Sumários

Probabilistic Turing machines (part 2)

20 dezembro 2019, 10:00 José Félix Costa

Class R. Proof that the sets in R can be decided by bounded error polynomial time probabilistic Turing machines with error probability (for probabilistic accepted words) approaching exponentially to 0 as time goes polynomially to infinity.

Proof (by padding and self-reducibility of SAT) that if NP is included in BPP, then NP = R.

Class ZPP. That ZPP = R \cap co-R.

Monte Carlo vs. Las Vegas.


Probabilistic Turing machines (part 1)

18 dezembro 2019, 16:30 José Félix Costa

Class PP. 

Structural relations between NP, co-NP, PP, and PSPACE. Closure of PP under complement. 

The intersection problem in PP.

Classe BPP. 

Proof that the sets in BPP can be decided by bounded error polynomial time probabilistic Turing machines with error probability exponentially approaching 0 as time goes polynomially to infinity.


Test 2

13 dezembro 2019, 10:00 José Félix Costa

TEST 2.


NP-completeness

11 dezembro 2019, 16:30 José Félix Costa

Boolean formulas. Quantified Boolean formulas.

NP-completeness of SAT, CNF-SAT.

PSPACE-completeness of QBF.


Polynomial time hierarchy

6 dezembro 2019, 10:00 José Félix Costa

The polynomial time hierarchy. 

Polynomial time hierarchy by means of bounded quantification. Alternation.

Collapse theorems.