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1. Consider the operations NoLeadingOrLaggingAs over languag...

1. Consider the operations NoLeadingOrLaggingAs over languages that include the letter a' in their alphabet and Third, where NoLeadingOrLaggingAs(L) = { X I W is in L and W = a*xa* where X neither starts nor ends in an 'a' } MidThird(L)= = y I there exists a X and Z, x = lyl = z and xyz is in L...

Problem 1. [15 points] Consider the DFA given by its transit...

Problem 1. [15 points] Consider the DFA given by its transition table below. Give the minimum equivalent DFA. Specify for each state of the minimized DFA the set of equivalent states of the original DFA. 1 A B J B H C *C D G D E C *E F G F C E * G J C H B G I H E J H...

Question 1 5 pts Given the following grammar: S W A B | ...

Question 1 5 pts Given the following grammar: S W A B | A B C S A B I W B B E | y B C Z W x What are the FIRST and FOLLOW sets? Question 2 5 pts Consider the grammar is Question 1, create the parse table. Draw a table and show your work. Is the grammar LL(1)? why? or why not? Use th...

1) Consider the reduction from 3-SAT to Independent Set. ...

1) Consider the reduction from 3-SAT to Independent Set. Given (x ∨ y ∨ z) ∧ (x ∨ ~y ∨~ z) ∧ (~z∨z) as an instance of 3-SAT, construct the instance of Independent Set. You do not have to give a true/false assignment. Just show the reduction diagram and explain it, illustr...

Problem 1 Give a DFA for each of the following languages. I...

Problem 1 Give a DFA for each of the following languages. In both cases, the alphabet is {0,1}. a). The language of strings that contain an odd number of 1’s (and any number of 0’s). b). The language of strings of length at least three. Problem 2 Give a DFA of NFA for the language o...

1) Prove that the class of context-free languages is closed ...

1) Prove that the class of context-free languages is closed under concatenation. (If you do this by constructing a grammar, prove that the grammar works. That is, prove that it generates the language you want.) 2) Describe a two-stack, single-scan, nondeterministic algorithm that recognizes the l...

Problem 1 Given a FA M, is there a string that it accepts? ...

Problem 1 Given a FA M, is there a string that it accepts? (i.e. is L(M) =∅?) Problem 2 Given two FA’s M1 and M2, are there any strings that are accepted by both? Problem 3 Given two FA’s M1 and M2, is L(M1) a subset of L(M2)? Problem 4 Given two FA’s M1 and M2,...

Problem1. Recall that M1 is the TM whose informal descriptio...

Problem1. Recall that M1 is the TM whose informal description is at the beginning of Section 3.1 of the text and whose state diagram is given in Example 3.9. Trace the sequence of configurations that M1 enters when started on the input string1#1. Problem2. Explain why this is not the (implementat...

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