instruction stringlengths 35 29.1k |
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Is it true that Sequential Consistency is a stronger property than Cache Coherence?
According to
Sorin, Daniel J; Hill, Mark D; Wood, David A: A Primer on Memory Consistency and Cache Coherence, Morgan & Claypool, 2011
sequential consistency can be described as (not formally):
Sequential consistency memory model sp... |
What is the intuitive idea behind automatic differentiation?
If I have a program which computes $f(x, y)=x^2+yx$, which steps lead to the program which computes the derivative $df/dx$ of f?
double f(double x, double y)
{
double res = x*x;
double res2 = x*y;
double res3 = res + res2
return res3;
}
If I... |
Consider two lambda expressions $\mu$, $\nu$ representing computable functions $f_{\mu,\nu}:\mathbb{N} \rightarrow \mathbb{N}$. If $\mu$ and $\nu$ are equivalent under the combination of $\beta$-reductions, $\alpha$-conversions and $\eta$-conversions then $f_\mu=f_\nu$.
Under what conditions does the converse hold? I... |
I have tried hard , but i'm unable to come up with the expected running time for the number of comparisons to find the Randomized Median (find the median of an unsorted array).
Also i wanted to make sure that we CANNOT take expectation of the recurrence that we use to find the randomized mean , or any other recurrence... |
I don't know an O(n) solution to the following:
Given an array of n integers, find the largest difference between any two pairs in the array: however, the larger integer must have a higher index in the array than the other.
Ex: alg({9, 2, 6, 7}) = 5
It seems straightforward, yet it eludes me.
|
What are differences in services provided by grid computing and cloud computing?
From http://ccskguide.org/cloud-computing-vs-grid-computing/ and http://www.ibm.com/developerworks/web/library/wa-cloudgrid/
While grid computing facilitates access to computing resources as if they were public utilities, cloud computing ... |
I come from an electronics background. I know that there are three types of implementations of multithreading (see Computer Architecture: A Quantitative Approach, 5th Edition):
Fine-grain multithreading issues instructions for different threads after every cycle.
Coarse-grain multithreading only switches to issue inst... |
I have some experiences of working on clusters and grids for parallel computing. But I wonder what distributed computing can do besides parallel computing?
If I understand correctly, parallel computing is to solve a common task by multiple processors (computers).
Are the Internet and a intranet considered distributed s... |
I read a paper which talks about "a logic formula in which each variable appears at most twice unnegated and once negated". The term "unnegated" is double-negative, which makes it slightly unclear. Is there a more positive term to denote a variable that is not negated?
I looked in an English thesaurus, but all suggesti... |
I am reading parser chapter from dragon book and I found a grammar over there -
$ S \rightarrow L=R $
$ S \rightarrow R $
$L \rightarrow *R $
$L \rightarrow id $
$R \rightarrow L $
Now I have created some of its items, not sure if they are correct -
$ I_{0} $
$S' \rightarrow .S ; \$ $
$S \rightarrow .L=R ; \$ $
$S \... |
Let $A$ be some alphabet.
$A$ itself is a regular language.
$E = A^*$ is regular language over $A$. $E$ is a superset of all languages over $A$, regular or otherwise, i.e $E$ contains every possible string from symbols of $A$.
Now let $L$ be some regular language over $A$.
What is $\tilde{L} = L \cdot E$ ? More specifi... |
I am looking for implementation of the set data type. That is, we have to
maintain a dynamic subset $S$ (of size $n$) from the universe $U = \{0, 1, 2, 3, \dots , u – 1\}$ of size $u$ with
operations insert(x) (add an element x to $S$) and find(x) (checks whether element x is a member of $S$).
I don't care about othe... |
We have had several questions about the relation of Cook and Karp reductions. It's clear that Cook reductions (polynomial-time Turing reductions) do not define the same notion of NP-completeness as Karp reductions (polynomial-time many-one reductions), which are usually used. In particular, Cook reductions can not sepa... |
The algorithm task is to find an integer (range is not known). the function guess(num) returns one of three chars: '>','<' or '='.
