{
  "id": "2409.00631",
  "version": "v1",
  "published": "2024-09-01T06:38:09.000Z",
  "updated": "2024-09-01T06:38:09.000Z",
  "title": "There is a deep 1-generic set",
  "authors": [
    "Ang Li"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "An infinite binary sequence is Bennett deep if, for any computable time bound, the difference between the time-bounded prefix-free Kolmogorov complexity and the prefix-free Kolmogorov complexity of its initial segments is eventually unbounded. It is known that weakly 2-generic sets are shallow, i.e. not deep. In this paper, we show that there is a deep 1-generic set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-01T06:38:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03D30",
      "68Q30"
    ],
    "keywords": [
      "infinite binary sequence",
      "time-bounded prefix-free kolmogorov complexity",
      "initial segments",
      "bennett deep",
      "computable time bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}