And that raises an interesting question: among real-world games those that people actually play, as opposed to the hypothetical ones game theorists usually consider , where does Magic fall in complexity? His team has measured the computational complexity of the game for the first time by encoding it in a way that can be played by a computer or Turing machine. First, some background. An important task in computer science is to determine whether a problem can be solved in principle. For example, deciding whether two numbers are relatively prime in other words , whether their largest common divisor is greater than 1 is a task that can be done in a finite number of well-defined steps and so is computable.
In an ordinary game of chess, deciding whether white has a winning strategy is also computable. The process involves testing every possible sequence of moves to see whether white can force a win. But while both these problems are computable, the resources required to solve them are vastly different.
This is where the notion of computational complexity comes in. This is a ranking based on the resources required to solve the problems. In this case, deciding whether two numbers are relatively prime can be solved in a number of steps that is proportional to a polynomial function of the input numbers. If the input is x , the most important term in a polynomial function is of the form Cx n , where C and n are constants.
This falls into a class known as P , where P stands for polynomial time. By contrast, the chess problem must be solved by brute force, and the number of steps this takes increases in proportion to an exponential function of the input. If the input is x , the most important term in an exponential function is of the form Cn x , where C and n are constants.
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The theme points to both that we have now risen from the depths TG10 - Submerged , and that "cloud computing" is becoming increasingly important in the world of computers. The technological Singularity. Simon McCallum at TG After the movie Back to the Future , released 30 years earlier. Binary , the base of how computers work. On or off, also known as bit.
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