TM M = (Q, E, I, 8, 90, 9a, gr), where Q = {90, 91, 92, 9a, ¶r}, Σ = {0, 1}, T = {0, 1, L}, and 8 is: 8(90, L) = (gr, U, R) 8(90,0) = (91, 0, R) 8(90, 1) = (go, 1, R) 8(q1, L) = (ga, L, R) 8(91,0) = (9₁, 0, R) 8(91, 1) = (92, 1, R) 8(92, L) = (92, U, R) 8(92,0) = (90, 0, R) 8(92, 1) = (92, 1, R) i. Prove that M is NOT a decider. ii. Mathematically describe the language A that M recognises. Prove that A CL(M). iii. Prove A = L(M). iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]

TM M = (Q, E, I, 8, 90, 9a, gr), where Q = {90, 91, 92, 9a, ¶r}, Σ = {0, 1}, T = {0, 1, L}, and 8 is: 8(90, L) = (gr, U, R) 8(90,0) = (91, 0, R) 8(90, 1) = (go, 1, R) 8(q1, L) = (ga, L, R) 8(91,0) = (9₁, 0, R) 8(91, 1) = (92, 1, R) 8(92, L) = (92, U, R) 8(92,0) = (90, 0, R) 8(92, 1) = (92, 1, R) i. Prove that M is NOT a decider. ii. Mathematically describe the language A that M recognises. Prove that A CL(M). iii. Prove A = L(M). iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.

Question

TM M = (Q, E, I, 6, 90, 9a, qr), where Q = {90, 91, 92, 9a, 9r}, Σ = {0, 1}, r = {0, 1, L}, and 8 is:
8(qo, U)
=
(qr, U, R)
8(90, 0) =
8(go, 1)
(91, 0, R)
(qo, 1, R)
=
8(g1, L) = (ga, U, R)
8(91,0) = (91, 0, R)
8(91, 1) =
(92, 1, R)
=
(92, U, R)
8(92, U)
8(92, 0) =
(90, 0, R)
8(92, 1) = (92, 1, R)
i. Prove that M is NOT a decider.
ii. Mathematically describe the language A that M recognises. Prove that A ≤ L(M).
iii. Prove A = L(M).
iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]

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