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Space complexity

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Space complexity

[AB 4]

The recorded state of a Turing machine at a specific time

- How many distinctconfigurationsmay a Turing machine that uses s cells have?

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n

s

T

- The input stays fixed (Read only tape)
- The output (or the output tape head) does not affect
- the next transitions (Right only, write only tape).

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n

s

T

For a given input string x {0,1}n

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n

s

Def: The space complexity of a Turing Machine T on input x is the maximal number of tape cells used throughout the computation.

Gx=(V,E)

V – All possible configurations for the given input x.

E – An edge between configurations c and c’,

if there exists a legal step from c to c’.

Proof: A deterministic run that halts must avoid repeating a configuration

its running time is bounded from above by the number of configurations the machine has,

which, for a PSPACE machine, is at most exponential