Exam 13: Modeling Computation

Which strings belong to the regular set represented by the regular expression (1∗01∗0)∗?

Let A = {1, 10}. Describe the elements of A∗.

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

What is the output produced by the following finite-state automaton when the input string is 11101?

Find a deterministic finite-state automaton equivalent to the nondeterministic finite-state machine shown.

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

Construct a finite-state machine that models a vending machine accepting only quarters that gives a container of orange juice when 50 cents has been deposited, followed by a button being pushed. (The possible inputs are quarters and the button, and the possible outputs are nothing, orange juice, and a quarter. The machine returns any extra quarters.)

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

What is the language generated by the grammar with productions $S \rightarrow S A , S \rightarrow 0 , A \rightarrow 1 A , \text { and } A \rightarrow 1$ where S is the start symbol?

What language is generated by the phrase-structure grammar if the productions are S → S11, S → λ where S is the start symbol?

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

Find a grammar for the set $\left\{ 0 ^ { 2 n } 1 ^ { n } \mid n \geq 0 \right\}$

Which strings belong to the set represented by the regular expression $0 ^ { * } \cup 11$

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