LECTURE 2-9 PSPACE-Complete

Slides:

Advertisements

Similar presentations

Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for Superlinear Space Chris Beck Princeton University Joint work with Paul Beame & Russell.

Advertisements

50.530: Software Engineering

Complexity Theory Lecture 3 Lecturer: Moni Naor. Recap Last week: Non deterministic communication complexity Probabilistic communication complexity Their.

INHERENT LIMITATIONS OF COMPUTER PROGRAMS CSci 4011.

Lecture 16: Relativization Umans Complexity Theory Lecturess.

1 Space Complexity. 2 Def: Let M be a deterministic Turing Machine that halts on all inputs. Space Complexity of M is the function f:N  N, where f(n)

Lecture 22: April 18 Probabilistic Method. Why Randomness? Probabilistic method: Proving the existence of an object satisfying certain properties without.

Dana Moshkovitz. Back to NP L  NP iff members have short, efficiently checkable, certificates of membership. Is  satisfiable?  x 1 = truex 11 = true.

Complexity of Games & Puzzles [Demaine, Hearn & many others] bounded unbounded 0 players (simulation) 1 player (puzzle) 2 players (game) team, imperfect.

Peter van Emde Boas: Playing Savage SOFSEM 2000 Milovy PLAYING SAVITCH Peter van Emde Boas ILLC-FNWI-Univ. of Amsterdam Bronstee.com Software and Services.

Online Ramsey Games in Random Graphs Reto Spöhel Joint work with Martin Marciniszyn and Angelika Steger.

Complexity 11-1 Complexity Andrei Bulatov Space Complexity.

More NP-completeness Sipser 7.5 (pages ).

February 23, 2015CS21 Lecture 201 CS21 Decidability and Tractability Lecture 20 February 23, 2015.

Computability and Complexity 15-1 Computability and Complexity Andrei Bulatov NP-Completeness.

1 Polynomial Time Reductions Polynomial Computable function : For any computes in polynomial time.

1 CSE 417: Algorithms and Computational Complexity Winter 2001 Lecture 23 Instructor: Paul Beame.

Fall 2006Costas Busch - RPI1 More NP-complete Problems.

CSE 421 Algorithms Richard Anderson Lecture 27 NP Completeness.

Lecture 20: April 12 Introduction to Randomized Algorithms and the Probabilistic Method.

INHERENT LIMITATIONS OF COMPUTER PROGRAMS CSci 4011.

PSPACE-Completeness Section 8.3 Giorgi Japaridze Theory of Computability.

Definition: Let M be a deterministic Turing Machine that halts on all inputs. Space Complexity of M is the function f:N  N, where f(n) is the maximum.

1 Chapter 9 PSPACE: A Class of Problems Beyond NP Slides by Kevin Wayne Pearson-Addison Wesley. All rights reserved.

CSEP 521 Applied Algorithms Richard Anderson Lecture 10 NP Completeness.

Space Complexity. Reminder: P, NP classes P NP is the class of problems for which: –Guessing phase: A polynomial time algorithm generates a plausible.

CS151 Complexity Theory Lecture 13 May 11, Outline proof systems interactive proofs and their power Arthur-Merlin games.

CSCI-256 Data Structures & Algorithm Analysis Lecture Note: Some slides by Kevin Wayne. Copyright © 2005 Pearson-Addison Wesley. All rights reserved. 33.

An Exact Algorithm for the Boolean Connectivity Problem for k-CNF Kazuhisa Makino (U. of Tokyo) Suguru Tamaki (Kyoto U.) Masaki Yamamoto (Tokai U.)

FPGA PLB Evaluation using Quantified Boolean Satisfiability Andrew C. Ling M.A.Sc. Candidate University of Toronto Deshanand P. Singh Ph.D. Altera Corporation.

A Problem That Is Complete for PSPACE (Polynomial Space) BY TEJA SUDHA GARIGANTI.

Pumping with Al and Izzy Richard Beigel CIS Temple University.

1 Finite Model Theory Lecture 14 Proof of the Pebble Games Theorem.

Lecture 25 NP Class. P = ? NP = ? PSPACE They are central problems in computational complexity.

Complexity 24-1 Complexity Andrei Bulatov Interactive Proofs.

NP-complete Languages

Space Complexity. Reminder: P, NP classes P is the class of problems that can be solved with algorithms that runs in polynomial time NP is the class of.

Prof. Busch - LSU1 Busch Complexity Lectures: More NP-complete Problems.

Theory of Computational Complexity Yuji Ishikawa Avis lab. M1.

 2005 SDU Lecture15 P,NP,NP-complete.  2005 SDU 2 The PATH problem PATH = { | G is a directed graph that has a directed path from s to t} s t

Complexity 27-1 Complexity Andrei Bulatov Interactive Proofs (continued)

Complexity of Compositional Model Checking of Computation Tree Logic on Simple Structures Krishnendu Chatterjee Pallab Dasgupta P.P. Chakrabarti IWDC 2004,

Introduction to Randomized Algorithms and the Probabilistic Method

Lecture 2-2 NP Class.

More NP-complete Problems

(xy)(yz)(xz)(zy)

NP-Completeness (36.4-5) P: yes and no in pt NP: yes in pt NPH  NPC

Intro to Theory of Computation

Great Ideas in Computing Complexity Theory

Intro to Theory of Computation

Cook’s Theorem Section 7.2 Mon, Dec 12, 2005.

Lecture 24 NP-Complete Problems

More NP-complete Problems

Car Race – Linear Sequences

Richard Anderson Lecture 28 NP-Completeness

Richard Anderson Lecture 28 NP Completeness

Finite Model Theory Lecture 6

CSE 6408 Advanced Algorithms.

LECTURE 2-7 Complete Problems in PH

CS21 Decidability and Tractability

CS21 Decidability and Tractability

More on NP-completeness

Lecture 4-4 #P-complete Problems

CS21 Decidability and Tractability

Theory of Computability

CSE 589 Applied Algorithms Spring 1999

Richard Anderson Lecture 25 NP Completeness

Instructor: Aaron Roth

Intro to Theory of Computation

§6 PSPACE and Polynomial Hierarchy

Presentation transcript:

LECTURE 2-9 PSPACE-Complete

SPACE BOUNDED HALTING PROBLEM (SBHP) THEOREM PROOF

QUANTIFIED BOOLEAN FORMULA QBF THEOREM

PROOF

3-QBF THEOREM

Geography Game

Example 1 BLUE ALWAYS WINS

Example 2 RED WINS

Example 2 BLUE WINS IF RED DOESN’T MAKE A MISTAKE, THEN BLUE CANNOT WIN.

Example 3 BLUE HAS A WINNING STRATEGY!!!

Geography Problem WIINNIG STRATEGY

THEOREM PROOF Construction Such that

BLUE HAS A WINNING STRATEGY!!!

BLUE HAS A WINNING STRATEGY!!!

BLUE HAS A WINNING STRATEGY!!! Means: there is an assignment for x-variables making every clause satisfied.

BLUE HAS A WINNING STRATEGY!!!

BLUE HAS A WINNING STRATEGY!!!

Questions Is go game on 19x19 grid PSPACE-complete? What do we mean that the go game is PSPACE-complete?

Thanks, end.