Find the secret number with O(logS) guesses, where S is the secret number. You can use find_secret(N1, N2) which operate with O(log(N2-N1)).. What it does is simply a binary search.
... |
I am trying to create a polynomial time algorithm for a problem defined as follows:
c-ZPath(cZP)
$c$ is an integer constant $\geq 1$
Input: An undirected graph $G=(V,E)$.
Question: Can the vertices in $G$ be colored with two colors such that
no edge’s endpoint vertices have the same color and
there is a path in this... |
I'm working on a small lambda calculus compiler that has a working Hindley-Milner type inference system and now also supports recursive let's (not in the linked code), which I understand should be enough to make it Turing complete.
The problem now is I have no idea how to make it support lists, or whether it already d... |
I have a directed graph with $N$ vertices. Every pair of vertices is connected by two edges (one in each direction), and each of these edges has a weight which may be negative.
On various occasions 'edge update' operations occur, where the weight of an edge is modified (although the edge is never deleted, and no new ed... |
Let $A/B$ = $\{ w \mid wx \in A$ for some $x \in B \}$. Show that if A is context free and B is regular, then $A/B$ is context free.
My interpretation of this is is that we need to show that if a string $wx$ is accepted by a CFG, and we know that $x$ is accepted by a regular language (and therefore is also accepted ... |
NOTE: Let me point out that I did try extensively to solve this on my own. The problem is that, based on that circuit, it would appear that this processor cannot jump. At best the jump instruction will propagate through the pipeline with no effect. There is no data path defined for a jump that tells the processor to ch... |
Im trying to draw an annotated parse tree for 3*5+4n, the text book shows the following:
[Compilers - Principles, techniques and tools (Dragon Book) by Aho, p308]
I have a few questions regarding this
Why is 3*5+4 considered as a single string? Can't I draw a parse tree something like
for the same string ie:with ope... |
In type theories, like Coq's, we can define a type with parameters, like this:
Inductive ListP (Element : Type) : Type
:= NilP : ListP Element
| ConsP : Element -> ListP Element -> ListP Element.
Alternatively, we can define a type with an index, like this:
Inductive ListI : Type -> Type
:= NilI : forall t, L... |
Latency is defined as the number of intervening cycles between an instruction that produces a result and an instruction that uses the result. The initiation or repeat interval is the number of cycles that must elapse between issuing two operations of a given type.
In the Appendix C, pages 52-54 of Computer Architecture... |
How do you find the minimum hamming distance of a code?
A naive way is computing the distance of each pair of codewords in our code.
It becomes hard when the code is sufficiently large. Is there a formula for minimum hamming distance?
|
I'm a novice to the topic of provability so bear with me...
During a discussion with a friend, the question came up whether it could be possible that proving that $NP \neq P$ (or $NP = P$) is an unprovable statement. My friend opposed that, if indeed it was unprovable, then this would imply that there cannot be a poly... |
I have a social network in the form of an undirected graph $G = (V,E)$ with distinct non-negative integer keys. For each node $u \in V$, let the set $\Gamma(u) = \{ v \in V : (u,v) \in E \}$ be the neighbourhood of $u$. Clearly, I got that $d(u) = \left | \Gamma(u) \right |$, where $d(u)$ is the degree of $u$.
I now wa... |
So my knowledge of CS is amateurish at best but to me, logically, it seems like the halting problem is solvable.
So any human can determine if a problem halts with rigorous inspection, so why can't a very advanced, say human AI, solve the halting problem?
Also, is there a machine, say more powerful than a turing machin... |
I have a more general question for you. I'm working in Parallel Data Structures and Parallel Algorithms. That is a nice topic with a lot of interesting challenges. However, I have some problem to argue for why is necessary use parallel solutions. The most common justification is "We need to take advantage of the curren... |
I have a little understanding problem with Appendix A ("Universal Codes") in the paper "Shannon Information and Kolmogorov complexity" by Gründwald and Vitanyi (Link).
