Problem Detail: I am working on an algorithm which approximates a certain optimal quantity. The approximation becomes better when the size of the problem ($n$) becomes larger: the difference from the optimum is approximately $1/n$. Initially, I wrote that the algorithm Read More …
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[Solved]: Why do some inference engines need human assistance while others don’t?
Problem Detail: I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here. Why is it that automated theorem provers, i.e. ACL2, and SMT solvers do not Read More …
[Solved]: Computing with the Monster
Problem Detail: The Monster M is the largest of the finite sporadic groups that arises in the classification of finite, simple groups in mathematics. M can be realized as a (very large!) set of 196882 X 196882 matrices with nothing more Read More …
[Solved]: What is the minimum square partition of an almost-square rectangle?
Problem Detail: This question is motivated by an older question about tiling an orthogonal polygon with squares. It is a generalisation of my former question about how to prove that the minimum square partition of a 3X2 rectangle has 3 squares). Read More …
[Solved]: How to measure the complexity of the discrete logarithm problem?
Problem Detail: The answers to this question on Crypto Stack Exchange basically says that, to measure the complexity of the logarithm problem, we have to take the length of the number representing the size of the group into account. It seems Read More …
[Solved]: Emulating boolean circuits using addition and multiplication (mod 5)
Problem Detail: I’m trying to use gates that do addition and multiplication modulo 5 to emulate logic gates. Assuming false and true are mapped to 0 and 1 respectively (with 2, 3, and 4 being invalid), I figured out I can Read More …
[Solved]: DFA: Can the set of States Q be empty by definition?
Problem Detail: Can the set of states Q be empty by definition? I was wondering about this question when doing exercises in the pumping lemma for finite automaton. Asked By : user8272 Answered By : Shaull In a DFA – no, because the Read More …
[Solved]: Relation between the size of sub-problems and number of sub-problems in a recurrence
Problem Detail: Below is a well-known equation for generalized recurrence relation in a divide and conquer paradigm (as described in CLRS) — $$T(n) = aT(n/b) + f(n), quad text{where} quad a gt 1 text{ , } b geq 1$$ If we Read More …
[Solved]: Is this a regular grammar?
Problem Detail: I went through a question asking me to categorize the following grammar. $$S → AA, S → AB, A → a, A→BB, B → b, B → e$$ From the production rules, clearly it is Context-Free. But it accepts Read More …
[Solved]: What is the complexity of recurrence $T(n) = T(n-1) + 1/n$
Problem Detail: What is the complexity of the follwoing recurrence? $$T(n) = T(n-1) + 1/n$$ I highly suspect the answer to be $O(1)$, because your work reduces by $1$ each time, so by the $n$th time it would be $T(n-n) = Read More …
