instances/low_autocorrelation_n12__v11_nh.json

{
  "name": "low_autocorrelation_n12__v11_nh",
  "problem_type": "low_autocorrelation",
  "params": {
    "n": 12
  },
  "prompt": "Find a binary sequence of length 12 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..11 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 25.\n\nReturn seq as a list of 12 integers, each -1 or +1, or state \"UNSATISFIABLE\" if no such sequence exists.",
  "satisfiable": true,
  "solution": {
    "seq": [
      -1,
      1,
      1,
      -1,
      1,
      1,
      1,
      1,
      -1,
      -1,
      -1,
      1
    ],
    "c": [
      1,
      -2,
      -1,
      -2,
      1,
      0,
      -1,
      -2,
      1,
      2,
      -1
    ]
  },
  "difficulty": {
    "solve_time_ms": 1544.4,
    "search_space": 4096,
    "num_variables": 23,
    "num_constraints": 18,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 87.41,
    "solve_pct_type": 45.83
  },
  "partial_assignment": null
}