instruction stringlengths 35 29.1k |
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[Input]: the begin and end points of an arbitrary line (small red points) and the line width (green line)
[Example]: begin=(20,20), end=(100,50), width=5
[Output]: The set of pixels (not the total area) that are in the yellow rectangle
[Example]: {(20,20), (20,21), (20,22),...etc.}
How can i calculate the output set?
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I'm facing some problems that deal with finding common elements between unsorted arrays and I'd like to know whether there are well-known lower-bounds for the worst-case and, eventually, what are these lower-bounds.
The problems are pretty simple:
Given two unsorted arrays of distinct integers, $A$ and $B$, of size
... |
i'm going to use the Christofides heuristic algorithm in order to solve a TSP for about 80 edges. Eventually i should have a solution, that is within the factor 1.5 of the optimum.
But when i'm finished, i'd like to check my solution but i don't know how. So i thought about using a computer-program to find the optimal ... |
I look for grammar which use letters $a,b,c$ that numbers of letters $c$ is greater than number of letters $b$.
Example: $acbccba$
I thought about:
$$S \rightarrow aS \mid bS \mid SCS$$
$$C \rightarrow cb \mid ca$$
but not sure if it work. Could you help me, please.
|
I've seen two definitions of a universal hash family, and my questions is if those are equivalent, i think they are and will explain why but i'm not sure if it is.
Definition 1:
$H$ is a universal hash family if and only if $$\mathbb{Pr_{h \in H}}[h(k) = h(l)] = 1/m$$
where $k \neq l$ and $k,l\in Key$ and $m$ is the Si... |
I am new in complexity theory and this question is a part of a homework that I have and I am stuck on it.
Let ${\sf coNP}$ be the class of languages $\{\overline{L}: L \in {\sf NP} \}$.
Show that if ${\sf NP} \neq {\sf coNP}$, then ${\sf P}\neq {\sf NP}$.
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How to prove that the largest number of leaves in an $n$-tree of height $k$ is $k^n$?
|
I've been recently studying Monte-Carlo and other randomized methods for a lot of applications, and one that popped into my mind was making an (approximate) convex hull by examining random points, and try to get them inside the convex hull. I would like to know if there are algorithms for convex hulls that can improve ... |
I am having trouble with a past exam paper. I have to design a Turing Machine to do the following, but I don't really know where to start with this question. Any help would be very much appreciated.
Design a Turing Machine TM checking if the numbers of sold apples and bananas are even. Formally, given a string w over ... |
Given a set of rectangles, $D = \{ (a_1, b_1), (a_2, b_2) \dots , (a_n, b_n) \}$, where in each pair $(a_i, b_i)$, $a_i$ represents the height of the rectangle and $b_i$ the width, and given another pair $(w, h)$ representing the width and height of a container $C$, does exist a way that taking some of the squares in $... |
I am reading two books, Computer organization and design by David A Patterson, and Digital Design and Computer Architecture by Harris and Harris. These books claim that a 1 bit branch predictor mispredicts on the first and last iterations of every loop.
I don't understand why it mispredicts on the first iteration. I th... |
I'm fairly new to the syntax of relational algebra, and I'm having a hard time understanding how I could set a "at least one" clause.
Example: I have:
a table with books (listing the title, year published and ID),
a table with authors (listing their name and ID),
a table which lists what author wrote what book (thro... |
Here's the problem:
I have a collection of collections, $C$, where each $c\in C$ is a collection of sets $X\subset U$. Denote $c_i$ as the i-th $X$ in $c$. Informally, I want to map all the sets in each collection to bins, where no two sets in a single collection can occupy the same bin, such that the sum of the size... |
How can I deal with recursive terminals in CFG when converting it to CNF? For example,
S -> MN
M -> AM | A
N -> BN | B
A -> a
B -> b
How can I reduce terminals M and N?
|
Radix sort is theoretically very fast when you know that the keys are in a certain limited range, say $n$ values in the range $[0\dots n^k -1]$ for example. If $k<\lg n$ you just convert the values to base $n$ which takes $\Theta(n)$ time, do a base $n$ radix sort and then convert back to your original base for an ove... |
Let $\mathbb{F}^n_2$ denote the set of $n$-bit 0-1 strings. How to construct an efficiently computable function $f:\mathbb{F}^n_2\to \mathbb{F}^m_2 (m>n)$ satisfying that $\forall u\neq v$,$f(u)\neq f(v)$ and $f(u)$ is not a circular rotation of $f(v)$?
