcdbe7cf0f396284367959ee1ab35133532539779d924415ee452","source":{"kind":"arxiv","id":"1112.5255","version":3},"attestation_state":"computed","paper":{"title":"Solving simple stochastic games with few coin toss positions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Peter Bro Miltersen, Rasmus Ibsen-Jensen","submitted_at":"2011-12-22T09:29:05Z","abstract_excerpt":"Gimbert and Horn gave an algorithm for solving simple stochastic games with running time O(r! n) where n is the number of positions of the simple stochastic game and r is the number of its coin toss positions. Chatterjee et al. pointed out that a variant of strategy iteration can be implemented to solve this problem in time 4^r r^{O(1)} n^{O(1)}. In this paper, we show that an algorithm combining value iteration with retrograde analysis achieves a time bound of O(r 2^r (r log r + n)), thus improving both time bounds. While the algorithm is simple, the analysis leading to this time bound is inv"},"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":"1112.5255","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-12-22T09:29:05Z","cross_cats_sorted":[],"title_canon_sha256":"652c8274c8a252d05475416fe69a22b824d6bebff6f1f9154615c2ed537d2647","abstract_canon_sha256":"b4b2edaee66eac12ad6d38eec891e76031dd7ed174377364511f8a3a33228de6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:39.750272Z","signature_b64":"hUNgaSUFVtkjtblsA8adxMdPpgsEkv2I/vCWNsCxSI90i0TzKNdWjJoUcOEbFrr/du/A8vJhZRfvI9cJtvJUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f7cb300e8cfcdbe7cf0f396284367959ee1ab35133532539779d924415ee452","last_reissued_at":"2026-05-18T03:59:39.749597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:39.749597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving simple stochastic games with few coin toss positions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Peter Bro Miltersen, Rasmus Ibsen-Jensen","submitted_at":"2011-12-22T09:29:05Z","abstract_excerpt":"Gimbert and Horn gave an algorithm for solving simple stochastic games with running time O(r! n) where n is the number of positions of the simple stochastic game and r is the number of its coin toss positions. Chatterjee et al. pointed out that a variant of strategy iteration can be implemented to solve this problem in time 4^r r^{O(1)} n^{O(1)}. In this paper, we show that an algorithm combining value iteration with retrograde analysis achieves a time bound of O(r 2^r (r log r + n)), thus improving both time bounds. While the algorithm is simple, the analysis leading to this time bound is inv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5255","kind":"arxiv","version":3},"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":"1112.5255","created_at":"2026-05-18T03:59:39.749703+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.5255v3","created_at":"2026-05-18T03:59:39.749703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5255","created_at":"2026-05-18T03:59:39.749703+00:00"},{"alias_kind":"pith_short_12","alias_value":"N56LGAHIZ7G3","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"N56LGAHIZ7G347HQ","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"N56LGAHI","created_at":"2026-05-18T12:26:37.096874+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/N56LGAHIZ7G347HQ6OLCQQ3HSW","json":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW.json","graph_json":"https://pith.science/api/pith-number/N56LGAHIZ7G347HQ6OLCQQ3HSW/graph.json","events_json":"https://pith.science/api/pith-number/N56LGAHIZ7G347HQ6OLCQQ3HSW/events.json","paper":"https://pith.science/paper/N56LGAHI"},"agent_actions":{"view_html":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW","download_json":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW.json","view_paper":"https://pith.science/paper/N56LGAHI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.5255&json=true","fetch_graph":"https://pith.science/api/pith-number/N56LGAHIZ7G347HQ6OLCQQ3HSW/graph.json","fetch_events":"https://pith.science/api/pith-number/N56LGAHIZ7G347HQ6OLCQQ3HSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW/action/storage_attestation","attest_author":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW/action/author_attestation","sign_citation":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW/action/citation_signature","submit_replication":"https://pith.science/pith/N56LGAHIZ7G347HQ6OLCQQ3HSW/action/replication_record"}},"created_at":"2026-05-18T03:59:39.749703+00:00","updated_at":"2026-05-18T03:59:39.749703+00:00"}