instruction stringlengths 35 29.1k |
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What is the best way to name documents and folders in windows? Im thinging about maybe there will be some conflict in some programs? Or when searching in terminal
This_Is_Best.doc
ThisIsBest.doc
This Is Best.doc
|
(This question is related to homework)
I am doing a cryptography course via long distance and we have been given an assignment which is based on lattice-based cryptography. I have spent the majority of the past week sifting through papers and videos in an attempt to build my understanding of the subject, but due to the... |
I know that a DFA has to have exactly one transition for each symbol in the alphabet, but is it allowed to have two symbols on the same arrow? If, for example, I have a DFA with states $q_0$ and $q_1$, can I have one arrow from $q_0$ to $q_1$ with both $a$ and $b$?
This may be a stupid question, but I need to be compl... |
In order to plot a curve a set of points is usually calculated based on some formula. The function FPLOT in MATLAB also supports plotting with some error tolerance. Its help says the following about this functionality:
The FPLOT function begins with a minimum step of size (XMAX-XMIN)*TOL.
The step size is subsequently ... |
When we declare a variable there will be a random part of memory will be allocated in RAM. Which component will allocate the memory? Is the processor or any other specific hardware doing the allocation?
|
What is the most efficient way to find all paths of length M to N in a large sparse graph?
Some general information:
Graph has 30,000 to 50,000 nodes
Average number of edges per node ~ 10
M=4, N=7
Graph has cycles
|
Let $L_r$ be a regular language with alphabet $\Sigma$ and $L_{\text{csl}}$ be a context sensitive language. Are any of the following questions decidable?
$L_r \cap L_\text{csl} \stackrel{?}{=} L_r$
$\Sigma^* \cap L_\text{csl} \stackrel{?}{=} L_r$
$L_r \cap L_\text{csl} \stackrel{?}{=} \Sigma^*$
$\Sigma^* \cap L_\text... |
This is a popular question:
What is the most efficient (in time complexity) way to sort 1 million 32-bit integers?
Most answers seem to agree that one of the best ways would be to use radix sort since the number of bits in those numbers is assumed to be constant. This is also a very common thought exercise when CS ... |
As per Tries slides (page 17) from Algorithm 4th edition book by Robert Sedgewick, the asymptotic expected runtime for an unsuccessful search in $R$-way tries miss is $O(\log_R N)$. Can someone please explain how this number can be derived?
|
Given a context-free grammar, is there an algorithm to determine if the CFG will ever produce an even length string? Or is this undecidable?
|
Knowing the frequencies of each symbol, is it possible to determine the maximum height of the tree without applying the Huffman algorithm? Is there a formula that gives this tree height?
|
I've been working and experimenting with an algorithm that may take time $O^*(2^\sqrt{n})$. Here $O^*(f(n))$ simply neglects all polynomial terms. I've seen a comment on Scott Aaronson's blog that mentions graph isomorphism algorithms run in this time, too. Actually, $O(2^\sqrt{n})$. Is there a designation for this... |
I have to show a property P is trivial.
This problem has to do with Rice's Theorem, which I do not completely understand. Can someone explain the difference between trivial and non-trivial properties?
|
I am reducing a given Turing Machine to the complement of the known undecidable problem,
$$ Complement(A_{TM}) = \{ \langle M,w \rangle \mid M \text{ is TM}, w \not\in L(M) \}$$
To this Turing Machine, known as SPARSE TM:
$$
SPARSE_{TM} = \{ \langle M \rangle \mid M \text{ is 1-tape TM}, |L(M)| \leq 1000\}
$$
Here i... |
I need to link facts to actions through rules. If a person bought soup 10 times and he is coming at midday every day, then the system should link the fact that the person bought soup so many times, using the rule "person, consecutively buying soup 5 or more times within a month is going to buy soup with 90% confidence"... |
I have a statement I am trying to prove, and I'm very close, but I think I'm missing a couple of key concepts about regular and context-free languages.
Question: Let
$
A = \{ ww \ | \ w \ \epsilon \ \Sigma^{*} \}
$.
