Correct predictions are in blue. If we detect only a subset of a labelled sentence, we highlight the caught part as blue, the missing part light blue. False positives are in green and false negatives are in red.

Problem 032 (Still life) — Constraint detection

This problem arises from the Game of Life , invented by John Horton Conway in the 1960s and popularized by Martin Gardner in his Scientific American columns . Life is played on a squared board , considered to extend to infinity in all directions . Each square of the board is a cell , which at any time during the game is either alive or dead . A cell has eight neighbours : The configuration of live and dead cells at time t leads to a new configuration at time t +1 according to the rules of the game : if a cell has exactly three living neighbours at time t , it is alive at time t +1 ; if a cell has exactly two living neighbours at time t it is in the same state at time t +1 as it was at time t ; otherwise , the cell is dead at time t +1 . A stable pattern , or still-life , is not changed by these rules . Hence , every cell that has exactly three live neighbours is alive , and every cell that has fewer than two or more than three live neighbours is dead . -LRB- An empty board is a still-life , for instance . -RRB- What is the densest possible still-life pattern , i.e. the pattern with the largest number of live cells , that can be fitted into an n x n section of the board , with all the rest of the board dead ?

Problem 032 (Still life) — Detection of the decisions and objects to be modeled

This problem arises from the Game of Life , invented by John Horton Conway in the 1960s and popularized by Martin Gardner in his Scientific American columns . Life is played on a squared board , considered to extend to infinity in all directions . Each square of the board is a cell , which at any time during the game is either alive or dead . A cell has eight neighbours : The configuration of live and dead cells at time t leads to a new configuration at time t +1 according to the rules of the game : if a cell has exactly three living neighbours at time t , it is alive at time t +1 ; if a cell has exactly two living neighbours at time t it is in the same state at time t +1 as it was at time t ; otherwise , the cell is dead at time t +1 . A stable pattern , or still-life , is not changed by these rules . Hence , every cell that has exactly three live neighbours is alive , and every cell that has fewer than two or more than three live neighbours is dead . -LRB- An empty board is a still-life , for instance . -RRB- What is the densest possible still-life pattern , i.e. the pattern with the largest number of live cells , that can be fitted into an n x n section of the board , with all the rest of the board dead ?

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