Sumários

Characterization P = NP

16 novembro 2018, 10:00 José Félix Costa

Characterization of P in terms of functions: a set is in P iff it is the range of a function computable in polynomial time with an inverse computable in polinomial time.

Characterization of NP in terms of functions: a set is in NP iff it is the range of an honest function computable in polynomial time.

Characterization of P = NP: The structural relation P = NP holds iff EVERY honest function computable in polinomial time has one inverse computable in polinomial time.

Applications to Cryptography.


Lifting

14 novembro 2018, 16:00 José Félix Costa

Book' technique for sufficient conditions.

DSPACE(n) incl. P implies P = PSPACE. Separation DSPACE(n) =/= P.

DTIME(2^kn) incl. NP implies DEXT incl. NP = PSPACE = EXPTIME. Separation DTIME(2^kn) =/= NP.

Tally sets. EXPSPACE =/= DEXT iff there exist tally sets in PSPACE - P.


Savitch' theorem

9 novembro 2018, 10:00 José Félix Costa

Savitch's theorem.

Relations between central complexity classes: LOG, NLOG, co-NLOG, P, DEXT, EXPTIME, NP, PSPACE, NPSPACE, EXPSPACE, NEXT, NEXPTIME.


Assessment

7 novembro 2018, 16:00 José Félix Costa

ASSESSMENT 1.


Revisions

2 novembro 2018, 10:00 José Félix Costa

Preparation for the assessment.