Show that any language $L$ is Turing-decidable if and only if $L$ is many-one reducible to $A$.
Where I ... |
I am learning Probabilistic Graphical Models with the help of the videos on Coursera. I am in week 4 and I see cliques being mentioned often. But the graphs being discussed are cluster graphs. So are the cliques and clusters the same?
|
I'll preface this by saying that this IS a homework question.
However, when asked about how to solve it in class, (I believe) my professor was unable to complete it.
The question is:
Compute the weakest precondition for each of the following
assignment statements and postconditions:
$$a = a + 2b - 1\ \{a > 1\}$$... |
My knowledge is very vague as all we have are visual diagrams etc, but we have memory address and registers, the ALU being the heart(apparently). Single core CPUs process one instruction at a time AFAIK and multi-core have parallelism to some degree. So where do the millions of transistors come in and how do 32 registe... |
My method of conversion is by creating a reachable set tree and each set within the tree would represent the new states.
I have never dealt with FSAs that has 2 or more initial states. How do i create my reachable set tree with two or more states?
|
I have a set of piecewise-linear curves (i.e. "points connected by line segments") as shown in the figure below:
additional points are added on the borders (drawn in red) "closing" the open regions of the figure. In fact, the figure can be any plot with some closed piecewise-linear shapes on it (i.e. there are no line... |
Given a set of colors $M$ and a graph $G=(V,E)$. Allocate the colors to minimize the number edges with same color on the two vertices of the edge (i.e. minimize pairs of adjoining vertices with same color.).
This problem is different from standard coloring problem. Could someone please provide some literature where thi... |
The following is Figure 1 in Gene M. Amdahl's "Validity of the single processor approach to achieving large scale computing capabilities" (1967) (PDF):
The text describes this as representing the performance (presumably vertical) as a function of the fraction of instructions that can be executed in parallel for three ... |
Consider this example: a problem of dimension $n$ and $m$ ($m,n$: any given integers).
has a search space of size $O(n^n * m^n)$.
It is clear that this problem is exponential in $n$,
whatsoever $m$ may be.
My question: is this same problem polynomial in $m$?
what are the assumptions if we can say that?
is this way of... |
Consider this nested loop:
for (i=0 to n)
for(j=0 to n)
for (k=0 to n)
sum := sum +k
end for
end for
end for
Do i,j and k have temporal or spatial locality?
I've considered j and k as temporal since they are revisited again in the loop. But I'm confused about i as it does not match the defin... |
We have $M$ bits. $M\le10^5$ Also we have N ranges in the form $[L,R]$. $N\le10^5$ We can choose any range from the given ranges and flip all bits in our number from $L$ to $R$, both inclusive. We can apply each operation any number of times and in any order. We have to calculate the number of $M$ bit numbers that can ... |
The problem statement is as follows:-
In a court case, a judge cited a court of contempt and ordered a fine of $2 for first day.
On subsequent days, the fine would be equal to the square of the previous day's fine.
e.g. 2, 4, 16, 256 and so on.
Find out:-
a) What would be the fine on day $n$?
b) How many days wo... |
Based on the Wikipedia implementation of insertion sort:
Given an input array $A$:
for i ← 1 to length(A)
j ← i
while j > 0 and A[j-1] > A[j]
swap A[j] and A[j-1]
j ← j - 1
is there a way to quantify how many swaps are needed to sort the input list? It's $O(n^2)$, but I want a more precise boun... |
I'm working on homework for my formal languages and automata course. The text we are using is the first edition of Hopcroft and Ullman (1979).
Specifically, I'm unsure how to justify that my regular expression for exercise 2.10 (c) is correct. The question asks for a regular expression for the set of all strings not c... |
A deterministic queue automaton (DQA) is like a PDA except the stack is replaced by a queue. A queue is a tape allowing symbols to be written (push) on the left-end and read (pull) on the right-end.
Actually I've proved that a 2-tape Turing Machine can simulate the DQA. Now I'm proving the DQA can simulate Turing Mach... |
From the proof of Miller-Rabin, if a number passes the Fermat primality test, it must also pass the Miller-Rabin test with the same base $a$ (a variable in the proof). And the computation complexity is the same.
