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I have a problem to solve this recurrence. I tried by myself but it doesn't look understandable. Solve the following recurrence
|
We know that every non-regular language can be recognized with $ \Omega
(\log\log n) $ space complexity.
I'm looking for an example of a language which is $ \Theta
(\log\log n) $ space complexity (if such exists).
|
At the needs of my HW at uni I need to transform some Horn clauses to Prolog but I cannot figure out how to do it. I found out some guides but they describe how to do it with only one fact. So can you give me a brief example on how to do it?
Eg John is beautiful and rich
we can transform it at: not (Beautiful(John)) ^... |
In the Wikipedia article on Rogers' theorem, it is stated that all total computable functions have a fixed point. The notation is a little hard for me to understand; a symbol is used that is used to denote "semantic equivalence." I do not know what semantic equivalence is; I would appreciate it if someone could shed ... |
The is the running time of an algorithm : $0.5 X^2 + 3X$ ,
Q1) i dont understand why my lecturer says that the Big O is $O(X^3)$, shouldnt it be $O(X^2)$ as it is bounded by the quadratic power of $X$.
Who is correct , me or my teacher ???
Q2) Why is the Theta of the equation : $X^2$, i cant understand why
|
I have a few small questions about section 2.4 ("Rule induction") in Practical Foundations for Programming Languages (p. 19).
(1) In the rule induction principles for nat,
To show P(a nat) whenever a nat, it is enough to show:
(1) P(zero nat).
(2) for every a, if (a nat and) P(a nat), then P(succ(a) nat).
why is ... |
Let me clarify:
Given a scatterplot of some given number of points n, if I want to find the closest point to any point in the plot mentally, I can immediately ignore most points in the graph, narrowing my choices down to some small, constant number of points nearby.
Yet, in programming, given a set of points n, in orde... |
My teacher pointed out to us during lectures that we could use Graph Search to help us solve Sudoku puzzles which has left me puzzled .
I dont see how this is possible as Graph Search is mostly about getting from Node A to Node B. He mentioned about how its a directed graph where the nodes correspond to partially comp... |
I would like to know whether there is a method to find similar questions for a given question, just like this stackexchange.com does.
Is there any paper or tools?
I tried keywords such as "deduplication" and "linking" but it was not successful.
|
I know these relations :
\begin{gather}
\mathrm{NC}^1 \subseteq \mathrm{NC}^2 \subseteq \dots \subseteq \mathrm{NC}^i \subseteq \dots \subseteq \mathrm{NC} \\
\mathrm{NC}^i \subseteq \mathrm{AC}^i \subseteq \mathrm{NC}^{i+1} \\
\mathrm{NC}^1 \subseteq \mathrm{L} \subseteq \mathrm{NL} \subseteq \mathrm{AC}^1 \subseteq... |
My lecturer told me that when I use an arithmetic I-Type command (ADDI,SUBI etc.) , the IMM field gets sign extended, and when I use a logic I-Type command (ORI,ANDI etc.) , the IMM field is just bits.
He also said that if the IMM field contains a negative number, it is represented in 2's complement.
Let's say I have a... |
I’m trying to find an algorithm that can give me an approximate solution for a wiring problem that I have been asked to look at. I believe this is closely related to finding a node weighted Steiner tree – e.g. http://www.cs.umd.edu/~samir/grant/gk98b.ps.
