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Ullman (TOC) Edition 3 Exercise 2.2.6 Problem 2.2.8 (Page No. 54)
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Theory of Computation
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Lakshman Patel RJIT
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ullman
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Ullman (TOC) Edition 3 Exercise 2.2.6 Problem 2.2.7 (Page No. 54)
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Theory of Computation
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Lakshman Patel RJIT
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Ullman (TOC) Edition 3 Exercise 2.2.6 Problem 2.2.6 (Page No. 54)
Give DFA's accepting the following languages over the alphabet $\{0,1\}$ $a)$ The set of all strings beginning with a $1$ that $,$ when interpreted as a binary integer $,$ is a multiple of $5$ For example $,$ ... a binary integer $,$ is divisible by $5.$ Examples of strings in the language are $0,10011,1001100,$ and $0101.$
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Theory of Computation
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Lakshman Patel RJIT
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4
Ullman (TOC) Edition 3 Exercise 2.2.6 Problem 2.2.5 (Page No. 53  54)
Give DFA's accepting the following languages over the alpabet $\{0,1\}:$ $a)$ The set of all strings such that each block of ve consecutive symbols contains atleat two $0's.$ $b)$ The set of all strings whose tenth symbol from the ... that the number of $0's$ is divisible by five $,$ and the number of $1's$ is divisible by $3.$
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Ullman (TOC) Edition 3 Exercise 2.2.6 Problem 2.2.4 (Page No. 53)
Give DFA's accepting the following languages over the alpabet $\{0,1\}:$ $a)$ The set of all strings ending in $00.$ $b)$ The set of all strings with three consecutive $0's$ (not necessarily at the end)$.$ $c)$ The set of strings with $011$ as a substring.
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Apr 2
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Theory of Computation
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Lakshman Patel RJIT
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Ullman (TOC) Edition 3 Exercise 2.2.6 Problem 2.2.3 (Page No. 53)
Show that for any state $q,$ string $x,$ and input symbol $a,$
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Apr 2
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Theory of Computation
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Ullman (TOC) Edition 3 Exercise 1.7 Problem 1.6 (Page No. 36)
The binary string $X$ [shown online by the Gradiance systems] is a member of which of the following problems$?$Remember$,$a $"$problem$"$ is a language whose strings represent the cases of a problem ... palindromes$,$ which are strings that are identical when reversed$,$like $0110110,$ regardless of their numerical value$.$
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Apr 2
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Theory of Computation
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Ullman (TOC) Edition 3 Exercise 1.7 Problem 1.5 (Page No. 35)
What is the concatenation of $X$ and $Y?$ [shown online by the Gradiance system from a stock of choices] is$:$
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Apr 2
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Theory of Computation
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Lakshman Patel RJIT
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Ullman (TOC) Edition 3 Exercise 1.7 Problem 1.4 (Page No. 35)
The length of the string $X$ [shown online by the Gradiance system from a stock of choices] is$:$
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Apr 2
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Theory of Computation
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Lakshman Patel RJIT
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Ullman (TOC) Edition 3 Exercise 1.7 Problem 1.3 (Page No. 35)
Suppose we want to prove the statement $S(n):$ $"$If $n\geq 2,$ the sum of the integers $2$ through $n$ is $\frac{(n+2)(n1)}{2}"$ by induction on $n.$ To prove the inductive step$,$ we can make use of the fact ... $,$ in the list below an equality that we may prove to conclude the inductive part.
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Theory of Computation
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Ullman (TOC) Edition 3 Exercise 1.7 Problem 1.2 (Page No. 35)
To prove $A$ $AND$ $(NOT$ $B)\rightarrow C$ $OR$ $(NOT$ $D)$ by contradiction$,$which of the statements below would we prove$?$Note$:$ each of the choices is simplified by pushing $NOT's$ down until they apply only to atomic statements $A$ through $D.$
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Apr 2
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Theory of Computation
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Ullman (TOC) Edition 3 Exercise 1.7 Problem 1.1 (Page No. 35)
Find in the list below the expression that is the contrapositive of $A$ $AND$ $(NOT$ $B)\rightarrow C$ $OR$ $(NOT$ $D).$ Note: the hypothesis and conclusion of the choices in the list below may have some simple logical rules applied to them, in order to simplify the expression.
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Apr 2
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Theory of Computation
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Lakshman Patel RJIT
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