The following is from the Fermat primality test:
While Carmichael numbers are substantially rarer than prim... |
I am reading Decompositions of Triangle-Dense Graphs by Gupta et al.
On page 2, in Definition 1 what is a wedge in a graph?
I know what triangle is but I don't know what wedge is and google isn't helping!
|
It is nice to know that every boolean formula can be expressed by zero-one
integer programming by this answered question. But are there any applications?
To be more precise: Are there papers which use the existense of zero-one
integer programming for boolean operations?
|
It says to solve the recurrence exactly for n a power of 2.
T(n) = {1}, if n = 1
T(n) = {5T(n/2) + (n lg n)^2, otherwise
I'm supposed to use Θ notation to express my answer.
Normally I would try to look for the characteristic equation but for this one I'm lost.
Is this the first step?
T(n) - 5T(n/2) = (n lg n )^2
... |
$$t(n)=\begin{cases}n&\text{if }n=0,1,2,\text{ or }3\\t(n-1)+t(n-3)-t(n-4)&\text{otherwise.}\end{cases} $$
Express your answer as simply using the theta notation.
I don't know where to go with this.
$$t(n) - t(n-1) - t(n-3) + t(n-4) = 0$$
Is the characteristic polynomial $x^3 - x^2 - x +1 = 0$?
|
I can't understand or imagine some fact about NP-hard problems. If I understand it correctly there is only one polynomial-time algorithm needed – for whichever NP-complete problem – to prove that P = NP.
Let's take the subset sum problem, which is NP-complete. It says that given a set such as $\{-7, -3, -2, 5, 8\}$, we... |
While reading some papers in AI (for a project I have to do), I see expressions "blocks world domain" and "logistics domain". I know what blocks world domain is, but I don't know the definition of logistics domain.
Any help would be appreciated.
|
Deep Learning, now one of the most popular fields in Artificial Neural Network, has shown great promise in terms of its accuracies on data sets. How does it compare to Spiking Neural Network. Recently Qualcomm unveils its zeroth processor on SNN, so I was thinking if there are any difference if deep learning is used in... |
We are given an array and numerous subarrays. What we can do is add or multiply some element to all elements of a subarray. The subarrays are given as start index and the end index. We have to find the largest number of independent subarrays from the subarrays given to us. For example:
If we have the array as given bel... |
Qualcomm is creating a Neuromorphic Processing Unit or an NPU called zeroth.
IBM is also working on a brain inspired chip under Synapse program.
Standford's Neurogrid might be a similar example.
Neuromorphic systems are inherently based on mixed signal and analog chips. Considering a wide application of neuromorphic co... |
We know algorithm to convert each PDA in the underlying grammar that generates the language the PDA recognize.
But we have also the algorithm for creating a two state pda from a grammar.
This algorithm use the first state for all the computation, with rules based on the stack and the input symbol, and when the stack i... |
More specifically, how can project administrators be sure that the answers they receive from nodes are correct and not just simple calculations performed quickly and submitted as complete work units? As various cheating scandals have shown, people are not above stooping to low levels to get to the top of project points... |
What is an upper bound on formula size when converting 3-SAT to UNIQUE 3-SAT?
We can use the Valiant Vazirani Therom, also found here (in more detail).
Essentially, it is a randomized algorithm that converts a SAT formula into another SAT formula that has only 1 satisfying variable assignment (called UNIQUE-SAT) with h... |
My language is the repetition of 0 to a length that's a power of 2:
$L = \{ 0^k \mid k=2^n, n \geq 1 \}$
I want to know how to use the Myhill-Nerode theorem to show that this language is not regular.
This is my first attempt at doing this although I am confident that I am wrong:
$j, p = 2^h$ for 2 distinct values of $h... |
As an applied person, I'm facing one practical problem deciding whether a set of Wang tile could tile the plane periodically or aperiodically. Although both problems seem undecidable, but I'm on a more practical aspect. Say, if the program accidentally ("or systematically") find some "periodic structure", then it stops... |
I have an equation $y=2x^4-20x^2-50x$ within a range of -4 to 6
I already have an algorithim that tell me the y value when I plug in the $x$. It simply uses a loop.
What I am trying to do is determine what will be be the y max value and what $x$ corresponds to it.
Is there some sort of loop or counter I can use. I am ... |
Assume $\{f_i^{(n)}\}_{i=0}^\infty$ is a Gödel enumeration of the $\mu$-recursive functions of $n$ arguments, such that the $S^m_n$ theorem and the universal function theorem hold. Denote the set of (total and partial) functions $\{f:\mathbb N^k\to\mathbb N\
\}$ by $\mathfrak F^k$
Definition: We call an operator $G:\ma... |
The problem:
Input: An $n \times n$ matrix of 0's and 1's, and a position pos of this matrix (i.e. a pair of integers $i,j$ with $1 \leq i,j \leq n$)
Output:
YES if there exists a path through adjacent matrix entries $\dagger$, starting at pos, covering each matrix entry with a 1 exactly once, and not covering the mat... |
I have a question about predicate logic. Suppose we have the following predicates:
$\text{Study}(x,y)$: x studies y
$\text{Comp}(x)$: x is a computing student
I want to encode the following sentence in predicate logic: "Some, but not all computer students study logic."
A potential answer is:
$$\exists x(\text{Comp}(x)\... |
While going through certain problems. it seems that more than one NFA is possible for the given language. Is it so?
For example for drawing: NFA ending with 1 where $\Sigma=\{0,1\}$ is
and also we can draw one without 0 from the edge P to P!
Which one should be considered "more" correct?
|
I saw this old post on stack overflow of a PDA that accepts a language where there are exactly twice as many a's as there are b's. The image they used is below and so is the link to the post itself.
PDA for language that accepts twice as many a's as b's.
It was commented that the PDA was not deterministic. So I'm wond... |
I am learning Compiler Design. Can somebody explain what type of Grammar this is? The answer given is $LL(1)$ but there exists a left recursion in the grammar so it cannot be $LL(1)$. I derived the parse table it had conflicts. Am I doing some thing wrong or is the answer given wrong?
My texbook defines:
For LL(1) Gr... |
The shannon entropy of a random variable $Y$ (with possible outcomes $\Sigma=\{\sigma_{1},...,\sigma_{k}\}$) is given by
$H(Y)=-\sum\limits_{i=1}^{k}P(Y=\sigma_{i})\;\log(P(Y=\sigma_{i}))$.
For a second random variable $X=X_{1}X_{2}...X_{n}$, where all $X_{i}$'s are independent and equally distributed (each $X_{i}$ i... |
I am currently learning about the Q-learning algorithm, so I therefore assume that it has some use or purpose. However I currently cannot see how it is in any way useful. In terms of complexity class, it appears to perform equal to or worse than brute force, which as far as I am aware, is the lowest you ever need to go... |
Is
$$
f(n) \in \Theta(g(n)) \Leftrightarrow f(n) = g(n) \cdot (1+o(1))
$$
true?
For clarity, here are the definitions I use:
$$
f(n) \in o(g(n)) \Leftrightarrow \forall \epsilon > 0 \exists n_o\forall n> n_0: |f(n)|\leq \epsilon \cdot |g(n)|
$$
$$
f(n) \in O(g(n)) \Leftrightarrow \exists c > 0 \exists n_o\forall n> n_... |
I have a question regarding regular languages. Given that $L_1$ and $L_2$ are non-regular languages, can a regular language $L$ exist so it is a subset of $L_2$ and $L_1$ subset of $L$?
To be more specific:
$\qquad L_1 \subset L \subset L_2$
for $L_1, L_2$ non-regular Languages.
|
Is there a way to show that for all finite sets $S$ of context free grammars, there exists a Turing Machine $M$ such that for all grammars $G_1, G_2 \in S$, we have that $M(G1,G2)$ terminates and answer yes if and only if $L(G_1)=L(G_2)$? Is that even true?
I know that this problem is in general undecidable, but I also... |
Is there a way to figure out what the following CFG accepts?
