For which of the listed languages an accepting PDA can be constructed, but there is no FA that accepts them? 1)L = {anb; n≥0} 2)L = {anbk; n≥1,k≥1} 3)L = {anbn; n≥1} 4)L = {anbk; n,kϵℕ,n=2k}

Q: Using the Pumping Lemma (for context-free languages), prove that the following language over E = {a,…

A: Suppose aibjck : k≥j≥i≥0 is context free Let S=apbpcp The pumping lemma says that for some split…

Q: Construct a PDA that recognizes the language: L = {aibj | i ≤ j}

A:

Q: giving 2 DFAs: M1 accepts a language, L1 = {all strings that contain 00} M2 accepts a language, L2…

A: Given M1 and M2 are : We need to find L1 intersection L2 ie DFA for language that contains 00 and…

Q: Prove that the following language is decidable by giving an implementation level TM. L3 = {anbnanbn…

A: A Turing machine is a computational model like Finite Automata, Pushdown automata, which works on…

Q: (3) {w € [0, 1]*: w has 001 as a substring} Testing strings: €, 0, 1, 01, 000, 001, 0001, 0010,…

A: We are given a language {w ∈ {0,1}*: w has 001 as a substring}.And we are asked to test given…

Q: The language we are using here is in Racket.  Please try tying each of the following (car '(11 12…

A: What do car and cdr do? That last line of the above should cause an error. Explain why the single…

Q: Design an NFA over Σ = {a,b,c} with no more than 5 states to accept the following language: L =…

A: We need to design an NFA for the given scenario.

Q: (2) Context-free languages: (a) Let ALLLENPDA = {{M) : M is an PDA for which lengths(L(M)) = 1*}.…

A: Answer: I have given answered in the handwritten format in brief explanation.

Q: Show that the language {ambn| m ≠ n} is context-free.

A: Context free grammar is a formal grammar which is used to generate all possible strings in a given…

Q: Consider the following languages over Σ = {0,1} L6 is the language of the NFA given by the…

A: The NFA (Non-Deterministic Finite Automaton) that you have provided defines the language L6. We need…

Q: Convert this PDA to CFG The language is L = {anbm : m >= n, where m-n is even}

A: Language L = {anbm | m ≥ n, m − n is even}.m-n can be even only when(case-1) Both m and n are even…

Q: Consider the language L = AEqB = {x ∈ {a, b}∗ | na(x) = nb(x)}. a. Show that if na(x) − nb(x) =…

A: Answer: I have given answered in the handwritten format in brief explanation

Q: Assumptions ... • Alphabet . = {a, b} • L₁ = {a"b": n ≥0 An mod 3=0} L2= {abm: n ≥0^m≥ 0^n=m-1} ● =…

A: For the above language, The context free grammar G is shown below: S -> aSbb | aSbbb | ε The…

Q: Prove the following statement using padding: NSPACE(n) = SPACE(n) ⇒ NSPACE(n2 ) = SPACE(n2 ). Hint:…

A: According to the question ,we have to Prove the statement using padding: NSPACE(n) = SPACE(n) ⇒…

Q: show that this language is not regular through the pumping lemma L = {w= {a,b,c}* #(a)=#(b) oder…

A: Pumping Lemma is used to test whether the given language is regular or not. It is negativity test,…

Q: Build PDA's for these languages over sigma set (0,1,2}. Clearly identify your designed PDA as DPDA…

A:

Q: (4) {w € [0, 1]* : w does not have 001 as a substring} Testing strings: €, 0, 1, 01, 000, 001, 0001,…

A: In this question we have to design a Nondeterministic Finite automata where a language consist of…

Q: L1 = { x ∈{a,b}* | x starts with b} L2 = { x ∈ {a,b}* | x ends with a}

A: Constructed a Finite automata  of the given languages

Q: Given the language L(r) defined over the alphabet Σ = {a,b}, where r = (0011)*, define a PDA that…

A: Given :  Given the language L(r) defined over the alphabet Σ = {a,b}, where r = (0011)*

Q: Create a complex CFG that produces L. s L = {0¹ 14 | i≥ 0}. Prove the ambiguity and construct a PDA…

A: Below i have given handwritten solution of the problem. see below steps.