At the end of page 50, they say something corresponding to:
For each Prefix-code, the fraction of sequences of length $n$ that can be compressed by... |
I'm trying to wrap my head around an NP-completeness proof which seem to revolve around SAT/3CNF-SAT.
Maybe it's the late hour but I'm afraid I can't think of a 3CNF formula that cannot be satisfied (I'm probably missing something obvious).
Can you give me an example for such formula?
|
I posted this question on math.SE but I haven't got any reply so I'm posting here also.
I am reading The Algorithm Design Manual by Steven S Skiena.
In Section 4.10.1 Recurrence Relations, I understand what a recurrence relation is, but after that following statements have been given:
Any polynomial can be represented... |
Background
I need to find a largest set of non-overlapping axis-parallel squares, out of a given collection of candidate squares.
This problem is NP-complete. Many papers suggest approximation algorithms (see Maximum Disjoint Set in Wikipedia), but I need an exact algorithm.
My current solution uses the following divi... |
I have an example for a reduction of 3CNF to Clique, there is one thing I don't get about it, hopefully you could clarify it. The reduction works like this:
Construct a graph G = (V, E) as follows:
Vertices: Each literal corresponds to a vertex.
Edges: All vertices are connected with an edge except the vertices of
... |
Here is a resource allocation graph asked in my Operating Systems Theory midterm. The question is, "Is there a deadlock here? Explain your answer in detail"
Ra and Rb are resource sets and every dot inside of them are resources. Circles are processes. An arrow from process to a resource set means that process is reque... |
Assuming we have an automaton that simultaneously accepts a string on two paths. Would this mean that the construction of the NFA might be faulty? In other words; at the end of any string over any alphabet, does the NFA have to end up accepting one single path only? Or could it accept several at the same time?
|
I am new to Automata Theory. I am studying the book thoroughly and understanding it well. I have got a confusion regarding NFA. Why does this automaton accept the empty string λ?
What I think is that: implicitly δ(q,λ)=q for all states q. But here also explicitly defined δ(q0,λ)=q2. As there is a walk to the final sta... |
I've been looking into computer assisted music composition lately for my school project. While searching for literature I came across GenJam, an interactive jazz improvisation software which uses genetic algorithms to produce musical phrases.
I was wondering If anyone has done some work on computer generated music and... |
My question concerns genetic algorithm searching along bit strings.
Given:
$N$ = population size
$l$ = length of bit strings
$p_c$ = probability that a single crossover occur (double crossover never occur)
$p_m$ = probability for a given bit that a mutation occur
$w(x)$, the fitness function is equal to the number of... |
So I have this code:
done <- false [1]
n <- 0 [1]
while (n < a) and (done = false) [(n+1)(1+1+1)]
done <- true [n]
for m <- (a- 1) downto n [n(1+1+1+1)]... |
Given normally distributed integers with a mean of 0 and a standard deviation $\sigma$ around 1000, how do I compress those numbers (almost) perfectly? Given the entropy of the Gaussian distribution, it should be possible to store any value $x$ using $$\frac{1}{2} \mathrm{log}_2(2\pi\sigma^2)+\frac{x^2}{2\sigma^2}\rm{... |
Is $L = \{ W_1W_2 \mid W_1,W_2 \in (a+b)^* , N_a(W_1) = N_b(W_2)\}$ context free? Can we construct an NPDA for the language?
There is a book here that claims $L$ is not CF (without any elaboration), but I think we can construct a NPDA that accepts the language. My guess is we can construct the language with an NPDA wh... |
For example, say I want to analyze $T(n)=3T(\lfloor n/3 \rfloor )+2n$ for $n>2$, and $T(n)=1$ otherwise. This is clearly $O(n\log n)$; however it seems that with induction you can prove it is $O(n)$:
Base case: $T(1)$ is $O(1)$, $T(2)$ is $O(2)$
Inductive step: $T(n) = 3\times O(n/3) + 2n \in O(n)$
Where does this go w... |
Consider the following schema: Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId)
What are the functional dependencies here? Ir seems that it would be:
Id --> Name AdvisorId AdvisorName FavouriteAdvisorId
If we know the student id then we know his name, his advisor, his advisor id and his favouriteadvis... |
I am trying to show that every 2-terminal SP-graph is $O(\log(n))$-outer-planar for a challenge question on my assignment. In particular, I am trying to prove this by induction on the number of combinations (either a series or a parallel combination). This is what I have so far.
