18-space-complexity

# 18-space-complexity - Space Complexity Time and space are...

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Space Complexity Time and space are two of the most important considerations when we seek practical solutions to computational problems. Space complexity shares many of the same features of time complexity Therefore, space complexity serves as a further way of classifying problems according to their computational difficulty. We will continue to use the TM as our model, but now we look at the tape space it consumes during its computation. –p

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Space Complexity Definition: Let M be a deterministic TM that halts on all inputs. We define the space complexity of M to be the function f : N N , where f ( n ) is the maximum number of tape cells that M scans on any input of length n . If the space complexity of M is f ( n ) , then we also say that M runs in space f ( n ) . If M is a nondeterministic TM wherein all branches halt on all inputs we define its space complexity f ( n ) to be the maximum number of tape cells that M scans on any branch of its computation on any input of length n . –p
Space Complexity Definition: Let f : N R + be a function. The space complexity classes , SPACE ( f ( n )) and NSPACE ( f ( n )) , are defined as follows,

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18-space-complexity - Space Complexity Time and space are...

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