COSC 3340 Final
Given L = {w | w is a binary string without consecutive 0s or 1s}, the regular expression is;
(01)* + (10)* + 0(10)* + 1(01)*
A language is context-free if and only if it can be accepted by:
A pushdown automaton
The set of strings accepted by a DFA is called the
Alphabet
Study of abstract computing devices or machines is known as:
Automata theory
The property ensuring that combining regular languages with an operator results in a regular language is:
Closure property
Recursive languages are closed under __
Complementation, Union, intersection, concatenation, etc.
TMs can be used as both:
Language recognizers and calculators/computers
Probabilistic models can be seen as extensions of which type of state machine?
NFA
The machine that can exist in multiple state at any given time is known as:
NFA
Does a PDA that accepts by empty stack need any final state specified in the design?
No
A language is not regular if:
No finite automaton can be built for it
Are recursively enumerable languages closed under complementation?
No. They are closed under union, intersection, concatenation
A type of automaton that uses a stack is called:
PDA
The langauge {a^n b^n | n >= 0} is:
context-free language
If y >= 4, then 2^y >= y^2" is an example of what type of proof?
deductive
PDA reads a given input string from
left to right
An intermediate result that we show to prove a larger result is known as:
lemma
The language of a palindrome is a context free because it supports:
recursive substitution
An NFA accepts w if there exists at least one path from the start state to an accepting (final) state that is labeled by w:
true
If a problem cannot be solved even using a Turing Machine then it implies that the problem is
undecidable
Which of following is not a context-free language? {a^n b^m | n, m >= 0} {a^n b^2n | n >= 0 } {a^n b^n | n >= 0 } {a^n b^n c^n | n >= 0 }
{a^n b^n c^n | n >= 0 }
Empty string is represented by
ε (epsilon)
Which of the following is true about context-sensitive languages?
- they include all context-free languages - they can be recognized by a linear-bounded automaton - they can be defined by context-sensitive grammars.
A DFA that accepts any string that ends with 10 will accept which of these strings?
00000010
Consider CFG: A => 0A | 0 | 1 | ε, which of these strings can be generated with this grammar? 00100 0110 001100 001
001
Which string will be accepted by a DFA that accepts "1010" as a substring?
00110100
Basic Turing Machine is equivalent to all of the following:
1. TM + storage 2. Multitrack TM 3. Multi-tape TM 4. Non-deterministic TM
String 00110100 will be accepted by a DFA that accepts?
1010 as substring
A language is recursively enumerable if:
A Turing machine can enumerate all the strings of the language
Which of the following operations is not closed for context-free languages?
Intersection or Complementation
Which of the following is true about a DFA?
It can be in a single state at a time
Regular expressions are more like program syntax
True
Regular languages only have terminals
True
Transitions into a dead state are implicit for an NFA.
True
Unix environments heavily utilize 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 that can be reached from q by repeatedly making an ε transitions
True
How to decide if a string w is accepted by a DFA
If the DFA ends in an accepting state
The machine that can exist in only one state at any given time is known as:
DFA
A transition without consuming an input symbol is known as:
Epsilon transition
A DFA is defined by a 3-tuple
False
Regular languages are not closed under intersection.
False
There can't be words which have more than one leftmost (or rightmost) derivation.
False
A DFA is defined by 3-tuple:
False (is defined by 5-tuple)
CFA that generates ()(((()))((())) is
G: S => (S) | SS | ε
A technique used to show a language is not regular is:
Pumping Lemma
How to minimize a DFA?
Remove unreachable states and Identify & condense equivalent states into one
Which of the following is not true about context-free languages? They are a subset of regular languages They can be defined by context-free grammars They include all regular languages They can be recognized by a PDA
They are a subset of regular languages
A PDA can also manipulate the stack as part of performing a transition.
True
A PDA can also manipulate the stack, as part of performing a transition.
True
A language L is accepted by some ε-NFA if and only if it is accepted by some DFA.
True
A language L is empty 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
A non-deterministic finite automaton (NFA) can be reached in multiple sates at once
True
A palindrome is a word that reads same from both ends.
True
An NFA accepts a string w if there exists at least on path from the start state to an accepting state labeled by w.
True
An NFA is defined by 5-tuple:
True
An alphabet is a finite set of symbols.
True
As FA to reg Lang, PDA is to CFL.
True
Explicit epsilon-transitions introduce non-determinism.
True
Explicit ε transitions between deferent states introduce non-determinism:
True
For a symbol X to be a useful, it has to be both reachable and generating
True
For every DFA A, there exists a regular expression R such that L(R) = L(A)
True
For every leftmost derivation, there is a rightmost derivation, and vice versa
True
PDAs are not better than Turing machines
True
Which of the following strings will be accepted by the regular expression (a+b)*abb?
abb
Which of the following is NOT a valid string for the regular expression a*b*c*?
abccba
A CFG that has a string which has more than one left-most derivation is called:
ambiguous