$m$ is expected to be as small as possible.
Thank you very much fo... |
May be it's a stupid question (sorry if it's the case).
What is the complexity the decision problem:
Input: $A\in\mathcal{M}_{n,m}(\mathbb{Z})$
does there exists $x\in\mathbb{N}^n,x>0$ such that $Ax\geq 0$?
Where $x\geq 0$ means for all $x_i\geq 0$ and $x>0$ means there exists $x_j>0$.
I know that integer linear progra... |
Consider the following universe problem.
The universe problem. Given a finite set $\Sigma$ for a class of languages, and an automaton accepting the language $L$, decide if $L=\Sigma^*$.
In [1], it is stated and proved that the universe problem is undecidable for a particular class of one-counter automata. This result... |
What's the difference between a stream and a queue? They both have the concept of an ordered set of elements, but tend to have different implementations and a different vocabulary of 'insert'/'extract' (streams) vs. 'enqueue'/'dequeue' (queue). Are these interchangable? Do they suggest different concepts or patterns? I... |
This was a question at SO, and I think it's very interesting, I thought about it, but I could not provide any efficient algorithm neither showing the NP-Hardness:
Find the length of the longest non-decreasing sequence through
adjacent, non-repeating cells (including diagonals). For example, in the
following grid, ... |
Given a weighted digraph, I can check whether a given vertex belongs to a negative cycle in $O(|V|\cdot|E|)$ using Bellman-Ford. But what if I need to find all vertices on negative cycles? Is there a way to do it faster than Floyd-Warshall's $O(|V|^3)$?
|
It is clear that any language in $\mathsf{EXP}^{\mathsf{EXP}}$ can be computed in $\mathsf{2EXP} = \mathsf{DTime}(2^{2^{\mathsf{poly}(n)}})$.
My question is whether the converse is true: is $\mathsf{2EXP} \subseteq \mathsf{EXP}^{\mathsf{EXP}}$?
|
I'm trying to find two languages, $L_1, L_2 \in RE \setminus R$, such that $L_1 \cup L_2 \in R$.
I have already proved that if $L_1\cap L_2 \in R$ and $L_1 \cup L_2 \in R$, such $L_1, L_2$ don't exist (because otherwise we'll be able to construct a Turing Machine $M_1$ which will decide $L_1$, for instance).
However, I... |
What I have
An iterative process based on the application of a very simple function to represent a rate, with total dependence among any iteration and its predecessor (one input parameter for (n)th iteration is the output parameter from the (n-1)th iteration). Specifically,
$\qquad f(x, y, z) = x + \frac{y - x}{z + 1}... |
Question:The set of all first names given to children born in New Zealand in 1996
I think this language is regular because every element in the set can be a accept state
How can I prove if the language is regular?
|
I am reading an article called The temporal semantics of concurrent programs
.
On page $9$, there is a small section (numbered as $2$) called "clean behavior".
I think that there is a problem with this part, what does Pnueli meant by "Let $\lambda_i$ be the leagality condition for the statement departing from $m^i$" ?
... |
Input: A set of $n$ Users $U=\{u_1, ..., u_n\}$ and a set of $m$ products $I=\{i_1, ..., i_m\}$. Associated with each pair $u \in U$ and $i \in I$ is the probability $p_{u,i}$ of $u$ purchasing the product $i$.
Task: Assign each user exactly $k$ products so that the following objective function is maximized:
$$\sum... |
BB(n) is roughly the maximum number of new states an n-state TM can run into without halting. So for a particular n, if we know BB(n), then we can find out if an arbitrary n-state TM halts by running it for BB(n) steps.