I have a number of connectors which have a fixed location in spa... |
Say I plugged in a hardware true-random number generator (TRNG) to my computer, then wrote programs with output that depends on the TRNG's output. Can it do anything non-trivial that a Turing machine with a psuedo-random number generator can't do? (a trivial thing it can do would be generating truly random numbers)
|
Suppose that I have a set of $N$ points in $k$-dimensional space ($k>1$), such as in this question, and that I need to find all pairs with a distance¹ smaller than a certain threshold $t$. The brute-force method would require $N(N-1)$ distance calculations, which is not acceptable. I attack the problem by first sorti... |
I've a set of grammar rules like this:
$$
\begin{align*}
&S \to AbB \\
&A \to aA|\epsilon \\
&B \to aB|bB|\epsilon
\end{align*}
$$
The grammar generates the following words:
$$
\begin{gather*}
AbB \to a^2AB \to a^3AB \to \cdots \to a^nAB \to a^nB \to \\
\to a^nB \to a^nbB \to a^nb^2B \to \cdots \to a^nb^mB \to a^nb^m,
... |
Let $T = (V, E)$ be a tree with a designated root $r \in V$. The fact that the tree is rooted allows us to speak of "subtrees of $T$ rooted at some node $x \in V$". Let's say we have a (not necessarily injective) function $c: V \rightarrow \mathbb{N}$ that assigns a color to every node.
We want to find for every node ... |
I have the languages $L_1$ and $L_2$ such that $L_1 = \{a^nba^n :n \in N\}$ and $L_2 =\{a,b\}^*\setminus L_1$.
I want to prove that $L_2$ is not a regular language. I know that to prove that $L_2$ is not a regular language I can use the pumping lemma but I'm unsure about the details.
I also want to prove that $L_2$ is ... |
I have a language where each string in the language has even amount of $0$'s as $1$'s (e.g., $0101$, $1010$, $1100$, $0011$, $10$ are all in the language). I was hoping to define a context-free grammar that describes this language. After defining a context-free grammar I want to formally prove that this context-free gr... |
I am studying for my algorithms final and came across the following problem:
Find three languages $L_1 \subset L_2 \subset L_3$ over the same alphabet such that $L_2 \in P$ and $L_1,L_3$ are undecidable.
I am having trouble coming up with an example of three such languages. My first thought was to use a form of the hal... |
I am reading the paper Color Coding by Alon, Yuster, and Zwick. They state a theorem (6.3) that says if $H$ is a graph on $k$ vertices with treewidth $t$ and $G = (V, E)$, then a subgraph of $G$ isomorphic to $H$ can be found in $2^{O(k)}V^{t+1}$ expected time. They do not include a proof, but do state that the proof i... |
I am working through Sipser, and I am trying to understand some of the algorithms described in Space Complexity, but I am having a hard time understanding the presentation of the material (especially Savitch's theorem). I have a very strong intuition for time complexity, but I don't understand how space complexity fits... |
Is there any limit to what we can define as a language? Is any set of symbols a language?
For example, given the alphabet $\Sigma$, do we say that the language $L = \Sigma$ has alphabet $\Sigma$?
Also, what is the intuitive modern equivalent to languages (as defined WRT complexity classes)? I always hear languages desc... |
In "Introduction to the Theory of Computation" by Sipser, Savitch's theorem is explained as an improvement to a naive storage scheme for simulating non-deterministic Turing machines (NTM). I am going to quote the text verbatim, because quite frankly I don't fully understand it (which is why I was unable to really ask m... |
I've been doing nand2tetris exercises and I'm quite interested in how compilation actually works. In nand2tetris when creating the VM language I had to create a "bootstrap" which called the main method of the program.
In other languages such as C, Java or even interpreted languages like PHP, does the OS/interpreter/VM ... |
We know that all graphs with odd cycles (odd number of vertices) are not 2-colorable. Is there a similar characterisation for 3-colorability? I am looking for undirected graphs that are not 3-colorable depending on a single graph property e.g. vertices/edges parity or anything else that can be generalised.
|
If I have a DCFG G for some language over {0,1}* and a DCFG H for its complement, with disjoint non-terminals, and a (perhaps partially reduced) string, can they both have a handle for the string? So the right hand sides of these rules would consist of only terminals and one would be a (maybe proper) prefix of the othe... |
I've just read in a discussion about dynamic typing
Reflective towers is an open problem for statically typed languages.
What are reflective towers?
I think it might be related to reflection, but I'm not sure.
If you create an example, I would prefer Java.
|
Let $G$ be a graph whose Shannon Capacity is $\Theta(G)$. Is there any graph product for which the Shannon Capacity is $\Theta(G)^k$ where $k$ is the number of times the product is taken?
|
What is a known strategy to approach a situation where short bursts of data are being sent very often over a high bandwidth, high latency cable? I am aware of cubic but even that does not utilize a 10GBps cable in a short burst scenario.
Lets say I have a distributed network where a single computer is sending tasks to ... |
I have a set of points $C$, and I have the distance between each point $D(P_i,P_j)$. These distances are euclidean but the points are actually in a feature space.
From the $C$ points I want to choose a subset of $n$ points. Call this subset $s$. I want to choose this subset so as to maximize the minimum distance betwee... |
If $P = NP$ would this imply that polynomial time reduction from an $NP$- to a $P$-problem would be possible? And if $P\neq NP$ does it imply that a polynomial time reduction from an $NP$- to a $P$-problem would be impossible?
|
If two regular languages $L_1$ and $L_2$ are both not context free languages then is $L_1 \cup L_2$ also not a context free?
I am aware that if $L_1$ and $L_2$ are context free languages then the language $L_1 \cap L_2$ is also context free but cannot quite connect the dots. If someone could help out that would be grea... |
I have to solve this problem: We have weighted $n$-node undirected graph $G = (V,E)$ and a positive integer $k$. We can reach all vertices from vertex 1 (the root). We need to find the weight of minimal spanning tree in which the degree of vertex 1 is at most $k$ (we don't care about other vertices' degrees). We can as... |
Wikipedia says
A list comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It
follows the form of the mathematical set-builder notation (set
comprehension) as distinct from the use of map and filter
functions.
A list comprehension has the sam... |
I have two shapes in a 2D space, not necessarily convex, and I'd like to compare how similar they are. How can I define a robust distance metric to measure their similarity, and how can I compute it?
I am looking for a method which provides a short distance in case of:
scaling;
rotation;
perhaps local scaling or rota... |
I'm trying to solve this problem:
Given a collection of cities and the number of commuters between cities, design a network of roads for minimal cost where cost includes the cost of building the roads, and traveling of commuters. (So if more commuters use one edge, that edge will have a modified cost since the commute... |
I've recently learned about the Big Oh notation and heard that the following aren't true:
$f(n)\in O(f(n)^2)$.
Either $f(n)\in O(g(n))$ or $f(n)\in\Omega(g(n))$ or both.
$f(n)\in\omega(g(n))$ implies $\log(f(n)) = \omega(\log(g(n))$.
I'm trying to find a good counter-example for each but it's proving to be a bit chal... |
I need to verify the type for the lambda expression: $\lambda f.\lambda x.f (f x)$
My method gives me: $(a\rightarrow c)\rightarrow b\rightarrow c$
Im trying to define it in Haskell (on Hugs) like this:
h= \f x -> f (f x)
When i call the :type comamnd it gives me:
(a -> a) -> a -> a
Is mi function correctly defined ... |
the P vs NP problem attracts a lot of attention, not all of it desirable, for a wide variety of reasons. there are many P=NP claims eg on this widely cited list maintained by mathematician Woegeorgi, P vs NP page. also, intermittently there are hot questions on SE sites related to P vs NP (eg recently [2],[3]) below, &... |
The definition of the both architecture looks pretty same. They are parallel computing architecture with different type of cores.
What distinguish their definition, actually?
|
I'm stuck on a theory/set proof question:
$S$ is the set of all total functions $f : \{0, 1\} \to \mathbb{N}$ (natural numbers), prove that S is countable.
I have found a sample solution already but I do not understand what is going on.
Quoting from here:
To show this, we define a mapping $g$ from $S$ to $N × N$ an... |
For a binary tree we define horizontal distance as follows:
Horizontal distance(hd) of root = 0
If you go left then hd = hd(of its parent)-1, and
if you go right then hd = hd(of its parent)+1.
The bottom view of a tree then consists of all the nodes of the tree, where there is no node with the same hd and... |
(The question is an extension of this unanswered question on stackoverflow)
If we have a set of strings, we can efficiently represent them with tries. Common branches can also be merged, resulting in a DAG instead of a tree that is even more compact.
However, if we have a set of sets (i.e. the order does not matter), t... |
I've searched online for this but I only seem to find answers for a similar equation:
T(n) = T(n/3) + T(2n/3) + cn
But the one I'm trying to solve is:
T(n) = T(n/3) + T(2n/3)
Base case: We can assume T(a) = Theta(1) for any constant a.
I've succeeded in proving (by induction) that T(n) = O(n*log(n)). I thought the a... |
Given some unrecognizable language $L$, is it possible for its complement $\overline{L}$ to also be unrecognizable?
If some other language $S$ and its complement $\overline{S}$ are both recognizable, then $S$ and $\overline{S}$ are decidable. If $\overline{S}$ is unrecognizable, then then $S$ is undecidable but still r... |
I am reading Prim's MST for the first time and wanted to implement the fast version of it .
$m$ - The number of edges in the graph
$n$ - The number of vertices in the graph
Here's the algorithm :
1) Create a Min Heap of size $V$ where $V$ is the number of vertices in the given graph. Every node of min heap contains ... |
For example, on x86, we have a set of general registers, each named to the function it carries out.
We have an Accumulator, which is a storage for a results of different fixed point operations, we have a Base register, which is used for addressing elements in the array, a Cycle register, which holds a incremented or d... |
Consider the following code segment :
for (int i = 1; i <= n; i++ ) {
for (int j = 1; j <= n; j = j + i ) {
printf("Hi");
}
}
Here, the outer loop will execute $ n $ times, but the execution of inner loop depends upon the value of $ i $.
When $ i = 1 $ inner loop will execute $ n $ times.
When $ i... |
I want to show that $CO-2Col \le_L USTCON$ (Log-Space reduction)
$USTCON$
The $s-t$ connectivity problem for undirected graphs is
called $USTCON$.
[Input]: An undirected graph $G=(V,E)$, $s,t \in V$.
[Output]: 1 iff $s$ is connected to $t$ in $G$.
$CO-2Col$
A graph is $2$-colorable if there is a way to color the ... |
I have been starting to learn about CFGs and PDAs and have gotten familiar with the simple stuff. I have been able to construct CFGs for simple languages but this question is more specific:
$\lbrace 0^a1^b2^c3^d4^e5^f |a,b,c,d,e,f \geq 0$ and $a+b=d+e\rbrace$.
My thought process has only gone so far. I see that if you ... |
This is a theoretical computer science question, regarding the proof of whether or not context-free languages are closed under an operation. This means basically that any context-free language which undergoes this operation would still be context-free.
For a language $A$ which is a subset $\Sigma^*$, define the langu... |
Given that Let S = {a | |a| is odd}. I know that since S is decidable, but does there exist a subset within S that is undecidable?
|
I am working out with the rooks problem. If there are m rooks on an nxn chessboard,i have to give describe a polynomial (in m and n) time algorithm that finds a maximum-sized subset of the rooks such that if we leave this subset on the chessboard and remove all other rooks, then no two rooks attack one another. (Two roo... |
This is a puzzle type question which asks to create a context-free grammar to match this language:
{ x#w | x,w are in {a,b}*, and w contains the reversal of x as a substring }
So some example strings to try:
#, a#a, b#b, ab#ba, ab#aaabbba
Does anyone have any advice on how to get better at these types of problems?... |
Suppose an algorithm goes through a list of n integers and for every iteration of the loop it is needs to check if the current evaluated element of the list is even. If it is even, return the index of the integer that is evaluated as even.
How come the algorithm would have 2n+1 comparison?
I thought linear search would... |
I was wondering if this language is context-free:
$L = \{ x \in \{ 0, 1 \}^* : |x| = 2^n $ for some natural number n $\}$
I know that this language is not regular because it fails the pumping lemma for regular languages but that does not necessarily mean it is not context-free. I'm not sure whether to use the pumping ... |
This link provides an algorithm for finding the diameter of an undirected tree using BFS/DFS. Summarizing:
Run BFS on any node s in the graph, remembering the node u discovered last. Run BFS from u remembering the node v discovered last. d(u,v) is the diameter of the tree.
Why does it work ?
Page 2 of this provides a... |
We used to have analog computers several decades ago. Modern days computers are Digital. What about Quantum computers? Is it analog or digital? I am asking this since qubit can be many things at the same time.
|
I have seen turing machines beeing represented with tapes infinite in one, and in two directions. Is there any difference in the power of such turing machines, or are they basically equivalent? In my head I think they are equivalent, since I guess that there must be some way to represent the two-way infinite tape as a ... |
Firstly, I'd like to say that my text below may contain errors, so feel free to point out any mistakes in my formulation of the question.
Consider an untyped lambda calculus with booleans and if-statements whose terms are given by this syntax:
t ::= v | t t | if t t t | x
v ::= \x.t | #t | #f
Contexts C in this case... |
I have studied the book "C++ Demystified". Now I have started to read "Object-Oriented Programming in Turbo C++ first edition (1st edition)" by Robert Lafore. I do not have any knowledge of programming which is beyond these books. This book might be outdated because it's 20 years old. I do have the latest edition, I am... |
I need to make a recursive relationship for a function f(m, n) nonrecursive to make it more efficient and succinct in my code.
I stumbled across an important recurrence relationship dealing with the number of vertices, edges, faces, and solids (m-polytopes) in an n-cube which is based off of a simpler algorithm for an ... |
Suppose you have a set of binary strings of length n, the magnitude of a string is the number of 1's it has. and you want the program to return true if there is a string of length n that has a magnitude of <= k and there is a index i for every y in the set string[i] = y[i] = 1 for all strings.
Example for n = 5, k = 3:... |
Which kind of machine learning concept / model is used in 20 Questions?
Is this kind of thing best solved by a neural network?
Where I can read something about it?
|
I'm currently studying deadlocks and I'm trying to learn myself the bankers algorithm.
In this example my teacher goes to B first, then C and finally A.
He adds (I think) 2 (row b, Has) with 3 (free) and then gets the new Free value 5.
After that he proceeds to row C where he adds 2 (row c, Has) with the free value 5 w... |
Imagine we have N houses, on a standard euclidean 2D plane. We also have N "packages", each of which contains several "objects" of different types, let's call them A, B, C, etc. We know the content of all boxes beforehand, but can't change them (they're randomly generated).
We need to send one package to every house, a... |
from Sipster's definition: Any language that can be generated by some context-free grammar (call it $G$) is called a context-free language (CFL). However, can $G$ generate strings that are not in the the language that recognizes $G$?
|
Let A and B be languages over $\sum$ = {0, 1, 2, 3}
Language A = {$(0U1)^a(1U2)^b(2U3)^c | a \geq b$}
Language B = {$(0U1)^a(1U2)^b(2U3)^c | a = c$}
Question: prove that A and B are context free
|
I was reading up on the four color theorem and am wondering if there is any practical application of it. (I dont think seperating the map into four different colors can be considered an application.)
I tried Googling for applications but couldn't find any.
|
I am trying to find the worst case $Θ$ bound for the following recurrence equation:
$$
T(n)=\sum_{i=1}^kT(a_i)+n+\lg k\sum_{i=1}^ka_i\quad
where\quad n=1+\sum_{i=0}^ka_i\quad and\quad
a_0\ge a_1, a_2, \dots,a_k\ge 1
$$
By master theorem, with $k=a_0=a_1=n/3$ and $a_2=a_3=\dots =a_k=1$, $T(n)=Θ(n\lg n)$. Now my freind a... |
In the book "Computational complexity" of Barak and Arora, on page 112, they state that:
Theorem 6.15: A language has logspace-uniform circuits of polynomial size iff it is in P.
The proof of this one is left as an exercise to the reader. I think both directions are trivial:
=> seems trivial, as a logspace TM that g... |
Consider the "Generalized Geography" game: on directed graph G with selected start node, players take turns moving along edges, without ever going back to previously visited nodes. Last player to move wins.
GG = { : G is a directed graph, b is a node in G, and the next
player to play has a winni... |
Given a language $L\subseteq \Sigma^*$ in $P$, is the language
$subwords(L) = \{v\in\Sigma^* : \text{there exist } u,w\in \Sigma^* \text{ with } uvw\in L\}$
that consists of all subwords of words in $L$ also guaranteed to lie in $P$?
|
The question is simple:
$\qquad \operatorname{DropMiddle}(L)=\{xy\in\Sigma^* \mid |x|=|y| \land \exists a\in\Sigma\colon xay\in L\}$.
Prove that CFL's aren't closed under $\operatorname{DropMiddle}$.
I should probably be looking for a counter example, but I'm coming up short. I know that the language $ww$ ($w$ is a w... |
Define the complexity class $C$ to be the class of all languages that can be verified by a TM that has:
Input tape: Read only, move in both directions.
Witness tape: Read only, move only in one direction.
Work tape: Read-Write, move in both directions.
The machine itself is deterministic (the guesses are the value of... |
I first learned about the Big O notation in an intro to Algorithms class. He showed us that function $g \in O(f(n))$
Afterwords in Discrete Math another Professor, without knowing of the first, told us that we should never do that and that it should be done as $g \in O(f)$ where g and f are functions.
The question is... |
what would the Turing machine state diagram be for this language:
$A=\{ (0 \cup 1)^a(1 \cup 2)^b(2\cup 3)^c \mid a \geq b\} $ ?
how would the turing machine design know the size of $(1 \cup 2)^b$ ? since this contains elements from the first and last parts, would it be impossible to determine?
|
In unification, given a set of equations, a standard problem is to compute a most general unifier (mgu). I am interested in a somewhat reversed problem. Imagine having a set of equations that do not have an mgu, like this one:
x = a
x = b
x here is a variable, whereas a and b are terms. I am interested are there any a... |
I'm a having trouble analyzing this algorithm.
This is a binary counter that supports only increments in $2^i$ values
it's implemented in this way:
starting from the $i$-th location change all the straight $1$'s to $0$'s and the first $0$ to $1$.
So I analyzed the W.C to be $O(\log n)$ because the worst case is we need... |
I have read that linear bounded automaton is a Non deterministic Turing machine. Why is it so?
|
I have read in Wikipedia and some other texts that
The halting problem is [...] decidable for linear bounded
automata (LBAs) [and] deterministic machines with finite memory.
But earlier it is written that the halting problem is an undecidable problem and thus TM can't solve it! Since LBA are defined as a type of TM... |
I would like to show that the following language is recognizable:
$$L:= \{ \langle M \rangle \mid M \text{ is a TM that halts on some string}\}.$$
How do I go about showing that this language is recognizable? I know that all recognizable languages are reducible to $HALT_\epsilon$, so I figure if I can show that this la... |
I'm interested in coding up a small project that solves uni-variate algebraic equations (up to cubic) by simulating the actions of a human expert in solving the equation. To do this, I've drafted a set of production rules (if/then rules applied to an equation when certain conditions hold). However, I'd like to compare ... |
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:
[], means, that the atom inside of it can be omitted
(), one of the atom... |
Currently I'm trying to classify spam emails with kNN classification. Dataset is represented in the bag-of-words notation and it contains approx. 10000 observations with approx. 900 features. Matlab is the tool I use to process the data.
Within the last days I played with several machine learning approaches: SVM, Bayes... |
Suppose $\{a_n\}$ is a sequence with moment generating function $A(z)=\sum_{k \ge 0} a_kz^k$.
Can a sequence $\{b_n\}$ with $b_n \neq a_n$ for at least one $n\in \mathbb N$ have the same moment generating function as $\{a_n\}$, that is $B(z)=A(z) \ \forall z$.