$\qquad\begin{align}
S &\to S \vee T \mid T \\
T &\to T \wedge F \mid F \\
F &\to p \mid\; \thicksim p
\end{align}$
I'm confused by the boolean algebra symbols. I know the first is S or T, the second is T and F and the third is not p but I'm not sure h... |
I am having hard time solving the following problem.
Are there any languages for which
$$
\overline{L^*} = (\overline{L})^*
$$
Assuming $\emptyset^* = \emptyset$, if I consider $\Sigma = \{a\}$ and L = $\Sigma^*$, I get that $L^* = L$ and that $\overline{L^*} = \emptyset$. For the right side I get $\overline{L} = \... |
I would like to find a algorithm that will do the following:
Given two sets $A, B \subseteq \mathbb{R}$, where $|B| > |A|$, find the largest subset $C \subseteq B$, such that:
$\qquad |\operatorname{mean}(A) - \operatorname{mean}(C) |< \delta$ and
$\qquad |\operatorname{std}(A) - \operatorname{std}(C) | < \epsilon$
I... |
I am an undergraduate computer science student at Cal Poly (SLO) and I have some flexibility in which math courses I can take, but I don't know which math courses would be most beneficial. I have already taken a statistics/probability course and Calculus 3. My options are pretty flexible for a Mathematics/Statistics el... |
I thought this would be the best place for a question like this. Anyway, I was wondering what minor would go well with a Computer Science degree. I was considering a minor in math but I am not entirely sure if that could help out or not. I am currently a second semester freshman and I suppose that this is the best/late... |
I am somewhat confused with the running time analysis of a program here which has recursive calls which depend on a RNG. (Randomly Generated Number)
Let's begin with the pseudo-code, and then I will go into what I have thought about so far related to this one.
Func1(A, i, j)
/* A is an array of at least j inte... |
I'm reading the Dragon Book. The following is from the start of Section 3.1.3.
When more than one lexeme can match a pattern, the lexical analyzer must provide the subsequent compiler phases additional information about the particular lexeme that matched. For example, the pattern for token number matches both 0 and 1,... |
While reading the research paper Polylogarithmic Concurrent Data Structures from Monotone Circuits [@JACM'2012] by James Aspnes, Hagit Attiya, and Keren Censor-Hillel, I am not sure about some points and need some verification and explanation.
In the first three sections of the paper, the authors presents constructio... |
Let $C\subseteq 2^X$ be a concept class over $X$ and let $\bar{C}:=\{X\setminus c\mid c\in C\}$ be the complement. Show that $VCdim(C)=VCdim(\bar{C})$.
Proof:
Let $d:=VC_{dim}(C)$, then there exists $S\subseteq X$, $|S|=d$, s.t. $S$ is shattered by $C$.
Let $d':=VC_{dim}(\bar{C})$, then there exists $S'\subseteq X$, $|... |
This is a follow-up question regarding Knuth's one formulation of the concept of an algorithm here. I am asking it here because I do not have enough reputation to post a comment to that question. To make my question self-contained, here it goes.
Knuth introduces the following formulation which "restrict the notion of a... |
I know that this is a known theorem but I can't find its proof. The theorem is:
The write-contention of any $n$-process wait-free consensus algorithm (implemented from any read-modify-write operations) is $n$.
Can someone link me to a proof or an explanation?
|
I'm trying to figure out which is better asymptotic complexity, $O(\log{\frac{n}{p}})$ or $O\left(\frac{\log{n}}{\log{p}}\right)$. $p$ is the amount of parallelism (i.e. number of cores), and $n$ is the problem size. When I plot them in Grapher.app with any constant value for $p$, the first looks better:
But when I tr... |
This is a follow-up question to this. Consider the 2-paths problem:
Given a directed graph $D=(V,A)$ and pairs of vertices $(s_1,t_1)$ and $(s_2,t_2)$, are there paths $P_1 = (s_1,\dots, t_1)$ and $P_2=(s_2,\dots,t_2)$ such that $P_1$ and $P_2$ are vertex-disjoint?