So given some n-state TM, can we construct an m-state TM, where m>n, to calculate BB(n) and thus dec... |
Given a PDA $P=(Q,\sum,\delta,q_0,F)$ construct formally a TM that accepts $L(P)$.
My idea is to construct a Turing machine with 2 tapes, one for the input and the other for the stack. Also to add $q_a$ for accept and $q_r$ for reject and to send to $q_a$ if the TM stops on states in $F$ and send to $q_r$ otherwise.
Bu... |
Given two arbitrary regular expressions, is there an "efficient" algorithm to determine whether they match the same set of strings?
More generally, can we compute the size of the intersection of the two match sets?
What algorithms are there to do this, and what complexity class do they live in?
If we disallow the Kleen... |
I need a little help with a lambda calculus reduction to normal form:
$$(\lambda xxxx.xx)(\lambda x.xx)(\lambda x.x)y((\lambda x.x)x)$$
It should be solved like this:
$$xx(\lambda x.x)y((\lambda x.x)x)$$
and then:
$$xx(\lambda x.x)y(x)$$
This is the result of any of the lambda calculators that you can find online.
My q... |
Here is my problem. I have to compute the amount of information that is possible to encode in a string of bits. This string of bits represent a stream.
Let us call such stream as $X_1,X_2,X_3,...,X_n$. Important: this succession of Random variable is not a Markov Process, but a process with memory!!
I suppose that the ... |
The government wants to create a team with one alchemist, one builder, and one computer-scientist.
In order to have good cooperation, it is important that the 3 team-members like each other.
Therefore, the government gathers $k$ candidates of each profession, and creates their "liking" graph. This is a tri-partite gr... |
I'm studying the PCP theorem.
While it is easy to prove that $\mathsf{P}=\text{PCP}(O(\log n),0)$ , proving that $\text{PCP}(O(\log n),1)\subseteq \mathsf{P}$ i.e. PCP that uses $O(\log n)$ random bits and read 1 bit of the proof is less obvious, what I tried to do is to take some proof $\pi$ of length $n^{O(1)}$ (be... |
Let,
game be the state of a 2-player, turn based game
actions game player -> [move] be a function that gets the state of a game and returns all valid moves, where a move if a function move game -> game that updates the state of the game
state game -> state returns wether a game is incomplete, won by player1 or won by... |
Reachability is defined as follows:
a digraph $G = (V, E)$ and two vertices $v,w \in V$. Is there a directed path from $v$ to $w$ in $G$?
Is it possible to write a polynomial time algorithm for it?
I asked this question on mathematics and got no answer by far.
|
Find the weight of the lightest path from u to v the goes through node a or/and b.
Do you have a suggestion on how it can be done?
|
Can a Boolean circuit by itself be considered an algorithm (a single step algorithm if you like)? For instance say you have a simple tree circuit with two AND gates as the input gates feeding a single OR gate for a depth two circuit. Now change the AND gates to XOR gates, is it correct to say that I now have a differen... |
Hello for a homework I have to show that deciding whether a regex over $\Sigma = \{0,1\}$ descibes $\Sigma^*$ is $\mathsf{coNP}$ complete (this is irrelevant for the question though).
The thing which irrs me is that I think this problem is in $\mathsf{P}$.
Here is my argumentation:
Let $R$ be a regex, then we have $$L(... |
let $L_c$ be the class of all languages that have a polynomial reduction to some language L, for example if $L=SAT$ then $SAT_c=NP$.
Assuming know that $NP\neq P$ we know that there exist languages that are not NP-hard and not in P, i.e. those in NPI. My question is there a language L in NPI such that $L_c \setminus \{... |
In database theory, there is a notion of transitive closure over relations. I am wondering if join operator over relations is also a special case of transitive closure?
|
I am trying to solve problem of preventing oversell of limited resources.
Consider resources (people) who are described by set of properties where each property belongs to different category (example properties from four categories: male, age 25-30, 2 children, interested in games).
