Homework Solution: Consider the ternary number system. a) Draw a state diagram for a DFA that accepts ternary strings th…

    3. Consider the ternary number system. a Draw a state diagram for a DFA that accepts ternary strings that are not divisible by three. b) What is the corresponding regular expression? c) Draw a state diagram for a DFA that accepts ternary strings that are not divisible by nine d) What is the corresponding regular expression? 4. Let w-k... To be a string of ternary digits (MSB first on the left) a) Draw a state diagram for a DFA that accepts strings that are divisible by two. b) Convert the given DFA to a regular expression c) Let ni(x) denote the number of digits in z that have value i. For example, for 1120, corresponding to the decimal number 2-3 + 32 + 33-42, we have no(x) = 1, ni (z) = 2 and n2(x) = 1 . Analyze the DFA and determine a simple rule based on the counts ni (z) for the divisibility by two.
    Consider the ternary number system. a) Draw a state diagram for a DFA that accepts ternary strings that are not divisible by three. b) What is the corresponding regular expression? c) Draw a state diagram for a DFA that accepts ternary strings that are not divisible by nine. d) What is the corresponding regular expression? Let omega = x_k... x_0 be a string of ternary digits (MSB first on the left). a) Draw a state diagram for a DFA that accepts strings that are divisible by two. b) Convert the given DFA to a regular expression. c) Let n_i(x) denote the number of digits in x that have value i. For example, for x = 1120, corresponding to the decimal number 2 middot 3 + 3^2 + 3^3 = 42, we have n_0(x) = 1, n_1(x) = 2 and n_2(x) = 1. Analyze the DFA and determine a simple rule based on the counts n_i (x) for the divisibility by two.

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    3. Consider the ternary calculate method. a Draw a recite diagram coercion a DFA that accepts ternary strings that are referable attributable attributable attributable separable by three. b) What is the selfsame coercionmal indication? c) Draw a recite diagram coercion a DFA that accepts ternary strings that are referable attributable attributable attributable separable by nine d) What is the selfsame coercionmal indication? 4. Let w-k... To be a string of ternary digits (MSB leading on the left) a) Draw a recite diagram coercion a DFA that accepts strings that are separable by brace. b) Convert the consecrated DFA to a coercionmal indication c) Let ni(x) play the calculate of digits in z that feel esteem i. Coercion development, coercion 1120, selfsame to the decimal calculate 2-3 + 32 + 33-42, we feel no(x) = 1, ni (z) = 2 and n2(x) = 1 . Analyze the DFA and enumerate a unartificial administration inveterate on the counts ni (z) coercion the divisibility by brace.

    Consider the ternary calculate method. a) Draw a recite diagram coercion a DFA that accepts ternary strings that are referable attributable attributable attributable separable by three. b) What is the selfsame coercionmal indication? c) Draw a recite diagram coercion a DFA that accepts ternary strings that are referable attributable attributable attributable separable by nine. d) What is the selfsame coercionmal indication? Let omega = x_k… x_0 be a string of ternary digits (MSB leading on the left). a) Draw a recite diagram coercion a DFA that accepts strings that are separable by brace. b) Convert the consecrated DFA to a coercionmal indication. c) Let n_i(x) play the calculate of digits in x that feel esteem i. Coercion development, coercion x = 1120, selfsame to the decimal calculate 2 middot 3 + 3^2 + 3^3 = 42, we feel n_0(x) = 1, n_1(x) = 2 and n_2(x) = 1. Analyze the DFA and enumerate a unartificial administration inveterate on the counts n_i (x) coercion the divisibility by brace.

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