Problem Detail: Consider a sequence of $n$ flips of an unbiased coin. Let $H_i$ denote the absolute value of the excess of the number of heads over tails seen in the first $i$ flips. Define $H=text{max}_i H_i$. Show that $E[H_i]=Theta ( Read More …
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[Solved]: Could two decidable languages ever not have a mapping reduction?
Problem Detail: Is it ever the case that two decidable languages $L_1$ and $L_2$ that cannot be reduced to one another (in either or both directions)? Intuitively, I would not expect there to be, but rigorously, are there extreme examples that Read More …
[Solved]: Is the language $L = {a^nb^m : n = 2^m}$ context-free?
Problem Detail: Is the language $L = {a^nb^m : n = 2^m}$ context-free? Assume L is a context-free language. Then $ exists pin mathbb{Z}^{+}:forall sin Lleft | s right |geq p. s = uvxyz,left | vy right |geq 1,left | vxy Read More …
[Solved]: undecidable problem and its negation is undecidable
Problem Detail: A lot of “famous” undecidable problems are nonetheless at least semidecidable, with their complement being undecidable. One example above all can be the halting problem and its complement. However, can anybody give me an example in which both a Read More …
[Solved]: Assignment problem for multiple days
Problem Detail: I have a problem that can be reduced to an assignment problem. (In a previous question i found out how to do that.) Which means we have a set $A$ of agents and a set $T$ of tasks as Read More …
[Solved]: How to feel intuitively that a language is regular
Problem Detail: Given a language $ L= {a^n b^n c^n}$, how can I say directly, without looking at production rules, that this language is not regular? I could use pumping lemma but some guys are saying just looking at the grammar Read More …
[Solved]: Easiest way to write a grammar?
Problem Detail: When I see a problem like “Write a grammar for a language $L$ if $L = {..}$” for me is a matter of “instinct” the way that one can define productions. For example given the following exercise: Let $L$ Read More …
[Solved]: Difference between system calls, system call interface and API?
Problem Detail: Lets take POSIX, whats the difference between POSIX API, libc and actual system calls? Asked By : BalaK Answered By : azam I’ll start with system call. a system call is how a program requests a service from an operating system’s Read More …
[Solved]: What is the role of mathematics in programming?
Problem Detail: I am almost totally uneducated in programming and computer science in general, though I am really fascinated by these topics. I read that mathematics is important in programming and that nowadays many mathematicians specialise in applied mathematics in this Read More …
[Solved]: Does immutability in functional programming really exist?
Problem Detail: Although I work as a programmer in my daily life and use all the trendy languages (Python, Java, C, etc) I still have no clear view of what functional programming is. From what I’ve read, one property of functionally Read More …
