Problem Detail: Given three numbers $m$, $n$ and $p$ in interleaved binary encoding1, it’s obviously possible to check in $O(1)$ space whether $m+n=p$. It’s less obvious2 that it isn’t possible to check in $O(1)$ space whether $mcdot n=p$. I wonder whether Read More …
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[Solved]: Finding all marked elements using Grover’s algorithm
Problem Detail: Grover’s algorithm uses an oracle function $f(x) to {0,1}$ to find the location of a single marked element from an unordered database of $2^n$ elements with high probability. As part of an assignment I am supposed to design a Read More …
[Solved]: Solving a complicated recurrence relation
Problem Detail: How to solve the recurrence relation below? $$T(n) = begin{cases} 2T(sqrt{n}) + log n/loglog n & text{if } n > 4 1 & text{if } n leq 4. end{cases}$$ Preferably by the master theorem; otherwise by any method. I Read More …
[Solved]: Reference request: proof that if $L in DCFL$, then $L Sigma^* in DCFL$
Problem Detail: So, it’s fairly easy to prove that if $L in DCFL$, then $L Sigma^* in DCFL$. Basically, you take the DPDA accepting $L$. You remove all transitions on final states, and then for each $a in Sigma$ and each Read More …
[Solved]: Decidability of the language that accepts a universal turing machine
Problem Detail: Is the language $L_{universal} = { left langle M right rangle | M textrm{is a universal turing machine} }$ decidable? I’m guessing it is decidable according to the definition of a UTM, that a UTM must be able to Read More …
[Solved]: Implications of Rice’s theorem
Problem Detail: Every time I think I get what Rice’s theorem means, I find a counterexample to confuse myself. Maybe someone can tell me where I’m thinking wrong. Lets take some non-trivial property of the set of computable functions, for example Read More …
[Solved]: No number is equal to Zero, is this statement true or false?
Problem Detail: While reading an article on logic, there is a sentence “No number is equal to zero” and we have to assign truth values to this sentence. I hope this is true and the article says it as false. Can Read More …
[Solved]: Understanding Intel’s algorithm for reducing a polynomial modulo an irreducible polynomial
Problem Detail: I’m reading this Intel white paper on carry-less multiplication. It describes multiplication of polynomials in $text{GF}(2^n)$. On a high level, this is performed in two steps: (1) multiplication of polynomials over $text{GF}(2)$, and (2) reducing the result modulo an Read More …
[Solved]: I/O in Theory of Computation
Problem Detail: I posted a question “Arbitrary Programs that halt” some days ago and now i think my doubt is a lot more clear. I concluded that in any arbitrary program that halts, control flow operations, calculation operations ( 2+3 , Read More …
[Solved]: Correcting two-bit error using a CRC
Problem Detail: What algorithm can be used to correct a two-bit error in a message protected by a 32-bit CRC, assuming the CRC polynomial allows that? I’m seeking something for 480-bit payload, able to detect uncorrectable errors, fast in the worst Read More …
