Finite-state automaton – Essaylink

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For each of the following languages construct a finite-state automaton
that accepts the language. i. x is in 0, 1*, and no two 0’s are adjacent in x
ii. x
iii. z = 3x + 5y for some natural numbers x and y
iv. x is in 0, 1*, and the number of 1’s between every two 0’s
in x is even
B. Find a deterministic finite-state automaton that is equivalent to the
finite-state automaton whose transition diagram is given in the figure
below

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