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Algorithms and complexity II: 2012-2013, fall semester

This is a course that has been given 18 times. For information about this course in general (not just for this specific semester), visit its page: Λ4. Algorithms and complexity II.

Taught by: Aristeidis T. Pagourtzis & Efstathios Zachos
Teaching assistant: Antonis Antonopoulos
Start date: Oct. 8, 2012
End date:

Teaching hours

  • every Monday, 17:00-19:00, 1.1.29, ece, NTUA (old buildings)
  • every Thursday, 13:45-15:45, 1.1.29, ece, NTUA (old buildings)

Course information

Ώρες γραφείου: Παρασκευή 12:00-16:00, στο Eργαστήριο Λογικής και Επιστήμης Υπολογισμών (CoReLab), Αίθουσα 1.1.3, Παλιά Κτίρια ΗΜΜΥ, ΕΜΠ.

Φυλλάδιο Μαθήματος-Syllabus

(Εξεταστέα) ύλη μαθήματος

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Enrolled students



Monday, 08 Oct 2012 Zachos

Εισαγωγή - Διαδικαστικά Hierarchies of Complexity Classes

Thursday, 11 Oct 2012 Zachos

Computational Models, Hierarchies, History

Monday, 15 Oct 2012 Zachos

Computational Model-Turing Machines: Equivalence of Computational Models, Turing Machines, Time and Space bounds, multiple strings, linear speedup, nondeterminism.

Thursday, 18 Oct 2012 Zachos

Computability and Undecidability: The Universal Turing Machine, Simulation, Diagonalization, The Halting Problem, Recursive and Recursive Enumerable Sets.

Monday, 22 Oct 2012 Antonopoulos

Complexity Classes: Complexity measures, Time and Space Classes Hierarchy Theorems, Gap Theorem, Basic inclusions between complexity classes, Quantifier Notation and characterization of NP (Theorem 9.1 [1]).

Monday, 29 Oct 2012 Zachos

Space Computation: The classes L and NL, Savitch’s Theorem, Immerman-Szelepscényi Theorem (NL=coNL), Reingold’s Theorem: L=SL (without proof) & Undirected REACHABILITY.

Thursday, 01 Nov 2012 Zachos

Second-Order Logic, Incompleteness, Fagin's Theorem

Monday, 05 Nov 2012 Zachos

Second-Order Logic, Incompleteness, Fagin's Theorem (cont'd)

Thursday, 08 Nov 2012 Zachos

Second-Order Logic, Incompleteness, Fagin's Theorem (cont'd). The Arithmetical Hierarchy.

Monday, 12 Nov 2012 Zachos

Diagonalization & Hierarchies, Case-Study: DTIME(n)⊂DTIME(n^1.5) Reductions: Reductions between problems, P-completeness, NP-completeness.

Monday, 19 Nov 2012 Zachos

Reductions: Different types of reductions (Karp, Cook, Cook[1], tt), and relations among them. NP-Complete Problems: - Cook’s Theorem, SAT and satisfiability variants - IS,CLIQUE, MAX-CUT

Thursday, 22 Nov 2012 Zachos

NP-Complete Problems: - HP, TSP, 3COL, 0/1 IP - 3DM, KNAPSACK, Pseudopolynomial Algorithms and Strong NP-Completeness

Monday, 26 Nov 2012 Zachos

Ladner’s Theorem, Density, Sparse sets The “Berman-Hartmanis” conjecture, NP-isomorphism, padding.

Thursday, 29 Nov 2012 Zachos

Function Problems: The classes coNP and ∆NP, Function classes (FL, FP, FNP, FPSPACE etc) and reductions, the classes PLS and PPAD.

Monday, 03 Dec 2012 Zachos

Randomized Computation: Randomized Algorithms, BPP, RP, coRP, ZPP classes.

Thursday, 06 Dec 2012 Zachos

Oracles & The Polynomial Hierarchy: Oracles and oracle classes, the Polynomial-Time Hierarchy.

Thursday, 13 Dec 2012 Zachos

Quantifier notation (∃+) and related results, semantic and syntactic classes, the “P vs BPP” question.

Monday, 17 Dec 2012 Zachos

2o Quiz σε Reductions & Randomized Complexity Classes. The equivalence between Oracle and Quantifier Polynomial Hierarchy

Thursday, 20 Dec 2012 Zachos

The Polynomial-Time Hierarchy and related theorems, The BPP Theorem, Swapping quantifiers, Operator-defined classes.

Thursday, 10 Jan 2013 Zachos

Non-Uniform Complexity: Boolean circuits, the class P/poly, Advice Turing Machines, Circuit Lower Bounds, Natural Proofs.

Monday, 14 Jan 2013 Zachos

Parallel computation (classes NC, RNC, AC, TC)

Interactive Proof Systems:

-Interactive Proofs (IP)

Thursday, 17 Jan 2013 Zachos

Interactive Proof Systems:

-Arthur-Merlin Games (AM)

Monday, 21 Jan 2013 Zachos

Interactive Proof Systems:

-Shamir’s Theorem: IP=PSPACE

-Zero Knowledge Proofs

Thursday, 24 Jan 2013 Zachos

Quantifier Notation and Arthur-Merlin Games

An introduction to Pseudorandomness and Derandomization

Introduction to PCPs

Monday, 28 Jan 2013 Zachos

Interactive Proof Systems:

-Probabilistically Checkable Proofs (PCP)

-Dinur's Proof of the PCP Theorem

Thursday, 31 Jan 2013 Zachos

Counting Complexity: #P, #P-completeness, Toda's Theorem, Gaps

Approximability and Approximation Schemes

Monday, 04 Feb 2013 Zachos

Reingold's Theorem: L=SL

Quantum Computation

Thursday, 07 Feb 2013 Zachos


Interactive Proof Systems: -Hardness of Approximations

Pseudorandomness & Combinatorial Constructions

The Unique Games Conjecture

Monday, 11 Feb 2013 Zachos

Algebraic Computation

The Bright Side of Hardness


# handout given on deadline solutions
1 1η Σειρά Ασκήσεων Monday, 29 Oct 2012 2012-11-29
2 2η Σειρά Ασκήσεων Sunday, 30 Dec 2012 2013-01-24
3 3η Σειρά Ασκήσεων Friday, 08 Feb 2013 2013-03-10


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