context sensitive language

Question

L = { ${\epsilon }$ } is a

a) regular

b) CFL

c) CSL

d) recursive language

Answer 1

L = ϵ is nothing but Null string if we draw the DFA the first state is final 

It is Perfectly Regular and since it i Regular according to chomsky hierarchy it is CFL,CSL,Recursive

Comments

Then it is also recursive. rt?
But epsilon is not accepted by a TM. Why?

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TM accepts  ϵ 

Ref: http://math.stackexchange.com/questions/668896/what-does-it-mean-for-a-turing-machine-m-to-accept-epsilon

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does it imply that TM or LBA can be built to accept  L = {ϵ}

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TM is nothing but Finite State Machine with 2 extra stack 

If  Finite State Machine + 1 Stack =PDA

Finite State Machine +2 stack =TM

So it is perfectly alright to say it is regular and since we can built a DFA so obviously yes TM can be build to accept  ϵ 

Ref: http://math.stackexchange.com/questions/668896/what-does-it-mean-for-a-turing-machine-m-to-accept-epsilon