{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1491",
  "content_hash": null,
  "slug": "deterministic-logspace-versus-nondeterministic-logspace-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: NL=coNL, undirected reachability is in L, and directed reachability has sublinear-space algorithms with larger time or other tradeoffs. Exact unresolved remainder: Deterministic logarithmic space for directed reachability remains unknown.",
  "relevance": "For Is L equal to NL?, record deterministic-logspace-versus-nondeterministic-logspace-claim-status-20260801 (“Current status and exact unresolved remainder”) records a bound, answer, status fact, or structural consequence. The record states: OPEN as checked on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: NL=coNL, undirected reachability is in L, and directed reachability has sublinear-space algorithms with larger time or other tradeoffs.\n\nThe exact unresolved remainder is: Deterministic logarithmic space for directed reachability remains unknown.\n\nA complete resolution must meet the following acceptance conditions:\n- Give a deterministic O(log n)-space algorithm for every NL problem, equivalently directed reachability.\n- Or prove a language in NL requires more than logarithmic deterministic space.",
  "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"
  },
  "relations": [
    {
      "slug": "R1490",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1488",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1489",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "deterministic-logspace-versus-nondeterministic-logspace",
      "title": "deterministic logspace versus nondeterministic logspace",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}