1. For each of the following languages of the form {w € {a,b}* | ... } where the rule... in each case is described below, construct a deterministic finite automa- ton over {a, b} accepting that language. (a) w has both ab and ba as (not necessarily disjoint) subwords. (b) w has an even number of a's and an odd number of b's. (c) w has an odd length and exactly two b's.

Q: 1. Given the following regular grammar: S→aSlalld, I→K1al, K→aK1d, J→ all bJ | ∧ one can use the…

A: please check explanationExplanation:Step 1 :In given regular grammar, S is the start…

Q: Question 1: Use the pumping lemma for context free languages to prove that the language B = {ww w E…

A: Given language: B={ww | w∈{a,b}*}     To prove: B is not a CFL     Concepts used: Context-free…

Q: Problem 1. Multi-Automata Decidability For each of the following languages, state whether or not…

A: For  language L, if there is a Turing machine that accepts all strings in L and discards all strings…

Q: a. L= {x€{a, b, c }* | na(x) < n»(x) and na(x) < nc(x) }, where n(x) is the number of occurrences of…

A:

Q: Using Pumping Lemma for regular languages, prove that the language L defined as follows is not…

A:

Q: Language L: S->A | AX X->АBY | AB Y->ABCY | ABC ВА -> АВ СА -> АС СВ -> ВС A->a B->b C->c Question…

A: Answer: I have given answer in handwritten format.

Q: 5. Is the following language A context-free? You either show that A is context-free by giving a…

A:

Q: Define the following operation, called BUD, on languages: BUD(X,Y) = {w | w E X and w £Y } Prove…

A: Proved the given language is closed for regular languages using DFAs

Q: Consider the NFA N₁ shown in Figure 1 over the alphabet Σ₁ = {0, 1}. 0 1 92 91 € X Figure 1: NFA N₁…

A: In this question we will find elements and transition state and further prove concatenation…

Q: L1) The set of all string except those containing substrings 001.

A: L1) We can draw a set of all strings containing 001 as a substring and then take its compliment. K={…

Q: 3. Consider the languages L= { ba" a b" | n > 0 } a.) Use the Pumping Lemma for Regular Languages to…

A: According to the Bartelby guidelines we are suppose to answer one question at a time. Kindly repost…

Q: Question 3. Consider the language L = {w€ {0, 1}* | the strings 01 and 10 occur the same number of…

A: Given language is, L={w ∈{0,1}* | the strings 01 and 10 occur same number of times in w} Pumping…

Q: How would you prove that a formal language is not regular?

A: Option 1 is correct i.e Pumping Lemma is used

Q: Let A1, A2, and A3 be languages defined over an alphabet Σ. Define Majority(A1, A2, A3) = {w | w is…

A: Let A1, A2, and A3 be languages defined over an alphabet Σ.Define Majority(A1, A2, A3) = {w | w is…

Q: Determine whether or not the following languages are regular. If the language is regular then give…

A: In this answer, we will determine whether or not the following languages are regular. If the…

Q: a) Based of your study for automata and theory of computer science, explain push down automata and…

A: Push down automata   A pushdown automaton (PDA) is a finite state machine which has an additional…

Q: 3. Consider the following language: L = {w€ {a,b}* | 2#a(w) # 3#b(w)}, where #c(w) denotes the…

A: Given:

Q: State the pumping lemma with all its conditions and indicate how you go about proving that a…

A: the pumping lemma with all its conditions and indicate  you go about proving that a language is not…

Q: a) A language is a finite set of strings over some finite set of alphabets. A language L can be…

A: As per company guidelines, only 3 sub parts will be answered. So, please repost the remaining agian.…

Q: For each of the following three languages over Σ = {a,b}, provide a regular expression and a DFA for…

A: Let's design regular expressions and DFAs for each of the given languages:

Q: 11) Construct an NPDA that accepts the following language on Σ = {a, b}, L = {w | na(w) = n(w) + 1}.

A: NPDA: The non-deterministic pushdown automaton and NFA are quite similar. We shall talk about…

Q: Question 2: Use the pumping lemma for context free languages to prove that the 0≤i≤j≤k} is not a…

A: The correct answer for the above question is given in the following steps.

Q: There are two key steps in using Pumping lemma to prove a language to be nonregular: pick w and i…

A: Please find the answer to the above question below:

Q: 15. Show that if L1 is deterministic context-free and L2 is regular, then the language L1∪ L2 is…

A: Proof of L1 U L2 and L1 ∩ L2 as deterministic context free language is detailed in step 2.

Q: Consider the following two statements: I If all states of an NFA are accepting states then the…

A: The answer for the following two statements are

Q: Problem 3 For a language LCE*, define odd(L) := {w E L : w| is odd} (a) Show that if L is regular…

A: Every finite set represents a regular language. Example 1 – All strings of length = 2 over {a, b}*…

Q: Question 2: Use the pumping lemma for context free languages to prove that the language C = {abick |…

A: Use the pumping lemma for context free languages to prove that the language C = {ai bj ck |…

Q: L* is regular, then L must be regular. For any language L, L* must be regular If L1L2 is regular,…

A: Note As Per over guidelines we will solve three sub part remaining sub part post separately i did 2…

Q: Problem 1: Considering the alphabet E (a,b} derive a Non-Deterministic-Finite Automaton (NFA) using…

A: Given regular expression is b*ab|bab*. The regular expression defines the language with strings…

Q: L= {a"bn+1}

A: Since you are asking multiple questions, we are answering first question for you. If you want…

Q: 3. Are the following languages A and B over the alphabet = {a, b, c, d} regular or nonreg- ular? For…

A:

Q: 1. For each of the following languages of the form {w {a,b}* ...} € | where the rule... in each case…

A: Here from question As per our only 3 sub-parts will be answered which are interlinked. So, please…

Q: Give a decision procedure for each of the following problems; argue that your procedure is correct:…

A: Below i have analysed both the question and provided answer with reason:

Q: Please use the pumping lemma to prove, thank you every much. Points Consider the following…

A:

Q: Question 1: Regular Languages and Automata Consider the regular expression E = (b | ab)* (a | e) on…

A: Answer a)   E=(b|ab)*(a|ϵ)   (b|ab)* = { ϵ, b, ab, bb, abab, abb ,…

Q: 1) For each of the following languages, say whether it is context-free. If so, write a CFG or draw a…

A:

Q: Show that the family of context-sensitive language is closed under reversal.

A: Consider that the Language L is a CFL. This means that there is a grammar G={N,?,P,S} that satisfies…

Q: 1. Deterministic Finite Acceptor (DFA) Find a dfa for the following language on E = {0,1} : All the…

A: find a dfa for language l={0,1} All string with exactly two 0's and more than two 1's

Q: Build a deterministic FA M3 for the following language L3 = L(M3)={x over {a, b}\x consists of…

A: Actually, DFA stands for Deterministic Finite Automata

Q: 1. Prove that in the alphabet Σ = {a,b}, the language A = {w/w has the form a"b" a" for some…

A: A language is defined as a set of strings of symbols that may be constrained by specific…