Answered! Let S_n = { + M is a TM and |L(M)| = n} for n = 0, 1, 2, 3, … a. Show that for every n greaterthanorequalto 0, S_n…

(16 points) Let Sn M) I M is a TM and IL (M) n for n 0, 1, 2, 3 a. Show that for every n 2 0, Sn reduces to S +1. b. Show that for every n 2 1, Sn+1 reduces to Sn.

Let S_n = { + M is a TM and |L(M)| = n} for n = 0, 1, 2, 3, … a. Show that for every n greaterthanorequalto 0, S_n reduces to S_n+1. b. Show that for every n greaterthanorequalto 1, S_n+1 reduces to S_n.

Expert Answer

S₀ = { <M>, | L(M) | = 0 }, n=0 Empty language

S1= { <M>, |L(M) | = 1} , for n=1, {0}

S2= { <M>, |L(M) | = 2 } , for n=2, { 0,1 }

By definition of Turing reductions, n>=0, S₀ is reducible to S₁ .

For,, n>=1, S₂ is reducible to S1

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