Exam 13: A: Modeling Computation

Let G be the phrase-structure grammar with vocabulary V={A, B, a, b, S} , terminal element set T={a, b} , start symbol S , and production set P= $\{ S \rightarrow A B a , S \rightarrow B a , A \rightarrow a B , A B \rightarrow b , B \rightarrow a b \}$ are derivable from S ? (1) ba , (2) ab , (3) baab, (4) aababa, (5) aba

Construct a finite-state machine with output that produces a 1 if and only if the last 3 input bits read are 0's.

let $V = \{ S , A , B , 0,1 \} \text { and } T = \{ 0,1 \} \text {. For each set of productions determine whether the }$ resulting grammar G is (i) type 0 grammar, but not type 1 , (ii) type 1 grammar, but not type 2 , (iii) type 2 grammar, but not type 3 , (iv) type 3 grammar. - $S \rightarrow 0 B , B \rightarrow 1 A , B \rightarrow 0 , A \rightarrow 0 B$

For the following Turing machine T , find the final tape when T is run on the following tape, beginning in the initial position (the first nonzero entry from the left): \@cdots 0 0 0 1 0 \@cdots ,0,,1,R , ,1,,0,R , ,1,,1,R , ,B,,0,R .

Suppose a phrase-structure grammar has productions S → S11, S → 0A, S → A1, A → 0. Find a derivation of 011111.

Suppose a phrase-structure grammar has productions S → S0, S → A1, A → 0. Find a derivation of 0100.

let $V = \{ S , A , B , 0,1 \} \text { and } T = \{ 0,1 \} \text {. For each set of productions determine whether the }$ resulting grammar G is (i) type 0 grammar, but not type 1 , (ii) type 1 grammar, but not type 2 , (iii) type 2 grammar, but not type 3 , (iv) type 3 grammar. - $S \rightarrow A B , A \rightarrow 0 B 1,0 B 1 \rightarrow 0$

determine the output for each input string, using -11000

What is the output produced by this finite-state machine when the input string is 11101?

Construct a Turing machine that computes $f ( n ) = n + 2 , \text { where } n \geq 0$

Suppose that A = {1, 11, 01} and B = {0, 10}. Find BA. this state table.

let $V = \{ S , A , B , 0,1 \} \text { and } T = \{ 0,1 \} \text {. For each set of productions determine whether the }$ resulting grammar G is (i) type 0 grammar, but not type 1 , (ii) type 1 grammar, but not type 2 , (iii) type 2 grammar, but not type 3 , (iv) type 3 grammar. - $S \rightarrow A 10 , A B \rightarrow 0$

Which strings are recognized by the following finite-state automaton?

For the following Turing machine T , find the final tape when T is run on the following tape, beginning in the initial position (the first nonzero entry from the left): \@cdots 0 0 0 1 0 \@cdots ,0,,1,R , ,1,,1,L , ,0,,1,L

Determine if 1101 belongs to the regular set (01)*(11)*(01)*.

let $V = \{ S , A , B , 0,1 \} \text { and } T = \{ 0,1 \} \text {. For each set of productions determine whether the }$ resulting grammar G is (i) type 0 grammar, but not type 1 , (ii) type 1 grammar, but not type 2 , (iii) type 2 grammar, but not type 3 , (iv) type 3 grammar. - $S \rightarrow 1 A , A \rightarrow 1 , S \rightarrow \lambda$

Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes $S \rightarrow A a$ and $A \rightarrow a$ and generates the language {a, a a} .

Let A = {1, 10}. Which strings belong to A∗?

$\text { The productions of a phrase-structure grammar are } S \rightarrow S 1 , S \rightarrow 0 A , A \rightarrow 1 \text {. Find a derivation of } 0111$ .

Suppose a phrase-structure grammar has productions S → S0, S → A1, A → 0. Find a derivation of 010.