Automata Exam 1

For a given state q and alphabet symbol c in an NFA, how many transitions out of q can be labeled with c? a. 1 or more b. Exactly 1 c. 2 or more d. 0 or more

0 or more

How many accept states can a DFA have? a. exactly 1 b. 0 or more (up to the number of states)

0 or more (up to the number of states)

Suppose that an NFA has states. What is the maximum number of states in a DFA that is equivalent to the NFA? a. 2^n b. n c. n^2 d. n!

2^n

When does an NFA accept a string? a. An NFA can have multiple computations for a given input string, and if for at least one computation an accepting state can be reached after all symbols have been scanned, then the input string is accepted. b. An NFA has only one computation for a given input string, and the rule for accepting an input string is the same as for a DFA - for a given input string, if the computation ends in an accepting state, then the string is accepted. c. An NFA can have multiple computations for a given input string, and if for all computations an accepting state can be reached after all symbols have been scanned, then the input string is accepted.

An NFA can have multiple computations for a given input string, and if for at least one computation an accepting state can be reached after all symbols have been scanned, then the input string is accepted.

In an NFA, what is the meaning of an epsilon transition? a. In a computation, the NFA can follow an transition while scanning the next symbol of the input, no matter what the symbol is. (So, represents a wildcard - any symbol can be scanned when following the transition.) b. In a computation, the NFA can (but does not have to) follow an transition without scanning a symbol from the input. c. In a computation, the NFA must follow an transition if the computation is in a state that has an transition out of it.

In a computation, the NFA can (but does not have to) follow an transition without scanning a symbol from the input.

Which of the following represents the set of all possible outputs to a DFA transition function? (That is, what is the range of the transition function?) a. Q x Summation b. Q c. Summation d. (Q, summation)

Q

the domain of the transition function: (set of all possible inputs)

Q x E

Which of the following represents the set of all possible inputs to a DFA transition function? (That is, what is the domain of the transition function?) a. Q b. summation c. Q x summation d. (Q, summation)

Q x summation

Which statement best describes the relation between languages that can be recognized by DFAs and languages that can be recognized by NFAs. a. Any language that can be recognized by a DFA can also be recognized by an NFA, but there are languages that can be recognized by an NFA that cannot be recognized by a DFA. b. Any language that can be recognized by an NFA can also be recognized by a DFA, but there are languages that can be recognized by a DFA that cannot be recognized by an NFA. c. The languages that can be recognized by DFAs and the languages that can be recognized by NFAs are exactly the same.

The languages that can be recognized by DFAs and the languages that can be recognized by NFAs are exactly the same.

Which of the following is not a base case in the definition of a regular expression? Base case means there is no self reference (to another regular expression). a. The empty set b. The empty string c. A single symbol from the alphabet d. A closing parenthesis

a closing parenthesis

To convert an NFA into a regular expression, the NFA is first converted into a generalized NFA (GNFA), which is then, through a series of iteration, converted into a regular expression. As the iterations proceed, what is each edge of the GNFA labeled with? a. a single regular expression b. A single symbol from the alphabet c. A set of regular expressions d. a single symbols from the alphabet, or epsilon

a singular regular expression

Which of the following are regular operations: a. Union b. Difference c. Concatenation d. Intersection e. Star f. Complement

all of the above

Which operation is both a regular operation, and is best described by the following statement: (In this statement, the DFAs refer to the DFAs that recognize the regular languages that are the operands to the operation.) An NFA to recognize the language that is the result of the operation has epsilon transitions from the accept states of one DFA to the start state of another. a. Complement b. Intersection c. Star d. Difference e. Concatenation f. Union

concatenation

How many start states can a DFA have? a. exactly 1 b. 1 or more (up to the number of states)

exactly 1

How many start states can an NFA have? a. 1 or more b. Exactly 1 c. 0 or more

exactly 1

Which of the following is not a recursive case in the definition of a regular expression? Recursive case means there is self reference (to another regular expression). a. Star b. Concatenation c. Intersection d. Union

intersection

Which operation is both a regular operation, and is best described by the following statement: (In this statement, the DFA refers to the DFA that recognizes the regular languages that is the operandsto the operation.) An NFA to recognize the language that is the result of the operator has epsilon transitions from the accept states of the DFA back to the start state of the DFA. a. Complement b. Star c. Concatenation d. Union e. Difference f. Intersection

star

In the absence of parentheses, what is the order of operations (that is, the precedence of operations) in a regular expression? a. star first, then concatenation, then union b. Union first, then concatenation, then star c. concatendation first, then union, then star d. star first, then union, then concatenation concatenation first, then star, then union

star first, then concatenation, then union

Which operation is both a regular operation, and is best described by the following statement: (In this statement, the DFAs refer to the DFAs that recognize the regular languages that are the operands to the operation.) An NFA to recognize the language that is the result of the operator has epsilon transitions to the start states of both DFAs. a. Complement b. Star c. Intersection d. Concatenation e. Difference f. Union

union