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Author: ignougroup

[Solved]: Building functionally complete boolean circuits out of trinary logic

February 8, 2017March 27, 2017 ignougroup

Problem Detail: There are some not-very-commonly considered forms of trinary logic using 3 truth values. Even entire (unusual/rare) ternary computers have been built from it. Is there some knowledge or reference of how to convert some trinary logic systems into functionally Read More …

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[Solved]: Difference between graph-partitioning and graph-clustering

February 8, 2017March 27, 2017 ignougroup

Problem Detail: What is the difference between graph-partitioning and graph-clustering in graph theory? Asked By : suhas bhairav Answered By : Yuval Filmus Graph partitioning and graph clustering are informal concepts, which (usually) mean partitioning the vertex set under some constraints (for example, Read More …

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[Solved]: Generating all strings that a regular expressions describe

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I’m having trouble generating the set of strings, which a regular expressions describe. A typical regular expression can look like this: [atom_0] atom_1 (atom_2 | atorm_3 | … | atom_n-1) <var> [atom_n] Or any other combination of the following: Read More …

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[Solved]: Is there a canonical definition of “pure” function?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: StackOverflow pointed me here, so the question might be a bit in a layman’s terms. Wikipedia defines pure functions as In computer programming, a function may be described as a pure function if both these statements about the function Read More …

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[Solved]: What precisely is infinite ambiguity in a grammar?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: From what I’ve read, an example of infinite ambiguity is usually given in a form of a loop: $S rightarrow aA A rightarrow B B rightarrow A B rightarrow b$ But a grammar is called ambiguous if there’s more Read More …

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[Solved]: From Guido’s essays, how does this function avoid quadratic behavior in a string concatenation algorithm?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I am reading one of Guido van Rossum’s essays on optimization in Python. We are interested in converting a Python list of integers to their character equivalents. Here’s the straightforward algorithm. def f3(list): string = “” for character in Read More …

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[Solved]: Why is the transform in Schönhage–Strassen’s multiplication algorithm cheap?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: The Schönhage–Strassen multiplication algorithm works by turning multiplications of size $N$ into many multiplications of size $lg(N)$ with a number-theoretic transform, and recursing. At least I think that’s what it does because there’s some other cleverness and I really Read More …

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[Solved]: Formally describing a new domain specific programming language

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I am about to implement a domain specific language for representation of social learning conventions. Part of the implementation is a formal description of a language – its ‘calculus’, symbols and logical expressions. My approach would be to describe Read More …

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[Solved]: What’s an intuitive distinction between semi-computable problems and noncomputable problems/functions?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: The definitions I’ve found were highly technical and using terms I’ve never seen before. Say, I have a certain irrational number e that I get get closer and closer to with a computer and I want to determine if Read More …

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[Solved]: Euclidean Steiner Tree Question in Approximation Algorithms

February 8, 2017March 27, 2017 ignougroup

Problem Detail: Given $n$ points in $mathbf{R}^2$, define the optimal Euclidean Steiner tree to be a minimum (Euclidean) length tree containing all $n$ points and any other subset of points from $mathbf{R}^2$. Prove that each of the additional points must have Read More …

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