This is equivalent to: Is the moment generating function fo... |
If someone (off-topic) asks a question (on-topic) like this:
Suppose that he claims that $\mathcal{P=NP}$. Suppose that someone else (on-topic) gives him an instance of an NP-complete problem that cannot be solved by any computer optimally, i.e., to get the optimal solution, one must run an algorithm for very long time... |
I was trying to understand the concept of Max-Heap. And to my understanding its a complete binary tree and each parent has a value greater than its children.The example I was going though had the following array which it said was a Max-Heap.
BookArray [] = {45,10,11,3,2,7,9,1,0}
I then decided to shuffle the elements ... |
Consider the "Generalized Geography" game: on directed graph G with selected start node, players take turns moving along edges, without ever going back to previously visited nodes. Last player to move wins.
GG = { : G is a directed graph, b is a node in G, and the next player to play has a winning strategy for general... |
I was wondering if anyone had any good references or book recommendations that cover abstract syntax trees (ASTs). Specifically, I am interested in the abstract syntax trees of different evaluation strategies (call by value vs. call by name) of the pure lambda calculus. I would like to be able to draw the AST of some p... |
Wikipedia's formal definition of NP based on deterministic verifiers states:
A language L is in NP if and only if there exist polynomials p and q,
and a deterministic Turing machine M, such that
For all x and y, the machine M runs in time p(|x|) on input (x,y)
For all x in L, there exists a string y of length q(|x... |
I have a grid environment which contains in each cell a static agent. When my agent enters a cell, the static agent in this cell might take points away from me, give me points, or do nothing. My agent can not observe adjacent cells until it moves into one them, it can only move up, down, left or right.
This agent can n... |
In the pure lambda calculus, we have the inductively defined set of terms (the grammar):
$$e::= x \mid \lambda x . e \mid e_1 e_2$$
Under the call-by-value evaluation strategy, we have the inference rules for beta-reduction and rules on how to evaluate applications (congruence rules). I am trying to understand how eval... |
In a Dispatcher-Worker model of parallel computation, we have $N$ worker machines simultaneously working on the task (for example, computing the checksum of network packets). There is no synchronization between these workers. A dispatcher distributes total amount of work $S$ to these workers.
Now consider the problem ... |
I've read that, incorporating many words(spatial locality) per cache blocks leads to lower miss rate. Is it the case always?
One possibility of such approach is to make a single cache block of size equal to the size of the cache, but that would be meaningless as far as benefits of memory hierarchy are concerned. Isn't... |
In the Wikipedia article on Simply Typed Lambda Calculus (among other places), there is a notion of a "term constant". This is particularly notable in the production grammar given:
In this production grammar, the c is the term constant. I am new to the simply typed variant of lambda calculus -- I do not understand w... |
In a normal CAPTCHA scenario, a computer creates a challenge and a correct response to it. (The challenge is an image of distorted text, for instance, and the response is the characters depicted.) These are constructed so that hopefully a human can easily determine the response from the challenge, but a computer cann... |
For school we have to make an assignment, and part of the assignment is this question:
Describe an unidrected graph that has 12 edges and at least 6
vertices. 6 of the vertices have to have degree exactly 3, all other
vertices have to have degree less than 2. Use as few vertices as
possible.
The best solution I... |
I want to code a solver for nonsingular systems of $N$ linear equations in $N$ unknowns (say up to $N=100$) with an asymmetric Toeplitz matrix. I know that the Levinson algorithm can solve it in time $O(N^2)$ and I am looking for a solution with this complexity. I have seen mentions of alternative approaches such as Sc... |
I want to learn maths for artificial intelligence. I heard that main areas of mathematics for AI are Multivariable Calculus, Linear Algebra, Probability and Statistics and Discrete Mathematics. But what level of these subjects do I need? For example the easy level is like Calculus of Gilbert Strang and 18.01 Calculus f... |
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