'Halting problem' presentation slideshows

Computability Decidability

Computability Decidability. Unsolvable problems. Computer scientists usually deal with problems which are solvable. We are supposed to find an algorithm to solve a particular problem. Why do we need to know about problems which are unsolvable ?

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NP-Hard

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Program Slicing for Refactoring

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Circuit Complexity meets the Theory of Randomness

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Reducibility

Reducibility. Problem is reduced to problem. If we can solve problem then we can solve problem. Problem is reduced to problem. If is decidable then is decidable. If is undecidable then is undecidable. Example:. the halting problem. is reduced to.

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Undecidable Problems (unsolvable problems)

Undecidable Problems (unsolvable problems). Decidable Languages. Recall that: A language is decidable , if there is a Turing machine ( decider ) that accepts the language and halts on every input string. Decision On Halt:. Turing Machine. YES. Accept.

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Undecidable Problems (unsolvable problems)

Undecidable Problems (unsolvable problems). Decidable Languages. Recall that: A language is decidable , if there is a Turing machine ( decider ) that accepts the language and halts on every input string. Decision On Halt:. Turing Machine. YES. Accept.

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FORMAL LANGUAGES, AUTOMATA, AND COMPUTABILITY

15-453. FORMAL LANGUAGES, AUTOMATA, AND COMPUTABILITY. * Read chapter 4 of the book for next time * . Lecture9x.ppt. REVIEW. A Turing Machine is represented by a 7-tuple T = (Q, ? , ? , ?, q 0 , q accept , q reject ): . Q is a finite set of states.

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Projects Schedule

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Chapter 12 Theory of Computation

Chapter 12 Theory of Computation. Introduction to CS 1 st Semester, 2014 Sanghyun Park. Outline. Functions and Their Computation Turing Machines Universal Programming Languages A Noncomputable Function Complexity of Problems. Functions and Their Computation.

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Overview of the theory of computation

Overview of the theory of computation. Episode 3. Turing machines The traditional concepts of computability, decidability and recursive enumerability The limitations of the power of Turing machines The Church-Turing thesis Mapping reducibilty Turing reducibility

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CSE115/ENGR160 Discrete Mathematics 03/10/11

CSE115/ENGR160 Discrete Mathematics 03/10/11. Ming-Hsuan Yang UC Merced. 3.3 Complexity of algorithms. Algorithm Produce correct answer Efficient Efficiency Execution time (time complexity) Memory (space complexity) Space complexity is related to data structure . Time complexity.

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The Halting Problem

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Reducibility

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Halting Problem

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Reducibility

Giorgi Japaridze Theory of Computability. Reducibility. Chapter 5. 5.1.a. Giorgi Japaridze Theory of Computability. The undecidability of the halting problem. Let HALT TM = {<M,w> | M is a TM and M halts on input w} HALT TM is called the halting problem . .

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The halting problem - proof

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600.103 Solutions to Homework #1

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