4 Answers. A language is regular == A language can be expressed by a Regular Expression == A language can be expressed by a finite automata. Your example is indeed a regular language. A finite language is what you would expect it to be, a language
that can be listed in a finite amount of time
.
Can a language be an infinite set?
(An infinite language is a language with
infinitely many strings in
it. {an | n ≥ 0}, {ambn | m, n ≥ 0}, and {a, b}∗ are all infinite regular languages.) Lemma 1. If A is an infinite language, then for every natural number n ≥ 0, there exists a string w ∈ A such that |w| > n.
Is regular language accepted by finite automata?
Finite automata can be
used to generate strings
in a regular language.
How many infinite languages are regular?
(1) There are
a countably infinite number
of regular languages. This true because every description of a regular language is of finite length, so there is a countably infinite number of such descriptions. (2) There are an uncountable number of languages. Thus there are more languages than there are regular languages.
Why is finite language regular?
All finite languages are regular; in particular the
empty string language {ε} = Ø* is regular
. Other typical examples include the language consisting of all strings over the alphabet {a, b} which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs.
Which Cannot be accepted by a regular grammar?
5. Which among the following cannot be accepted by a regular grammar? Explanation:
There exists no finite automata to accept the given language
i.e. 0
n
1
n
. For other options, it is possible to make a dfa or nfa representing the language set.
How do you prove a language is regular?
To prove a language is regular:
construct a DFA, NFA or RE that recognizes it
. To prove a language is not regular: show that recognizing it requires keeping track of infinite state (hard to be completely convincing in most cases) or use the pumping lemma to get a contradiction.
Can a DFA accept an infinite language?
The language accepted by a deterministic finite automata is
infinite if and only if there exists some cycle on some path from which a final state is reachable
. If you minimize your automaton, then there is at most one state from where you cannot reach a final state anymore (a so called sink state).
Is Kleene star infinite?
The Kleene closure is defined to only have finite strings.
There are an infinite number of such strings
, just as there are an infinite number of integers. … A string from the Kleene closure can not contain every character from an infinte alphabet.
Is a finite language fo definable?
All finite languages are regular
; in particular the empty string language {ε} = Ø* is regular. Other typical examples include the language consisting of all strings over the alphabet {a, b} which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs.
What makes a language not regular?
A simple example of a language that is not regular is
the set of strings { a
n
b
n
| n ≥ 0
}. Intuitively, it cannot be recognized with a finite automaton, since a finite automaton has finite memory and it cannot remember the exact number of a’s.
Which grammar is always unambiguous?
Explanation:
Deterministic CFGs
are always unambiguous , and are an important subclass of unambiguous CFGs; there are non-deterministic unambiguous CFGs, however. Explanation: The closure property of a context free grammar
When a string is accepted by a PDA?
In final state acceptability, a PDA accepts a string when,
after reading the entire string, the PDA is in a final state
. From the starting state, we can make moves that end up in a final state with any stack values. The stack values are irrelevant as long as we end up in a final state.
Which of the following can be accepted by a Dpda?
Which of the following can be accepted by a DPDA? Explanation: Theorem:
The language pal of palindromes
over the alphabet {0,1} cannot be accepted by any finite automaton , and it is therefore not regular. Explanation:The possible change in the stack contents is a change in the number of A’s on the stack.
Which language is accepted by DFA?
A language L is accepted by a DFA < Q , , q
0
, , A > , if and only if L = { w |
*
( q
0
, w ) A } . That is, the language accepted by a DFA is the
set of strings
accepted by the DFA.
