14 Theory of computation - S2 2021units / FIT2014_S2_2021 / Week 8 / Deferred Mid-Semester TestWrite a regular expression for the language of all strings over the alphabet {a,b} in which the letter a occurs an evennumber of times.Answer:Next pageture 21: Mapping reductionsTute 5: Context-Free Languages andJump to...(4s/p)the Pumping Lemmas

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Answered: Write a regular expression for the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Computer Science State whether the languages over binary strings below are Regular, Context-Free or Turing-recognizable. Use the simplest type. Explain. {ww^r} where w^r is the reverse of string w. And {ww} for any binary string w And {w : w is not a palindrome}
1.Let Σ = {a, b, c} and f : Σ∗ → Σ ∗ the function that for input w yields the string obtained by duplicating each a. E.g. f(baaca) = baaaacaa. Prove that if L is a regular language, then so is {f(w) | w ∈ L}. [Hint: Use induction on regular expressions.] 2.Assume given a non-basic language K . Find an infinite collection of basic languages, all different, whose intersection (i.e. the strings that are in at least one of them) is not basic. Hint: This problem is dual to the previous one. But in place of the union of trivial finite languages, consider here the intersection of trivial co-finite languages.
2. Prove or disprove: (rs ꓴ r)*r = r(sr ꓴ r)*, where s and r are regular expressions. (Must show that the languages represented by the two regular expressions are the same.)
dont copy from any existing answers I have previous answers SUrely dislike dont answer without any knowledge Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize L1? If yes, construct it.If no, explain why. Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2.…
Mathematical Logic First-order or predicate logic. Show that the sum relation, {(m,n,p)|p=m+n}, is not definable on (N; ∙). Hint: Consider an automorphism of (N; ∙) that interchanges two primes. Where N is the set of natural numbers. Please be as clear as possible. Show and explain all the steps. Thank you very much.
Fill out the table for executing the polynomial-time dynamic programming algorithm for deciding whether the string 1001 is in the context-free language generated by the following CFG. Fill the table completely—do not stop the algorithm early. (Note: This CFG is not quite in Chomsky Normal Form since A appears on the right-hand side of a rule, but the same algorithm still works.) A → BC | CC B → BA | 0 C → AB | BB | 1
4. LetΣ ={a, b}. LetL={aibai|i≥0}.Give a Turing machine (TM) that accepts the languageL.Assume (as in the examples done in our course videos) that, when theTM starts, the head is on a blank symbol,∆, and the input string isimmediately after that blank symbol on the tape. For example, if theinput string wereaaabaaa, then the inital tape configuration would be∆aaabaaa
Q.No.3 (a) Define through recursive definition , The language L of strings that start and end with different latters and also must contain aa in middle of each string, defined over Σ={a,b,c}. also Write at least 2 Valid and 2 Invalid strings belongs to this language (2+2) (b) Write the Regular expression for the language which accept no pair of consecutive a’s over Σ ={a,b} (1+1+1) i.R.E= ______________ (1) ii.3 Valid strings= _______________(1) iii.3 Invalid strings= _________________(1) (c) Construct a DFA which accepts all strings over Σ ={a,b} in which second last symbol is a and last symbol is b. also Write at least 2 Valid and 2 Invalid strings for the designed DFA.
Computer Science 5. Consider a language L over the binary alphabet. For any two binary strings x, y we say x, y are distinguishable by L if there exists a string w ∈ L such that exactly one of the strings xw, yw is in L. x, y are indistinguishable by L otherwise (denoted by idL. Prove that idL is an equivalence relation.
subject : theory of computer science The strings of this languages, L = {abb, aabbbb, aaabbbbbb, aaaabbbbbbbb, ...}, CAN BE defined by Finite Automata. select one A. True B. False
Computer Science 1. Let Σ = {0, 1} be an alphabet.(a) Let w = 101 be a word over Σ. Compute |w|, the length of w.(b) List all of the words in Σ32. Let {a, b, c} be an alphabet. List all of the words in Σ23. Let Σ = {a, b} be an alphabet and let · denote concatenation. Compute (ba · ε) · abb,where ε is the empty word.4. Let Σ = {0, 1} be an alphabet and let L ⊆ {0, 1} ∗ be the language defined as L = {w ∈ {0, 1} ∗ |w = x10y, x, y ∈ {0, 1}∗}. (a) Determine whether 01 ∈ L.(b) Determine whether 0101 ∈ L. 5. Let Σ = {0, 1} be an alphabet and let L ⊆ Σ ∗ be the language consisting of all wordsover Σ that contain the substring 10. Construct a DFA that accepts L. Thank you in advance
(a) Give a regular expression that describes all strings accepted by the automaton. (b) Use a subset construction to construct DFA that accepts the same language. Clearly specify the transition table and the start and accepting states. (c) Explain concisely how you can use reachability in the graph to reduce the number of states as much as possible. You might need to draw the unreduced DFA first (for yourself, no need to submit) to better see what is going on. How many states do you end up with? Draw the resulting DFA (with the reduced number of states).

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Write a regular expression for the language of all strings over the alphabet {a,b} in which the letter a occurs an even number of times. Answer: