1. Space Complexity
Costas Busch - LSU

2. for deterministic Turing machine:
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

3. for non-deterministic Turing machine:
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

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

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

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

7. Savitch’s Theorem
Costas Busch - LSU

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

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

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

11. Recursion
Costas Busch - LSU

12. recursion
Possibilities for :
Costas Busch - LSU

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

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

15. Trivially:
From Savitch theorem:
Costas Busch - LSU

16. Costas Busch - LSU