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FORMAL LANGUAGE & AUTOMATA THEORYDesign a single-tape Turing Machine that multiplies two unary numbers, where the input is of the form 1^m 0 1^n and the output is 1^{m \times n}. Clearly define the input alphabet, tape alphabet, and halting condition. Simulate the working of the Turing Machine on the input string 1101.20257mFORMAL LANGUAGE & AUTOMATA THEORYDesign a Turing Machine that increments a binary number by 1.20247mFORMAL LANGUAGE & AUTOMATA THEORYDesign a Turing machine that recognizes strings containing equal number of 0’s and 1’s.20237mFormal Language & Automata TheoryDesign a Turing Machine that accepts the language L = \{a^{n}b^{n} \mid n \ge 0\}. Show the transition diagram/table and trace for input aabb.20257m