Problem Detail: In Types and Programming Languages, the family of sets of terms with de Bruijn indices in the untyped $lambda$-calculus is defined in this way: Let $T$ be the smallest family of sets ${T_0, T_1, T_2, …}$ such that $k Read More …
Category: Uncategorized
[Solved]: Matching girls with boys without mutual attraction (variant of maximum bipartite matching)
Problem Detail: Let us say you have a group of guys and and a group of girls. Each girl is either attracted to a guy or not, and vice versa. You want to match as many people as possible to a Read More …
[Solved]: Frame Pointers in Assembler
Problem Detail: I am currently learning assembly programming on wombat 4, I am looking at Frame pointers. I understand exactly what a frame pointer is: it is a register and are used to access parameters on a stack. But i’m confused Read More …
[Solved]: A framework to capture common variation of sequence alignments
Problem Detail: The global alignment problem can be generalized by setting the cost of some boundary gaps to 0. Gaps at both end in both strings have 0 cost, then we get the semiglobal alignment. Gaps are at the left end Read More …
[Solved]: What is the reason of inaccuracy of operations on float numbers?
Problem Detail: I wonder why in JavaScript 0.1 + 0.2 // return 0.30000000000000004 4%0.1 // return 0.09999999999999978 http://jsbin.com/oHISAfU/1/edit (Example) In C the math.h library fmod function printf(“%f”, fmod(4.0,0.1)); // print 0.100000 http://ideone.com/RG5Wyv (Example) And in Spotlight (search feature in the Mac Read More …
[Solved]: Is the set of Gödel numbers of computable constant functions recursively enumerable?
Problem Detail: I’ve been working on the following exercise: $S = { x | f_x text{ is constant} }$. Is $S$ recursively enumerable? Here, $fx$ is the function computed by the $text{x-th TM}$. So it is a computable function. Intuitively, I Read More …
[Solved]: Lower bounds of calculating a function of a set
Problem Detail: Having a set $A$ of $n$ elements, let’s say I want to calculate a function $f(A)$ that is sensitive to all parts of the input, i.e. depends on very member of $A$ (i.e. it is possible to change any Read More …
[Solved]: What precisely is infinite ambiguity in a grammar?
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 …
[Solved]: From Guido’s essays, how does this function avoid quadratic behavior in a string concatenation algorithm?
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 …
[Solved]: Why is the transform in Schönhage–Strassen’s multiplication algorithm cheap?
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 …
