Read Sipser §8.1 and §8.2
- The reading proves that while SAT is NP-complete, it only takes a linear amount of space, i.e. it is in PSPACE. Adapt this proof technique to show that CLIQUE is also in PSPACE.
- In the machine described on page 333, the machine seemingly runs in exponential (ie greater than polynomial) time. Describe why this is not a problem for this analysis.
- Savitch’s theorem tells us something about the difference in space complexity between deterministic and nondeterministic Turing Machines. What could we say about time complexity between deterministic and nondeterministic Turing Machines?
- In the proof of Savitch’s theorem, summarize why the constructed machine M correctly simulates N in a deterministic way.