Question 2–Decidability–True or False? For each of the following statements: determine (and state clearly) whether it is true or false, and give a brief argument (proof) of your claim: (a) Every DFA D halts computation on input e. (b) Every TM M halts computation on input e. (c) We can decide if there exists a word w that a given DFA D accepts by verifying if there is a directed path from the start state 4o to some accept state in a state diagram of D. (d) We can decide if there exists a word w that a given TM M accepts by verifying if there is a directed path from the start state do to accept state goccent in a state

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
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Question 2–Decidability–True or False?
For each of the following statements: determine (and state clearly) whether it is true
or false, and give a brief argument (proof) of your claim:
(a) Every DFA D halts computation on input e.
(b) Every TM M halts computation on input e.
(c) We can decide if there exists a word w that a given DFA D accepts by verifying
if there is a directed path from the start state qo to some accept state in a state
diagram of D.
(d) We can decide if there exists a word w that a given TM M accepts by verifying
if there is a directed path from the start state qo to accept state qaccept in a state
diagram of M.
(e) The problem of determining if a directed graph is strongly connected can be
phrased as a language and is decidable.
Transcribed Image Text:Question 2–Decidability–True or False? For each of the following statements: determine (and state clearly) whether it is true or false, and give a brief argument (proof) of your claim: (a) Every DFA D halts computation on input e. (b) Every TM M halts computation on input e. (c) We can decide if there exists a word w that a given DFA D accepts by verifying if there is a directed path from the start state qo to some accept state in a state diagram of D. (d) We can decide if there exists a word w that a given TM M accepts by verifying if there is a directed path from the start state qo to accept state qaccept in a state diagram of M. (e) The problem of determining if a directed graph is strongly connected can be phrased as a language and is decidable.
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