Ch11 - Chapters 11 and 12 Decision Problems and...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapters 11 and 12 Decision Problems and Undecidability
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 11.1 Decision Problems A decision problem consists of a set of questions whose answers are either yes or no is undecidable if no algorithm that can solve the problem; otherwise, it is decidable The Church-Turing thesis asserts that a decision problem P has a solution if, and only if, there exists a TM that determines the answer for every p P if no such TM exists, the problem is said to be undecidable An unsolvable problem is a problem such that there does not exist any TM that can solve the problem
Image of page 2
3 Decision Problems Algorithm L that solves a decision problem should be effective , i.e., Complete : L produces the correct answer (yes/or) to each question Mechanistic : L consists of a finite sequence of instructions Deterministic : L produces the same result for the same input The Church-Turing Thesis for Computable Functions : A function f is effective, i.e., effectively computable, if, and only if, there is a TM that computes f .
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 11.2 Recursive Languages Defn . A recursive language L is a formal language for which there exists a TM that will halt and accept an input string in L , and halt and reject , otherwise. Example 11.2.1 The decision problem of determining whether a natural number is a perfect square (represented by using the string a n ) is decidable. Example 11.2.2 The decision problem of determining whether there is a path P from node v i to a node v j in a directed graph G (with nodes v 1 , …, v n ) using a NTM M with 2-tape is decidable. G
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern