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"name": "low_autocorrelation_n11__v3_h",
"problem_type": "low_autocorrelation",
"params": {
"n": 11
},
"prompt": "Find a binary sequence of length 11 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..10 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 23.\n\nReturn seq as a list of 11 integers, each -1 or +1, or state \"UNSATISFIABLE\" if no such sequence exists.\n\nPartial assignment (fixed values that must be respected):\n- seq[1]=1, seq[8]=1\n- c[6]=0, c[9]=1\nReturn a complete solution consistent with these fixed assignments.",
"satisfiable": true,
"solution": {
"seq": [
-1,
1,
-1,
1,
1,
-1,
1,
1,
1,
-1,
-1
],
"c": [
-2,
-1,
0,
-1,
2,
-3,
0,
-1,
0,
1
]
},
"difficulty": {
"solve_time_ms": 974.3,
"search_space": 2048,
"num_variables": 21,
"num_constraints": 17,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 66.73,
"solve_pct_type": 4.17
},
"partial_assignment": {
"seq": {
"1": 1,
"8": 1
},
"c": {
"6": 0,
"9": 1
}
}
}
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