Can a language be context free if it is limited to a certain number of symbols?...
Can a language be context free if it is limited to a certain number of symbols? How would you represent that if possible?
Ex. { w | |w| <= 5 }, with alphabet Σ={x, y}
Homework Answers
If a language is finite then it can be context free. Moreover it will be regular language and in turn it will be context free as well. Now below diagram gives you the corresponding DFA:
Hope it helps, feel free to comment in case of any query.
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Can a language be context free if it is limited to a certain
number of symbols?...
Give a context-free-grammar describing the syntax of the following language. Thank you =) Give a context-free-grammar...
Give a context-free-grammar describing the syntax of the
following language.
Thank you =)
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indicate what language is generated by the context-free grammar. The alphabet is Σ = {a, b}...
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Prove that the following language L is not a Context Free Language using the Pumping Theorem...
Prove that the following language L is not a Context
Free Language using the Pumping Theorem
D = { 0, 1, 2, 3, 5}
V = { a, e, i, o, u}
C = { d, f, g, h, j }
? = D ? V ? C
L = { w : amount(D) <
amount(V) < amount(C) }
"Amount of symbols in w that are elements of
D" < "Amount of symbols in w
that are elements of V"...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that are pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
4. (Non-CFLs) Prove that the following languages are not context-free. (b) The following language over the...
4. (Non-CFLs) Prove that the following languages are not context-free. (b) The following language over the alphabet {a, b, c}: B = {aix | i ≥ 0, x ∈ {b, c}* , and if i = 1 then x = ww for some string w}. (Careful: B satisfies the pumping lemma for CFLs! Make sure you understand why, but you don’t need to write it down.)
5. Is the following language A context-free? You either show that A is context-free by giving...
5. Is the following language A context-free? You either show that A is context-free by giving a context-free grammar for A, or prove that A is not context-free language using the context-free language pumping lemma
Suppose alphabet Σ = {a} and consider the following regular language A, A = {w |...
Suppose alphabet Σ = {a} and consider the following regular language A, A = {w | |w| ≥ 4}, i.e., strings whose length is at least 4 (equivalently, unary numbers x ≥ 4). a) Construct a DFA that recognizes A with as few states as possible (draw a state diagram). b) Construct a PDA that recognizes A with as few states as possible (draw a state diagram). Note that the stack alphabet may include additional symbols.
Automata Theory Give a context-free grammar producing the following language over Σ = {0, 1}: {w...
Automata Theory Give a context-free grammar producing the following language over Σ = {0, 1}: {w : every odd position of w is 1 and w = wR} (HINT: All strings in the language will be of odd length).
Give a Context Free Grammar (CFG) for the following language: L = { w | the...
Give a Context Free Grammar (CFG) for the following language: L = { w | the number of a’s and the number of b’s in w are equal, ∑= {a, b} }
1)Convert the following context free grammar to Chomsky Normal Form S → a X | Yb...
1)Convert the following context free grammar to Chomsky Normal Form S → a X | Yb X → S | λ Y → b Y | λ 2)Some languages distinguish between uppercase and lowercase in identifiers. What are the pros and cons of this design decision? 3)Use the pumping lemma to prove that the following languages are not regular. (The alphabet is Σ = {a, b}.) a) L = {an b1 ak: k >= n+ l} b) L = {ww:...
Give a context-free-grammar describing the syntax of the
following language.
Thank you =)
Give a context-free-grammar describing the syntax of the following language: L = { ww| we{a, b }" } is a context- free language, where w is a non-empty string from alphabet {a, b } and wt denotes the reversal of string w.
Prove that the following language L is not a Context
Free Language using the Pumping Theorem
D = { 0, 1, 2, 3, 5}
V = { a, e, i, o, u}
C = { d, f, g, h, j }
? = D ? V ? C
L = { w : amount(D) <
amount(V) < amount(C) }
"Amount of symbols in w that are elements of
D" < "Amount of symbols in w
that are elements of V"...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that are pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
5. Is the following language A context-free? You either show that A is context-free by giving a context-free grammar for A, or prove that A is not context-free language using the context-free language pumping lemma
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