Buyers want to allocate access to r... |
First I apologize if the title is unclear, but I didn't find anything better.
I'm solving a differential equation that has two parameters , here denoted by points of a plane.These parameters are real numbers. For some points of the plane (or, equivalently, for some parameters of the differential equation) , the solutio... |
I would like to build an online web-based machine learning system, where users can continuously add classified samples, and have the model updated online. I would like to use a perceptron or a similar online-learning algorithm.
But, users may make mistakes and insert irrelevant examples. In that case, I would like to ... |
I'm having a problem with proving the following statement:
For every infinite language $L$, does there exists an infinite language $L' \subseteq L$ such that $L'$ is not decidable?
|
Starting to use nanoflann to do some point cloud nearest neighbor searching and it got me thinking about just how "approximate" ANN methods are.
If I have a (more or less) randomly distributed point cloud what is the likelihood that I get the exact nearest neighbor given a target point within the clouds bounding box? ... |
I'm trying to understand Little's law and can't seem to get past this scenario:
Let's say people arrive at the register at 12 per hour. It takes 10 minutes (1/6 of an hour) to service each one of them. The law says that the long-term average number of customers is 12 * 1/6 = 2. After the first hour, my assumption is th... |
In the 8-queen puzzle, to reduce the search space, we can use an incremental approach. We put the first queen in the first column, then the 2nd queen in the 2nd column etc., avoiding the slots that are already being occupied.
According to Peter Norvig's book, there are only 2057 possible sequences. Where does that numb... |
If I have a hard problem, one standard approach is to express it as a SAT instance and try running a SAT solver on it. Another standard approach is to express it as a constraint satisfaction problem, and try using a CSP solver. The two feel somehow vaguely similar in what sorts of problems can be naturally expressed ... |
So we know that there exists a Turing Machine $M$ and a polynomial $T$ such that:
$M$ halts on all inputs within at most $T(|x|)$ steps
If $x$ is in $L$ then $M$ accepts $x$
If $x$ is not in $L$ then $M$ rejects $x$
We need to show that for any other problem $L'$, there exists a polynomial time computable function $f... |
I am looking for the English name of the following algorithm:
We are given an array a with numbers and we need to be able to efficiently retrieve the sum of a continuous interval [f,t] of numbers in that array. In order to do that we precompute an array sums(of size size(a) + 1) that stores the sums of the prefixes of ... |
Is it theoretically possible to have a nondeterministic finite state machine without any initial state or does it need at least one initial state?
|
I am not sure whether this is the right place to ask this question, but since it involves register machine and computability, hopefully this is the right place.
I have tried to post on Programmers and Stack Overflow, but they redirected me to this site, they said it is more related to CS.
The question is about how can ... |
The busy beaver max shifts function, $S(n)$, has known values for $n\leq4$. Is there some basic, structural reason why it's inconceivable that we will ever find $S(n)$ for $n>4$? What is so different about $n=4$ than $n=5$? Or $n=6$? Somewhere along the way there must be some fundamental difference, otherwise $S(n)$ ... |
This question is an extension of a previous question I've asked.
Consider the rectangle $a<x<b , c<y<d$ in the $\mathbf R^2$ plane. Each point in this rectangle can be of kind #1 or #2 (We have to check each point to know its kind).
Assume that somehow we know that the points of kind 1 (and so the points of kind 2) for... |
So, there are multiple possible definitions of "np-complete", two of which being:
A decision problem $L$ is np-complete if and only if: $L \in \text{NP}$ and $\forall L' \in \text{NP}: L' \preceq_{p} L$
A decision problem $L$ is np-complete if and only if: $L \in \text{NP}$ and there exists a np-complete probl... |
As I understand emulation a rule of the thumb says that a computer must be around a order of magnitude more powerful to emulate another system without resorting to tricks. This is because for every clock cycle of the system to be emulated, the host machine must process that cycle in the correct time and also process it... |
Given $k$ numbers $A_1 \leq A_2 \leq ... \leq A_k$ such that $\sum\limits_{i=1}^k A_i = k(2k + 1)$ is there an assignment of numbers $i_1, i_2, ... , i_{2k}$ which is a permutation of $1, 2, ... , 2k$ such that
$i_1 + i_2 \leq A_1\\ i_3 + i_4 \leq A_2\\ .\\.\\.\\ i_{2k-1} + i_{2k} \leq A_k$
?
