Automata Midterm 1
A DFA that accepts any string that ends with 10 will accept which of these strings?
00000010
What is the regular expression for a DFA that accepts 01 as a substring?
1*00*1(0+1)*
String 00110100 will be accepted by a DFA that accepts?
1010 as substring
String 00110010 will be accepted by a DFA that accepts?
1100 as substring
A DFA that accepts only even number of 1s and 0s will accept which of these strings?
11000011
Study of abstract computing devices or machines is known as:
Automata theory
Regular Languages are NOT closed under union operation.
False
True or False: (RS + R)* RS = (RR*S)*
False
How to decide if a string w in language L is accepted by a DFA?
If the DFA ends in an accepting state
When a language is NOT regular?
If we can show that no FA can be built for a language
What is Pigeon Hole Principle?
at least one hole must contain more than one pigeon
If y >= 4, then 2^y >= y^2 is an example of what type of proof:
deductive
A transition from one state to another state without consuming any additional input symbol is known as:
epsilon-transitions
A DFA is defined by 3-tuple:
false
An alphabet is not a finite set of symbols:
false
Regular languages are regular under reunion.
false
When a language is regular?
if we are able to construct a DFA or NFA or epsilon-NFA or regular expression
An intermediate result that we show to prove a larger result is known as:
lemma
If we are able to construct one of the following: DFA or NFA or ε-NFA or regular expression then the language is called:
regular
A language L is accepted by some e-NFA if and only if L is accepted by some DFA.
true
A language L= Ø if and only if the reachability test fails.
true
A language is a collection of sentences of finite length all constructed from a finite alphabet of symbols:
true
An NFA accepts w if there exists at least one path from the start state to an accepting (or final) state that is labeled by w:
true
An NFA is defined by 5-tuple:
true
Explicit epsilon-transitions between different states introduce non-determinism:
true
For every DFA A there exists a regular expression R such that L(R)=L(A).
true
If we introduce ε then the regular expression (01)* + (10)* + 0(10)* + 1(01)* can be simplified to (ε +1)(01)*(ε + 0).
true
L U M = all strings that are either in L or M.
true
Regular Expressions are more like program syntax.
true
Transitions into a dead state are implicit for a NFA.
true
Unix environments heavily use regular expressions.
true
We use the symbol Σ(sigma) to denote an alphabet:
true
ε-closure of a state q, ECLOSE(q), is the set of all states (including itself) that can be reached from q by repeatedly making an arbitrary number of ε-transitions.
true
Empty string is represented by:
ε (epsilon
L = { w | w is a binary string which does not contain two consecutive 0s or two consecutive 1s anywhere}. What is the regular expression for this language?
(01)* + (10)* + 0(10)* + 1(01)*
A containment hierarchy of classes of formal languages is known as:
Chomsky hierarchy
A property that confirms If a set of regular languages are combined using an operator, then the resulting language is also regular is called:
Closure property
The machine that can exist in only one state at any given time is known as:
DFA
A transition from one state to another state without consuming any additional input symbol is known as:
Epsilon transition
Probabilistic models could be viewed as extensions of which state machines?
NFA
The machine that can exist in multiple state at any given time is known as:
NFA
Which of these is great for modeling regular expressions?
NFA
A technique that is used to show a given language is not regular is known as.
Pumping Lemma
How to minimize a DFA?
Remove unreachable states and Identify & condense equivalent states into one