The base case on $0$ combinations is tha... |
There is a new Quantitative Finance SE site. However, I am interested in asking the "CS crowd":
What are some interesting key references or surveys on applying algorithms to stock trading analysis?
There are many such references, however, I am particularly interested in those that would appeal to those with a CS bac... |
Suppose we have the following schema: Drinkers(name, addr, phone, beersLiked)
Also suppose $\text{name} \twoheadrightarrow \text{phone}$. Consider the following tuples:
Sue a p1 b1
Sue a p2 b2
What other tuples must also be in Drinkers ? Would it be:
Sue a p2 b1
Sue a p1 b2
|
Considering programming languages with significant whitespace for indentation, such as Python or Haskell. How does this whitespace fit into the grand schemes of programming language grammars.
I can see that a "preprocessor" can convert indent changes into tokens which are then handled in grammars, yet can one also perf... |
this might be a bit philosophical question , but i haven't really gotten a good answer.
Theoretical computer science vs Software engineer / developer whatever, which one is better for making good money.
I love maths and theoretical computer science. I am very ambitious, slightly arrogant guy from Estonia. I am first y... |
There is a famous part-of-speech tagging problem in Natural Language Processing. The popular solution is to use Hidden Markov Models.
So that, given the sentence $x_1 \dots x_n$ we want to find the sequence of POS tags $y_1 \dots y_n$ such that $y_1 \dots y_n = \arg\max_{y_1 \dots y_n}p(Y,X)$.
By Bayes Theorem, $P(X,Y)... |
I have an algorithm and I determined the asymptotic worst-case runtime, represented by Landau notation. Let's say $T(n) = O(n^2)$; this is measured in number of operations.
But this is the worst case, how about in average? I tried to run my algorithm 1000 times for each $n$ from $1$ to $1000$.I get another graph which ... |
The OSI model can be used for LAN and WAN networks, allowing the interconnection of [vendor] closed systems and it only informs what each layer have to do.
Someone said that this phrase is false, because OSI (Open Systems Interconnection) model, "as the name says", only allows the connection of "open systems".
So I'm... |
I've been wondering lately how GPUs compute sines and cosines, and Google hasn't helped me finding a precise answer.
Initially, I was thinking that in order to make the computations as fast as possible, the GPU would use some kind of lookup table. But then I realized, storing all sin values in a table of the range of d... |
Specifications in Kripke structures are verified by Computation tree logic (CTL). However, refering to this Wikipedia article the CTL-operators are relative to a current state. So, when we want to verify if EF q is satisfied in a Kripke structure
Do we only need to check if EF q holds starting from the starting state o... |
It's quite a short question: Refering to this Wikipedia article p U q means, that p has to hold at least until at some point q holds.
So, does it mean:
On each path starting from the current state p has to hold in each state until a state is reached in which q holds.
On each path starting from the current state p has ... |
Petersen's Theorem states that every cubic, bridgeless graph $G(V, E)$ contains a 2-factor $F$ (and therefore a perfect matching $E-F$). Alternatively, 2-factor is a set of vertex disjoint cycles that cover $V$. I'm interested in the computational properties of 2-factors in connected bridgeless cubic graphs. I conjectu... |
The optimization version of TSP asks for the length of the shortest tour. Unlike the decision version of TSP, there's no obvious way to verify a proposed solution of the optimization problem in polynomial time. But is there a proof of whether or not it can be verified in polynomial time assuming P ≠ NP?
|
This is a cross-post from a post on MathSE due to lack of answers.
To illustrate my question I provide the following example.
The website Online Turing Machine provides a Turing Machine simulator. The following program adds 1 to any binary number.
q0,1 => q0,1,>
q0,0 => q0,0,>
q0,_ => q1,_,<
q1,0 => q3,1,>
q1,1... |
I wanted to give the following as a homework question, but my first few attempts to solve it failed, so now I'm just curios for a solution:
For two words $x,y\in \Sigma^*$ and for a letter $\sigma\in \Sigma$ we define the glue-concatenation of $x\sigma$ and $\sigma y$ to be $g(x\sigma,\sigma y)=x\sigma y$, and for word... |
In case of binary classification problem, what are the $y_i$ 's in the training data set $\{(x_1, y_1), (x_2, y_2), \dots (x_n, y_n)\}$?
I guess they are from $\{1,-1\}$. Now I see a method for finding a scoring function $f(x) = w^Tx + b$ by minimizing the squared error between the $f(x_i)$'s and $y_i$'s over $w$ and $... |
Given an undirected graph $G(V,E)$ and two nodes $s$ and $t$, $s,t\in V$, find a path whose length $L$ is bounded by a lower bound $N$ and an upper bound $M$, $N\leq L\leq M$.
So, for example, $N=4, M=7$, I want to confirm that there is at least one simple path of 4,5,6 and 7 between two nodes in a graph? Nodes of the ... |
I want to know if longest remaining time first (LRTF) CPU scheduling has starvation or not. Also give reason how it starve/does not starve a process.
I know longest job first (LJF) may starve a process if all other incoming processes have longer CPU burst.
|
As a matter of curiosity I've been trying to determine at what point a 64-bit float no longer reflects the addition of 1 as expected; that is, at what point the digits as printed do not correspond to the digits of a 64-bit integer that is incremented in sync.
Around 1e15 I can continually add 1 or subtract 1 and the re... |
I know that (1 + 0)* is the set of all bit strings; but isn't 1* + 0* the same thing?
|
I'm having trouble finding the language represented by the following:
(AA|BB)*
Should the expression be read as... ( A (A|B) B ) *
or... ( (AA) | (BB) )*
If that isn't clear, should this produce something like... ABABAB or should it produce AABBAABBBBAA
My guess is that AABBAA is part of the represented language, while... |
Although I have already learned something about the asymptotic runtimes of matrix multiplication algorithms (Strassen's algorithm and similar things), I have never found any explicit and satisfactory reference to a model of computation, which is used to measure this complexity. In fact, I have found three possible answ... |
Language:
$ L = a^{n+m}b^{n}c^{m} $
As per a recent test I gave, this language is not context free.
However, I think it is.
Corresponding Grammar:
$ X \rightarrow aXY \space |\space \epsilon $
$ Y \rightarrow b \space | \space c $
Pushdown Automata:
Keeping pushing all $a$ to the stack, until a $b$ is scanned. Keeping ... |
I wonder if high-performance computing and parallel computing always mean the same?
If not,
what are the differences and relations between them?
what are some examples of high-performance computing that are not parallel computing?
what are some examples of parallel computing that are not high-performance computing?... |
Given that A is a context free language and B is a regular language, B-A can be not context free as it is equal to B ∩ A', and context free languages are not closed under complement. Could you give me a counterexample?
|
Given a set of line segments, how do we identify a subset of maximal cardinality where all line segments are pairwise non-intersecting?
Brute force we would get $2^n$ sets to check where $n$ is the number of line segments, so that isn't viable. Anyone got a bright idea how the do this efficiently? I tried doing it this... |
I am a little confused on how to prove/disprove Big O.
For the problem, $2^{n+3}= O(2^n)$, I did the following:
$$2^{n+3} \leq K \times 2^n$$
Set $K = 1$
$$2^{n+3} \leq 2^n$$
Test for large values of n (so I plugged in n = 100)
$2^{103} \leq 2^{100}$ --- which is false therefore Big O is disproven
Is this process corr... |
How would you prove/disprove that $e^n = O(2n^2)$? It's unclear to me which function grows faster.
|
We have 2 stations that communicate with each other, but we need to detect (or even correct) when something is wrong.