Q: Show that the language is not context-free. L = {an-1bncn+1: n ≥ 1}

A: Below I have provided the handwritten solution to the given question

Q: 2- Write CFG for the following languages a) L= {anb²n, n>0} b) L= {a²nbn, n>0} c) L= {ww}, w={a,b}*…

A: 2. a) The given language is :  L = { a n b 2n , n >= 0 } So, in this language, the number of a's…

Q: For each of the following languages L, state whether L is regular, context-free but not regular, or…

A: When PDA(push-down automata )is possible then it is context free ,if PDA is not possible then it is…

Q: a) L= {anb²n, n≥0} b) L= {a²nbn, n>0} c) L= {ww}, w={a,b}* d) L= {anb²n, n≥0} U {ww}, w={a,b}* 1-…

A: Note:- As per our guidelines we are supposed to answer only one question in multiple questions and…

Q: 1. Find a pda that accepts the language : (anb2n :n>= 0} 2. Show the sequence of instantaneous…

A: Given:

Q: Consider the following languages over the alphabet Σ = {a,b, c} L₁ = {a¹ b¹ck: i, j, k € N such that…

A: The pumping lemma for regular languages can be defined in such a way that it is a crucial end result…

Q: Convert this PDA to CFG The language is L = {anbm : m >= n, where m-n is even}

A: Below is the answer to abobe question. I hope this will meet your requirements.

Q: (a) L = {all words with exactly one b}. (b) L = {all words with at least one a}. (c) L = {all words…

A: For the alphabet Σ ={a, b}, construct an FA that accepts the following languages.(a) L = {all words…

Q: Use the Pumping Lemma to show that each of the languages below is not context-free. 1. B = {0″ #0²…

A: 1. B = {0" #02" #03" In > 0} Suppose B is a context-free language. Then there exists a number p…

Q: Draw the state diagram of an NPDA that recognizes the language {a2n b3m c2m d³n |m, n > 0}.

A: Given : L = {a2nb3mc2md3n| m,n>=0} a2nb3mc2md3n => (aa)n(bbb)m(cc)m(ddd)n logic to build NPDA…

Q: For problems 3-5, use the pumping lemma for context-free languages to prove that L is not a CFL. 3.…

A: The pumping Lemma for Context free languages is, If L be a CFL and w∈L such that |w|>=n for some…

Q: Construct a PDA that accepts the language L = {0n 1n | n ≥ 0}

A: L ={ε, 01, 0011, 000111,............................. }is supported in this language. The number of…

Q: Find minimal dfa's for the following languages. Justify that the result is minimal. (a) L=…

A:

Q: Assumptions ...   Alphabet = {a, b}   • L1 = { a"b" : n ≥ 0 ^ n mod 3 = 0}   L2 = {anbm : n ≥…

A: Note: i cannot upload the file here i will provide you solution and explanation

Q: Give the state diagram of a NPDA that recognizes the language L ={anbm | m < n ≤2m}

A: Answer: The NPDA for the given language is as follows:- Now we have to consider m and n; where m = 2…

Q: S → [0_E_E] E → [O_E_E]|N N → 0|1|2|3|4|5|6|7|8|9|NN 0 → add|sub|mul|div|mod|shl|shr

A:

Q: Solve whether that the following languages on Σ = {a, b, c} are not context-free. (a) L = {anb j : n…

A: a)

Q: Minimum number of states in a DFA that accepts the language L= {w| w has an even number of a's and…

A: Introduction :

Q: Given N = (Q, {a, b}, δ, q0, F) is an NFA that recognizes language L. Define a new language…

A: To construct an NFA that recognizes a language L, we will need to define a set of states, an…

Q: Convert this PDA to CFG The language is L = {anbm : m >= n, where m-n is even}

A: Given The answer is given below.