Exam 13: Modeling Computation

Determine if 1101 belongs to the regular set $( 01 ) ^ { * } ( 11 ) ^ { * } ( 01 ) ^ { * }$ .

Determine if 1101 belongs to the regular set $( 11 ) ^ { * } 0 ^ { * } ( 11 ) ^ { * }$ .

Find the Kleene closure of A = {0, 1, 2}.

The productions of a phrase-structure grammar are S → S1, S → 0A, A → 1 Find a derivation of 0111 .

Construct a Turing machine that computes $f \left( n _ { 1 } , n _ { 2 } \right) = n _ { 2 } + 1$ where $n _ { 1 } , n _ { 2 } \geq 0$

Suppose a phrase-structure grammar has productions $S \rightarrow 1 S 0 , S \rightarrow 0 A , A \rightarrow 0$ Find a derivation of 00 .

Which strings belong to the set represented by the regular expression 0∗ ∪ 11?

What is the language generated by the grammar with productions S → SA, S → 0, A → 1A,and A → 1, where S is the start symbol?

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

Find the Kleene closure of A={1} .

Determine if 1101 belongs to the regular set $\mathbf { 1 } ( \mathbf { 1 0 } ) ^ { * } 1 ^ { * }$ .

Construct a finite-state automaton that recognizes the set represented by the regular expression 10∗.

Consider the Turing machine $T : \left( s _ { 0 } , 0 , s _ { 1 } , 1 , R \right) , \left( s _ { 0 } , 1 , s _ { 1 } , 1 , R \right) , \left( s _ { 1 } , 0 , s _ { 0 } , 1 , L \right) , \left( s _ { 1 } , 1 , s _ { 0 } , 0 , R \right) , \left( s _ { 0 } , B , s _ { 1 } , 1 , R \right)$ For the following tape, determine the final tape when T halts, assuming that T begins in state s₀ at the leftmost nonblank symbol. \@cdots 1 0 1 \@cdots

Suppose a phrase-structure grammar has productions $S \rightarrow S 11 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0 ,$ of 011111.

$\text { Find a grammar for the set } \left\{ 0 ^ { 2 n } 1 ^ { n } \mid n \geq 0 \right\}$ In questions $24 - 29$ let $V = \{ S , A , B , 0,1 \}$ and $T = \{ 0,1 \}$ . 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.

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

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 derivable from S? (1) ba , (2) ab , (3) baab, (4) aababa, (5) aba .

Suppose A = {0, 1}. Describe all strings belonging to A∗.

Let A={0,11} . Find A³ .