I cannot find an efficient... |
I want to perform some interval-operations, and for addition, subtraction, and logic-/shift-operators, that works very well.
The only problem I have is the multiplication.
An interval $[a, b]$ denotes all two's complement numbers $x$ with the property $a \leq x \leq b$.
An interval-operation means that if i have a bina... |
These lecture slides sketch a proof that $L=\{ a^n b^n \mid n \geq 0 \} \cup \{ a^n b^{2n} \mid n \geq 0 \}$
cannot be accepted by any Deterministic Pushdown Automaton. Unfortunately, the slides give no references as to where the proof comes from.
I was wondering, does anybody know of an academic paper or textbook tha... |
I'm exercising for an upcoming exam and I find this exercise:
Say whether or not the language
$$L = \{a^jb^ia^{j-i}\mid i,j \ge 0\ , j > i\}$$
is a context-free language. Justify your answer.
I have already tried (using the pumping lemma for CFL) with two different words:
$$w1 = \ a^pb^{p-1}a$$
$$w2 = \ a^{2p}... |
I think of type as a range of values that the variable can take whereas the rest is known constant or does not matter. Variables (instances or objects), which share common properties, are considered to belong to the same type/kind/class. That is, the type properties are constant across the type. The type is actually a ... |
For my thesis, I have created a development approach (consisting of schemes, an application template and prototype code) that should make it easier to develop and adapt applications for a specific platform.
I have conducted interviews with developers of that platform to evaluate my approach. There have been 5 interview... |
I am looking for references that talk about the existence of a general pattern in mouse tracking data of humans when they do a matching game. I am going to use this knowledge to differentiate between humans and the robots trying to play the game as humans.
Does anybody know a reference about the mouse movement pattern ... |
I'm studying CLRS, and solving problems listed after each chapter. I'm curious about problem 1-1. That is right after Chapter 1.
The question is, what is the best way to find the largest integer $n$ such that $n \lg(n) \leq 10^6$.
The simplest but the longest one is substitution. Are there some elegant ways to solve th... |
I am interested in the following version of TSP:
Assumption: TSP where the distances are non-negative. We know the algorithm A which computes the optional solution for such instances of TSP.
Task: State an algorithm that uses the algorithm A and computes an optimal solition for instances where negative distances are al... |
In both CLRS (third edition) and Erik Demaine's lecture, the van Emde Boas tree is defined to store max but not min recursively. Why store max recursively?
If it is not stored recursively, insert(V, x) can take advantage of the special case where a cluster or summary contains one element (min = max), although I think ... |
I'm having trouble understanding reduction. Lets say you have a decision problem A that is NP-Complete. Also, another problem B the can be reduced from A.
What can you say about B if:
1) The reduction is done in polynomial time
2) The reduction is done in exponential time
I know that if A is reduced to B means that i... |
In the seminal distributed systems paper The Part Time Parliament (the Paxos protocol), Leslie Lamport names fictional legislators who are involved in the Paxon parliament protocol.
According to this writing, he notes that:
I gave the Greek legislators the names of computer scientists working in the field, translitera... |
Is there any convex hull algorithm that can be extended to non-euclidean metric, such as the geodesic distance on the surface of a sphere?
|
I'm trying to find complexity class of finding winning strategy for first player in following game:
Intance of 'Stones' game is:
finite set $X$
relation $R \subseteq X^3$
set $Y \subseteq X$ and node $f \in X$
At the beggining we place stone in every element of $Y$.
Every player in his turn can move stone from $x$ t... |
The problem is defined as:
Given $N$ points on an infinite line, find the least number of line segments of length $L$ that cover all points (including endpoints) after changing one point.
That means that if I have the points $P = 1,10,15,28$ , $L = 10$ , 3 line segments are needed , changes will occur that the point ... |
Consider a deterministic Turing Machine $D$ which has an infinite tape in both directions. We don't have exact information about it; what we know is that its alphabet is $\{a, b, c\}$ and there are at least three states $q_1, q_s, q_f$ where $q_s$ is the start state, $q_f$ is the final state. At some step of the comput... |
I would like to show that
$$EQ_{DTM} = \{ (\langle M_1\rangle,\langle M_2\rangle) \mid M_1\text{ and } M_2 \text{ are DTMs and } L(M_1)=L(M_2)\}$$
and
$$\overline{EQ_{DTM}}$$
are not semi-decidable. I think there must be a reduction from the complement of the halting problem.
|
It's a school assignment:
The problem is:
Write a BN grammar for +67.
The given solution I have been given is following:
<digit> ::= 6 | 7
<number> ::= <digit> | <digit> <number>
<+67> ::= + <number>
My question is, when given this simple task, could it be derived like this?
<digit> ::= 6 | 7
<number> ::= <digit>... |
What does the capital R superscript notation mean in regular languages? I am working on a homework assignment and don't recall my professor mentioning what the what the R superscript means. For example in this syntax:
$L = \{ww^R\mid w \in \Sigma^{\ast} \}$
|
I have a question about definability of truth assignments. Suppose that I am working in the context of propositional logic. Let me give some definitions first.
Let $L$ be a propositional language with the set $Prop_{L}$ of propositional variables. A truth assignment is a map $v\colon Prop_{L}\to\{F,T\}$. Denote the col... |
Do you know the name of the following problem and can you give a reference for its complexity (especially the relation to $\mathsf{GraphIsomorphism}$ and/or other isomorphism/homomorphism problems)?
Given two metrics $d_1$ and $d_2: V^2 \to \mathbb{N}$. Does there exist a permutation $\pi$ on $V$ such that $d': V^2\t... |
I am reading Algorithm design manual by Skiena. It gives proof of Insertion sort by Induction. I am giving the proof described in the below.
Consider the correctness of insertion sort, which we introduced at the beginning of this chapter. The reason it is correct can be shown inductively:
The basis case consists of a... |
I'm trying to understand what this text means in my textbook about distributed leader election algorithms, but I can't make any sense of it. Either they didn't explain what was meant, or I missed it somewhere.
In this section, we show that the leader election algorithm of Section 3.3.2 is asymptotically optimal. That ... |
I'm studying for an exam on software testing and in my notes I found this:
Many more paths than branches. A pragmatic compromise will be needed
I cannot understand the difference between paths and branches; each time I work out the paths and branches of a graph I end up with the same number. Thanks!
|
There are $n$ bins and $m$ type of balls.
The $i$th bin has labels $a_{i,j}$ for $1\leq j\leq m$, it is the expected number of balls of type $j$.
You start with $b_j$ balls of type $j$. Each ball of type $j$ has weight $w_j$, and want to put the balls into the bins such that bin $i$ has weight $c_i$. A distribution of ... |
A Bloom filter uses a hash function to test membership in a given set $S$, by checking if an item is present of not at the specified position.
To mitigate the effect of hash collision, multiple functions are used, yielding probabilistic bound if using universal hash.
We can use 10 bits per elements to have 'reasonable... |
Here is the question:
I have a given tree with n nodes. The task is to find the number of subtrees of the given tree with outgoing edges to its complement less than or equal to a given number K.
for example: If n=3 and k=1
and the given tree is 1---2---3
Then the total valid subtrees would be 6
{}, {1}, {3}, {1,2}, ... |
When trying to decide on the choice of a programming language for a
specific task, people will often tell me: "use this language because it
has the best library for the type of problems you are addressing".