We use 8 binary words: each consisting of 3 bits and to send it we code it as
where is the complement of and is the even parity check bit of .
We need to find the capabilities of this code (up t... |
There is something in the pumping lemma that I do not quite understand, namely if $s$ is at least of length $p$, then we could split it to $xyz$ such that the following conditions are met:
For each $i \geq 0$, $x(y^i)z \in A$
$|y| > 0$
$|xy| \leq p$
But if $i = 0$ then $|y|$ cannot be strictly greater than $0$. Isn't... |
I have been reading about Dijkstra's algorithm and I think I understand it. I followed the algorithm in pseudo-code from Wikipedia, and now I wonder:
If my graph is bi-directional and I add each edge to my graph twice (once "forwards", once "backwards"), will the "standard" Dijkstra's algorithm work?
Is it ok that som... |
From wikipedia:
The PageRank values are the entries of the dominant eigenvector of the
modified adjacency matrix. This makes PageRank a particularly elegant
metric
Can anyone please elaborate on the connection between the eigenvector and the PR vector? Why are they related?
|
I am having a hard time understanding closure properties of recrusively enumerable languages. I have read the explanation on this site but still unable to fully understand why they are not closed under complementation?
Explanation also says,
This fails because $M$ only needs to halt if $w \in L(M)$ - doesn't have to s... |
I'm not sure how to word this because I'm not familiar with this, but I'm sure a process like this is rather common.
Basically, I've got members signing up for our website, and each one is assigned a normal sequential ID (a MySQL auto_increment ID), i.e. 1, 2, 3, ....
The client wants these users to have a "member numb... |
I want to prove that any polynomial of degree $k$ is in $\Theta(n^k)$. The coefficient of $n^k$, $a_{k}$, is positive.
I know I need $0 \leq c_{1}n^k \leq a_{k}n^k + ... + a_{0} \leq c_{2}n^k$ for all $n \geq n_0$.
The upper limit is easy to prove by taking $c_{2} = \sum\limits_{i=0}^k |a_i|$
I don't know how to prove ... |
My language is the repetition of 0 to a length that's a power of 2:
$L = \{ 0^k \ni k=2^n, n \geq 1 \}$
I want to know how to prove that this language is not regular. I have attempted the proof below, but think it may be incorrect due to my potentially wrong assumption that the Myhill-Nerode theorem allows me to break ... |
I have been trying to solve this question and am kinda stuck. Wondering on how to proceed and finish this proof. Prove that the language $ L = \{a^{2^n} | n >= 0\} $ is not regular. I have been trying to use the pumping lemma but am stuck at:
Suppose L were regular, let p be the pumping length given by the pumping lemm... |
CFG can specify structure of sentences but Regular grammar can only specify strings sequentially. Is it because DFA has only one bit memory?
|
So the dual problem of max-flow is min-cut. What's the dual problem of stable matching?
|
There are two languages,
$\qquad L_1 = \{w\in\{a,b\}^*: N_a\leq N_b\}$ and
$\qquad L_2=\{w\in\{a,b\}^*: N_b\leq 2N_a\}$
where $N_a$ means the number of occurrences of $a$ in the string $w$. Same for $N_b$.
I've proved that $L_1$ has a DPDA (hope this is right).