This problem has been shown to be NP-complete (refer... |
If $f(x) = \Omega(n)$ and $g(x)= O(n)$, what would be the order of growth of $f(x) \cdot g(x)$ ?
First I figured it should $\Theta(n)$ , as two extremes would cancel each other and the order of growth will be same as $n$
But, where I came across this question, the answer given was $\Omega(n)$, and no proof was mention... |
I have two algorithms which I would like to implement:
First, given a (very long) list $\{\mathbf{r}_{i}\}_{i=1}^{n}\subset \mathbb{R}^{3}$, a point $p \in \mathbb{R}^{3}$, and a distance $d>0$, find all $i$ such that $|\mathbf{r}_{i} - \mathbf{p}| < d$.
Currently, I sort the list over the $x$-coordinate, so that if $x... |
I'm a CS undergrad so my math/CS knowledge is not that deep so please correct me if my premise is flawed or I have made some incorrect assumptions.
So I was thinking, much in the way that some primality testers are probabilistic(they give you yes or no but have a chance to be wrong). Would it be possible to build a pro... |
I'm curious if there is a name for this way of ordering finite sets of natural numbers (shown here for the case 3 elements, but can be extended to any number of them):
{0, 1, 2} < {0, 1, 3}
< {0, 2, 3}
< {1, 2, 3}
< {0, 1, 4}
< {0, 2, 4}
< {1, 2, 4}
< {0, 3, 4... |
I believe the following question in summary is: How to approximate Euclidean distance in a digital plane?
When a pebble falls on a calm surface of water a circular wave propagates. I want to color the pixels with time to show this effect. So I discretize the time and in each time step, starting from the center, I col... |
I am trying to construct NFA for all languages ending in 00.
I got this
and this
First one I could convert to DFA by subset construction and I got the correct DFA. For the second one I got the DFA by subset construction, but it is not the correct one since it couldn't accept strings like 100.
Is this beacuse, there ... |
We know VC dimension of 1-NN classifier is infinite for continuous metric space. Is there any proof of VC dimension of 1-NN classifier if the metric space is discrete?
|
$1+3+5+...+(2n+3)=n^2+4n$
For this series using induction proof.
Base case 1,2,3,.. not working. But induction step works well.
Base case is not given in question.
|
I read a book which says that in Predicate Calculus, syntactic theorem proving is identical (complete and sound) with semantic entailment and this is very useful because it is easier to prove positive witnesses in natural deduction whereas when you seem to fail you better switch to semantic account to demonstrate a cou... |
In case of branch Instructions such as beq, bne, we use PC-relative addressing. But I am not clear why it is said in most of the books that MIPS address(while calculating branch target) is actually relative to the address of following(or sequentially next) instruction (PC+4) as opposed to the current instruction (PC)?
... |
I've been reading text books about distributed algorithms. They usually present a large collection of algorithms under various hypothesis and guarantees, with their proof of correctness. But they often fail to mention the practical application of those algorithms, and their relative usefulness and importance. For insta... |
given a turing machine M over the input alphabet $\Sigma $ , any state q of M and a word w $\epsilon\Sigma $* , does the computation of M on w visit the state q ?
Is this problem decidable ?
|
If any problem P is NP complete then if there is a polynomial time reduction of P to another problem R then what can we say about R.Is it NP-hard or NP complete ?
From Theory of computation of Hopcroft,Ullman theorem 10.4 it says it would be NP complete but there some times when i see that it is NP-Hard in some other r... |
I am currently writing lists with lazy semantics in the pure
lambda-calculus with call-by-value reduction strategy.
I tried to construct pleasant to use and relatively efficient "lazy" functions on lists. As in the Church encoding I identify list with its right fold function, but with some differences. Here is nil and... |
This question is prompted by Undecidable unary languages (also known as Tally languages)
How does the countability of a language imply (un)decidability?
|
I read several times that it is not possible to flip the answer of a NDTM efficiently. However, I don’t understand why. For instance, given a NDTM $M$ that runs in $O(n)$, this text (section 3.3) states that it is unclear how another NDTM $T$ can determine in $O(n^{100})$ time how to flip $M$’s answer.
