CS 461 – Dec. 2 Major results Automata: 3 models of computation

Slides:



Advertisements
Similar presentations
Lecture 24 MAS 714 Hartmut Klauck
Advertisements

CS 461 – Nov. 9 Chomsky hierarchy of language classes –Review –Let’s find a language outside the TM world! –Hints: languages and TM are countable, but.
Rice ’ s Theorem. Def: A property of the Turing-recognizable languages is simply a subset of all Turing- recognizable languages.
NP-Completeness Lecture for CS 302. Traveling Salesperson Problem You have to visit n cities You want to make the shortest trip How could you do this?
Recap CS605: The Mathematics and Theory of Computer Science.
Reducibility 2 Theorem 5.1 HALT TM is undecidable.
CSCI 2670 Introduction to Theory of Computing October 19, 2005.
CS 302: Discrete Math II A Review. An alphabet Σ is a finite set (e.g., Σ = {0,1}) A string over Σ is a finite-length sequence of elements of Σ For x.
Final Exam Review Cummulative Chapters 0, 1, 2, 3, 4, 5 and 7.
Remaining Topics Decidability Concept 4.1 The Halting Problem 4.2
Decidability A decision problem is a problem with a YES/NO answer. We have seen decision problems for - regular languages: - context free languages: [Sections.
Theory of Computing Lecture 15 MAS 714 Hartmut Klauck.
CSE 326: Data Structures NP Completeness Ben Lerner Summer 2007.
P, NP, and Exponential Problems Should have had all this in CS 252 – Quick review Many problems have an exponential number of possibilities and we can.
CSCI 3160 Design and Analysis of Algorithms Tutorial 10 Chengyu Lin.
Midterm 2 review Jundong Liu School of EECS
Saeid Pashzadeh Jan 2009 Theory of Computation 1.
Decidable languages Section 4.1 CSC 4170 Theory of Computation.
1Computer Sciences Department. Book: INTRODUCTION TO THE THEORY OF COMPUTATION, SECOND EDITION, by: MICHAEL SIPSER Reference 3Computer Sciences Department.
D E C I D A B I L I T Y 1. 2 Objectives To investigate the power of algorithms to solve problems. To explore the limits of algorithmic solvability. To.
2101INT – Principles of Intelligence Systems Lecture 3.
Strings Basic data type in computational biology A string is an ordered succession of characters or symbols from a finite set called an alphabet Sequence.
CS 461 – Nov. 18 Section 7.1 Overview of complexity issues –“Can quickly decide” vs. “Can quickly verify” Measuring complexity Dividing decidable languages.
Computability NP complete problems. Space complexity. Homework: [Post proposal]. Find PSPACE- Complete problems. Work on presentations.
CSCI 2670 Introduction to Theory of Computing October 13, 2005.
CS 154 Formal Languages and Computability May 12 Class Meeting Department of Computer Science San Jose State University Spring 2016 Instructor: Ron Mak.
Review : Theory of Computation. Regular Language and Finite Automata Context-free Language and Pushdown Automata Turing Machine and Recursive Enumerable.
Graphs 4/13/2018 5:25 AM Presentation for use with the textbook, Algorithm Design and Applications, by M. T. Goodrich and R. Tamassia, Wiley, 2015 NP-Completeness.
CSE 105 theory of computation
CSCI 2670 Introduction to Theory of Computing
NP-Completeness NP-Completeness Graphs 5/7/ :49 PM x x x x x x x
Probabilistic Algorithms
ماشین های تورینگ، تشخیص پذیری و تصمیم پذیری زبان ها
CSE 105 theory of computation
CSCI 2670 Introduction to Theory of Computing
Review : Theory of Computation
Busch Complexity Lectures: Reductions
FORMAL LANGUAGES AND AUTOMATA THEORY
CSCI 2670 Introduction to Theory of Computing
CS21 Decidability and Tractability
Automata, Grammars and Languages
CSCE 355 Foundations of Computation
Computability and Complexity
NP-Completeness NP-Completeness Graphs 11/16/2018 2:32 AM x x x x x x
Summary.
RAJALAKSHMI ENGINEERING COLLEGE
Jaya Krishna, M.Tech, Assistant Professor
Intro to NP Completeness
Intractable Problems Time-Bounded Turing Machines Classes P and NP
CSE 105 theory of computation
Automata and Formal Languages (Final Review)
CSE 105 theory of computation
NP-Completeness NP-Completeness Graphs 12/3/2018 2:46 AM x x x x x x x
Context-Free Languages
Richard Anderson Lecture 29 Complexity Theory
CS21 Decidability and Tractability
CS21 Decidability and Tractability
Chapter 1 Regular Language - 02
CS21 Decidability and Tractability
CSE 105 theory of computation
CSE 105 theory of computation
NP-Completeness Lecture for CS 302.
CSE 105 theory of computation
Automata, Grammars and Languages
CSE 105 theory of computation
Sub: Theoretical Foundations of Computer Sciences
Instructor: Aaron Roth
CHAPTER 1 Regular Languages
CSE 105 theory of computation
CSE 105 theory of computation
Presentation transcript:

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

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.

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