I would rather choose my language for its intrinsic qualities as a
programming medium. That implies that librarie... |
If I use a balanced tree instead of lists in a hash table implementation, and also after initializing my table I don't enlarge nor reduce the size of the table, what would be the worst case complexity?
|
In the classic crypto textbook "Introduction to Modern Cryptography" by Jonathan Katz and Yehuda Lindell, there is a definition for indistinguishable encryption in the presence of an eavesdropper as such that for every probabilistic polynomial time adversary A there is a negligible function negl(n) such that
$\Pr[PrivK... |
I have an exercise which I can't solve.
Exercise. Consider a game where the players have $2$ pure strategies each and assume that the graph $G$ is a tree with maximum degree $3$. Give a polynomial time algorithm to decide if such a game has a pure Nash equilibrium.
The idea seems pretty obvious, every vertex of the tre... |
On the wikipedia article about the polynomial hierarchy http://en.wikipedia.org/wiki/Polynomial_hierarchy
it says "$A^B$ is the set of decision problems solvable by a Turing machine in class A augmented by an oracle for some complete problem in class B"
What is a "Turing machine in class A" for classes P, NP, and coNP?... |
I want to prove that grammar
$$
\begin{cases}
S'\rightarrow S\\
S\rightarrow aSb ~|~ A\\
A\rightarrow bA~|~b
\end{cases}
$$
isn't $LR(1)$. I've constructed parser table and got Shift-Reduce conflict.
I want to prove that without parser table, using another $LR(1)$ definition.
Here's definition:
Grammar is $LR(1)$, if f... |
Recently I got interested in a game called Toads and Frogs and I'm trying my best to come up with some software which would be able to beat an average (i.e. not knowing the strategy) human though I'm struggling with the strategy.
I read on it everything I could google out but turns out there's not that much to read abo... |
I am somewhat a beginner, and I have often seen complexity being calculated for various algorithms but they never actually gave me a very clear idea about how it is done. Can someone please point some resources where I can learn to calculate the complexity of an algorithm?
Secondly, is there some software that calculat... |
I am working with HOL-Light parser and keeping seeing references to preterm parser.
What is a preterm parser?
The most informative statement I find is from the HOL-Light reference for the parse_pretype function.
This is mostly an internal function; pretypes and preterms are used as
an intermediate representation fo... |
What does $A^B$ mean where A and B are complexity classes?
The "Polynomial Hierarchy" page says:
$A^B$ is the set of decision problems solvable by a Turing machine in class A augmented by an oracle for some complete problem in class B
In that case what is a Turing machine in class A?
(besides just a machine of some sor... |
I want to solve the Physical Travelling Salesman Problem using an evolutionary algorithm.
The objective of the PTSP is to visit the maximum number of waypoints of the map in the minimum number of time steps.
The map takes the form of a two-dimensional board, where ten waypoints are scattered around and multiple obstac... |
I have a good understanding of how to program using logic languages, but I'm currently writing up a paper describing some of my work, and I wanted to ensure that I wasn't abusing the proper terminology when describing logic languages. I have a few questions:
What exactly is a predicate? How does a predicate relate to ... |
Constructivist logic is a system which removes the Law of the Excluded Middle, as well as
Double Negation, as axioms. It's described on Wikipedia here and here. In particular, the system doesn't allow for proof by contradiction.
I'm wondering, is anyone familiar with how this affects results regarding Turing Machines ... |
Wikipedia says:
Complete lattices appear in many applications in mathematics and computer science
Is it just referring to the fact that the standard Boolean algebra used in computation is a complete lattice? Is there anything we gain by working at the abstract level of lattices instead of with Boolean logic specifica... |
Consider this small picture of a sunflower, and its histogram:
What would the Fourier transform of the first picture look like? Is there any relationship between the histogram and the Fourier transform?
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I understand the four necessary conditions, mutual exclusion, hold and wait, no preemption, and circular wait, for deadlock to occur. However, does there exist a situation where the four conditions are true and the system is not in a deadlock state?
If a deadlock occurs, there exist the four conditions. However, if th... |
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