Let be an alphabet. For any languages A, B, C , define the minority of A, B, and

Question

Let be an alphabet. For any languages A, B, C , define the minority of A, B, and C as the language

Minor(A,B,C)={ x | xiscontainedinatmostoneofA,B,orC }. i.e., x is not contained in A or B or C, or x is contained in exactly one of them.

Prove that if A, B, and C are regular, then Minor(A, B, C) is regular. Your proof should be a direct construction of a DFA recognizing Minor(A,B,C), similar to the product construction covered in lecture. In other words, fully define a DFA recognizing Minor(A,B,C), which works by simulating DFAs for A, B, and C as in the product construction, rather than simply proving that it exists via closure properties of regular languages.1

Explanation / Answer

class Array2DWrapper { int *ptr; public: Array2DWrapper(int *ptr) : ptr(ptr) {} int * operator[](int i) { return ptr + i*N; } }; // USAGE: void exampleFunction(int *arrPtr) { Array2DWrapper arr { arrPtr }; ... arr[i][j]; ... }

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