My Problem is as... |
Let $G=(V,E)$ a directed graph. We define $v \in V$ to be "nearly root" of there's a path from $v$ to at least $|V|/2$ vertices. How do you find the set of all "nearly roots" in linear time?
What we've tried is to build the strongly connected graph $G_{scc}$ obtained from $G$ and then to do a topological sort. Now we w... |
It seems to me to be incorrect to say that lexicographic DFS is P-complete, since it isn't a decision problem. There is a corresponding decision problem, first DFS ordering, which is known to be P-complete. However, I want to talk about complexity of DFS, not it's decision problem. What complexity class should I say DF... |
I'm currently trying to find an efficient algorithm to solve a discrete optimization problem that arises when constructing decision trees. The problem is as follows:
Say we are given $N$ ordered data points on the real line: $x_1,\ldots,x_N \in \mathbb{R}$ such that $x_1 < x_2 < \ldots < x_N$.
Each of the points $x_i$... |
First of all, I would like to apologize if this question is in the wrong section. For all I know, it could be placed in Super User, Reverse Engineering, or Stack Overflow.
Now lets get back the experiment I tried:
What I did was took an executable file and changed its file type to a text document type. Then I opened th... |
I have the following context-free language:
S -> ASa | b
A -> aA | a
I don't understand why this is not regular. I first said that it's generated by the regular expression a+ba+. The following is regular however
S -> ASa | b
A -> aA | e
e stands for the empty string. I don't understand their differences.
|
My textbook says: "We define the function $f\colon \mathbb{N}\to\mathbb{N}$ as follows: $f(1)=2$ and $f(i+1)=2^{f(i)^{1.2}}$. Note that given $n$, we can easily find in $O(n^{1.5})$ time the number $i$ such that $n$ is sandwiched between $f(i)$ and $f(i+1)$."
How can I convince myself that we can in fact easily find $i... |
a spin lock solution to the critical path problem is shown below . my question is will this or will this not result in starvation ?
Thread A Thread B
leave note A; leave note B;
while (note B) {\\X if (noNote A) {\\Y
do nothing; if (noMilk) {
} ... |
In most (all I have seen) work on cellular automata, the state of a cell is from a finite set. Such as a cell can take value from a binary set, or from among few colors. Can we define the state to be something more complicated such as a function of the coordinates of the neighbor cells? (assuming there is a initial coo... |
the standard List type in Coq can be expressed as:
Inductive List (A:Set) : Set :=
nil : List A
| cons : A -> List A -> List A.
as I understand, W-type express a well-founded tree of elements of this type. so, what if nil is not qualified by A? i.e. we have:
for all A: Set nil : List A
instead of
for all A: Set ... |
I am asked to find two functions that are not big-oh of each other.
Is it correct if I pick say $f(n)=2\sin (n)$ and $g(n)=1$? That way, $f$ will never always be greater than $g$.
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What is the correct way?
Hamilton path, Hamilton's path or Hamiltonian path?
To be clear, I am referring to the correct way to name a graph such that there exists a single path (without repeated vertices) through all the vertices.
In Wikipedia it says "Hamiltonian path", whereas in an article I found "Hamilton path".
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I have Java function as input and want to get it's order for example O( n )
I search in the internet very hard but didn't find any thing can help me, is there any algorithms or package may help me.
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A popcount order of a two bit vector {1,1}=3 can be given by:
{{1, 1}, {1, 0, 1}, {1, 1, 0}, {1, 0, 0, 1}, {1, 0, 1, 0}, {1, 1, 0, 0}, {1,
0, 0, 0, 1}, {1, 0, 0, 1, 0}, {1, 0, 1, 0, 0}}
and as a sequence of integers:
{1, 2, 4, 8, 16, 32, 64, 128, 256}
We are basically just shifting bits...
A Mathematica code for it ... |
As we all know the million dollar question in Computer Science P=NP or not. I was trying to understand it and got some doubts please tell me whether I'm right or wrong
N=NP in two cases
Case 1: We have found an algorithm which can solve a NP-Complete problem in P-Time. This implies that P=NP=NP-Complete. But still we... |
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