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Space complexity

Space complexity. [AB 4]. Input/Work/Output TM. Configurations (First try). The recorded state of a Turing machine at a specific time. How many distinct configurations may a Turing machine that uses s cells have?. |  | T. |  | n. . |  | s. | Q |. n. . s. . T. . . .

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Space complexity

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  1. Space complexity [AB 4]

  2. Input/Work/Output TM

  3. Configurations (First try) The recorded state of a Turing machine at a specific time • How many distinctconfigurationsmay a Turing machine that uses s cells have? ||T ||n  ||s |Q| n  s  T   

  4. Configurations • 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). ||T ||n  ||s |Q| n  s  T   

  5. Configurations For a given input string x  {0,1}n ||s |Q| n  s  

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

  7. Space-Complexity

  8. Space vs. Time

  9. The Configuration graph for a given input x. 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’.

  10. PSPACE  EXP 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

  11. Name the Class

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