3b. Consider the language FIN = { | M is a Turing machine and L(M) is finite }. Prove FIN is not decidable.
Added by Purificaci-N B.
Step 1
This means that there exists a Turing machine H that takes as input the description of another Turing machine M and decides whether L(M) is finite or not. Now, we will construct a new Turing machine D that uses H as a subroutine to solve the Halting problem, Show more…
Show all steps
Your feedback will help us improve your experience
Avi Bukys and 78 other AP CS educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let $M=\left(S, I, f, s_{0}, F\right)$ be a deterministic finite-state automaton. Show that the language recognized by $M, L(M),$ is infinite if and only if there is a word $x$ recognized by $M$ with $l(x) \geq|S|$ .
Modeling Computation
Language Recognition
Consider language, $A=\{\angle M>: M$ is a DFA which doesn't accept any string containing odd number 1's Which of following is true about $A$ ? (A) A is Trivially decidable (B) A is undecidable (C) A is decidable (D) None of these
Theory of Computation
RECURSIVELY ENUMERABLE SETS AND TURING MACHINES, DECIDABILITY
Question 3-Undecidability: Show, using a reduction from ATM, that the following problem/language is undecidable: Given (encodings of) two Turing Machines M1 and M2 and an input string w, do M1 and M2 have the same output (both accept or both not accept) on input w? That is, prove that the following language is not decidable, by means of a reduction from ATM: E2TM = {<M1, M2, w> | M1 and M2 both accept or both don't accept w}
Sri K.
Recommended Textbooks
Computer Science and Information Technology
Introduction to Programming Using Python
Computer Science - An Overview
Watch the video solution with this free unlock.
EMAIL
PASSWORD