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in 2020 there was a breakthrough result involving the halting problem and quantum entanglement this video explains what it was decision problems are problems that have a yes or no answer is anna prime is string s a palindrome is boolean formula f satisfiable does program p halt lets focus on the primes problem wed like to build a computing machine that solves it for every valid input it should think for a while then output the correct yes or no answer we can characterize a decision problem by the set of strings for which the correct answer is yes in this case its the infinite set of strings that represent a prime number such a set is called a language for the palindromes problem the language is the set of all strings that are palindromes over some alphabet that we chose so generally we can define any decision problem using a language given some arbitrary language l wed like to build a computing machine that solves the corresponding decision problem its also common to say this mach