Now I want to know whether $L=L_1\cap L_2$ has a DPDA or... |
I want to analyze the runtime of this algorithm:
int fun (int arr[], int n) {
int result = 1;
int i, j;
if (n == 1)
return 1;
else {
result = fun(arr, 2n/3);
for (i = 1; i <= sqrt(n); i=i*2);
for (j=0; j<sqrt(n)/i; j++)
result += arr[... |
So, i was trying:
$(-10.75)_{10}$ and to convert it into 32 bit binary floating point representation.
i did this:
According to IEEE standard: $(-1)^{-s} * 1.M * 2^{E-bias} $
sign bit= 1 bit
exponent= 8 bits
mantissa= 23 bits
bias= $2^{n-1}-1 = 127$
- 10 . 75
⇓ ⇓ ⇓
= 1 1010 . 11
= 1 1.01011 x 2^-3
= 1 1... |
Consider following grammar:
$$X\to Yc|ZY$$
$$Y\to ab|cX$$
$$Z\to d|\epsilon$$
Can this be converted to LL(1)?
Cleary, its not LL(1) because of First/First conflict at first production. Can anyone suggest something to make it LL1?
|
I noticed that in write-back caches, when the cpu wants to write to a block, it fetches the block from memory and then updates it. If the block is going to be overwritten and changed by processor, why does the cpu need to read that block from memory?
|
I am preparing for my exams and was solving problems regarding Sliding Window Protocol and I came across these questions..
A 1000km long cable operates a 1MBPS. Propagation delay is 10 microsec/km. If frame size is 1kB, then how many bits are required for sequence number?
A) 3 B) 4 C) 5 D) 6
I got the ans as C opti... |
Should the size of its cache line, the width of bus between memory and CPU, and the size of its registers be all equal to the CPU bit?
Is CPU bit determined by the size of its cache line, the width of bus between memory and CPU, or the size of its registers, something else?
Thanks!
|
What aspects of linguistics are necessary or good to know for natural language processing? What references do you recommend for studying those aspects? Thanks!
|
I have dug in simple binaries, such as though like x86 bootloaders, sega video game binaries, etc. I know that these files tend to use assembler macros to define data, etc.
What I am having trouble figuring out is what assemblers tend to translate macros into exactly (are they instructions, custom formatted data entrie... |
Is there a way to state Blum's speedup theorem in terms of Big-O (Landau) notation?
|
Do any of Blum's theorems prove that there exist decidable languages that are unclassifiable anywhere in the time hierarchy? In other words, asserting they (mentioned in the proofs) are computable within any time $O(f(n))$ for some time-constructable function $f(n)$ leads to a contradiction?
|
In general, how can we go about proving that union of two languages as non regular. In this case, the individual languages can be proved as non regular using pumping lemma. How can we apply pumping lemma to union of two languages ?
|
Difference between “average length” and “entropy” gives the percent of optimal. The optimal case is when the average length of a code is equal to the entropy. For example if average length is 1 and entropy is 0.72: (1- 0.72) = 0.28 -> 28% worse than optimal.
If both “average length” and “entropy” are 1, the compression... |
I have a genetic algorithm for an optimization problem.
I plotted the running time of the algorithm on several runs on the same input and the same parameters (population size, generation size, crossover, mutation).
The execution time changes between executions.
Is this normal?
I also noticed that against my expectatio... |
everyone! I don't know a whole lot about the fields of encryption or quantum computing, but I've read a lot of articles on the subjects and that is prescisley what caused this question. I've been a little scared about the whole NSA quantum computer that is build for the sole purpose of cracking encryption codes. I am f... |
Is this true? If I change all final states of a given Deterministic Finite Automata to non final states and all non final states to final states then does this new automata represent the complement of the language that was accepted by the original automata?
What if we talk about a Non deterministic finite automata inst... |
OS Book written by Galvin et all states that if page size is 4KB and size of virtual space is 32 bits then 2^(32-12) page entries would be required which is too huge to store in memory!!
Therefore it recommends to break it down by paging the inner page table as well. Now my question is how does that reduce memory requ... |
I am confused about clustered index is dense or sparse. I searched for that, sources saying it is sparse, but can be dense also. What is it exactly?
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I would like an example of a quine in pure lambda calculus. I was quite surprised that I couldn't find one by googling. The quine page lists quines for many
"real" languages, but not for lambda calculus.
Of course, this means defining what I mean by a quine in the lambda calculus, which I do below. (I'm asking for som... |
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