1. CS 461 – Dec. 2 Major results Automata: 3 models of computation
Definitions, properties, corresponding language classes, text representations
Decidability
Complexity: classes of decidable languages
P: polynomial algorithm
NP-complete: exponential algorithm & polynomial verifier
NP-hard: exponential algorithm, no known polynomial verifier

2. Graham’s talk Minimum spanning tree vs. minimum Steiner tree
Helpful lemmas don’t reduce exponential complexity
NP-complete: “I can’t find an efficient algorithm, but neither can all these famous people!”
One common feature of NP-complete problems:
A solution that’s almost right is no good.
TSP tour that is 2 miles too long.
Subset sum that might be off by 1.
It may be good enough to
approximate solution
e.g. Unfortunately, sum of square roots can be difficult to compare!
Restricted problem – special case
Sometimes even the verifying requires exponential time.

3. Major results NFA = DFA FA = regular expression
Can simplify FA’s (Myhill-Nerode theorem)
Pumping lemmas
PDA = CFG
CYK algorithm O(n3) time
Bottom-up parsing (linear time)
Variants of TM
Countable, uncountable
ATM undecidable
 non Turing recognizable language
Rice’s theorem
PCP undecidable
SAT is NP-complete
Many other NP-complete problems
We don’t know if P = NP