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Problem Detail: In Algorithmic Randomness and Complexity from Downey and Hirschfeldt, it is stated on page 129 that $qquad displaystyle sum_{K(sigma)downarrow} 2^{-K(sigma)} leq 1$, where $K(sigma)downarrow$ means that $K$ halts on $sigma$, $sigma$ being a binary string. $K$ denotes the prefix-free Read More …

Problem Detail: I am looking at an example Turing machine in my textbook, Automata and Computability by Dexter C. Kozen, and I’m confused as to how they determine the number of states this particular machine has. Here is the example: “Here Read More …

Problem Detail: While trying to improve the performance of my collision detection class, I found that ~80% of the time spent at the gpu, it spent on if/else conditions just trying to figure out the bounds for the buckets it should Read More …