{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1490",
  "content_hash": null,
  "slug": "deterministic-logspace-versus-nondeterministic-logspace-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "NL=coNL, undirected reachability is in L, and directed reachability has sublinear-space algorithms with larger time or other tradeoffs.",
  "relevance": "For Is L equal to NL?, record deterministic-logspace-versus-nondeterministic-logspace-claim-literature-frontier (“Strongest checked neighboring result”) records a bound, answer, status fact, or structural consequence. The record states: NL=coNL, undirected reachability is in L, and directed reachability has sublinear-space algorithms with larger time or other tradeoffs.",
  "relevance_source": "recorded",
  "body": "NL=coNL, undirected reachability is in L, and directed reachability has sublinear-space algorithms with larger time or other tradeoffs.\n\nThis leaves the following boundary unresolved: Deterministic logarithmic space for directed reachability remains unknown. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1137/0217058",
      "locator": "N. Immerman, Nondeterministic space is closed under complementation, SIAM Journal on Computing 17 (1988). NL=coNL theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1137/0217058",
    "locator": "N. Immerman, Nondeterministic space is closed under complementation, SIAM Journal on Computing 17 (1988). NL=coNL theorem"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1491",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "deterministic-logspace-versus-nondeterministic-logspace",
      "title": "deterministic logspace versus nondeterministic logspace",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}