Space Complexity Costas Busch LSU 1 Space complexity

Space Complexity Costas Busch - LSU 1

Space complexity for deterministic Turing machine: Maximum number of cells that the machine scans on any input string of size …… …… input string …… …… total space used Costas Busch - LSU 2

Space complexity for non-deterministic Turing machine: Maximum number of cells that the machine scans on any input string of size in any computation path …… …… input string …… …… total space used Costas Busch - LSU 3

all deterministic decidable languages that use space all non-deterministic decidable languages that use space Costas Busch - LSU 4

Example linear space problem SAT: given a formula check in linear space each possible assignment to variables Costas Busch - LSU 5

An interesting problem: it is not known if it is in NP However, the problem is in Costas Busch - LSU 6

Savitch’s Theorem Costas Busch - LSU 7

Given NTM Build DTM that decides in Costas Busch - LSU space 8

Assume NTM clears the tape when it aceepts and enters a special configuration Costas Busch - LSU 9

Key idea: Does configuration yield Costas Busch - LSU in steps? 10

Recursion Costas Busch - LSU 11

recursion Possibilities for : Costas Busch - LSU 12

Run: Depth of search tree: Info stored at each tree level: Total space: Costas Busch - LSU 13

Difficulty: is not known Guess it: Checks also if space used by NTM is more than f(n) Costas Busch - LSU 14

Trivially: From Savitch theorem: Costas Busch - LSU 15

Costas Busch - LSU 16