what are the steps to answering this question: 1. Complete the following proof that there cannot be a perfect data compression program, i.e. a program that will reduce the length of any file it encounters. [Hint: a data compression program must be a 1-1 function. If two input files had the same compressed output, then the compressed output would not contain the information which one of the two input files it came from, and the decompressor then could not restore the input file. ] Suppose we had such a program. It follows that when we apply this program to an input file of bit length ????, it produces an output file of bit length at most ???? − 1. There are 2???? possible input files of length ????, and at most 2???? − 1 output files of length at most ???? − 1.
what are the steps to answering this question:1. Complete the following proof that there cannot be
a perfect data compression program,
i.e. a program that will reduce the length of any file it encounters. [Hint: a data compression program must be a 1-1 function. If two input files had the same compressed output, then the compressed output would not contain the information which one of the two input files it came from, and the decompressor then could not restore the input file. ]
Suppose we had such a program. It follows that when we apply this program to an input file of bit length ????, it produces an output file of bit length at most ???? − 1. There are 2???? possible input files of length ????, and at most 2???? − 1 output files of length at most ???? − 1.
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