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