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I'm trying to understand DPLL algorithm for solving SAT problem. And here it is:
Algorithm DPLL
Input: A set of clauses Φ.
Output: A Truth Value.
function DPLL(Φ)
if Φ is a consistent set of literals
then return true;
if Φ contains an empty clause
then return false;
for every unit clause l in... |
As it is explained in Sipser's book, the following language is undecidable and he proves this using the computation history method.
$\qquad E = \{\langle M \rangle \mid M\ \mathrm{LBA}, L(M)=\emptyset\}$
I wanted to see if we could use the same method used for proving undecidability of the following language in the cas... |
I have on a few occasions trained neural networks (back propagation networks) with some rather complicated data sets (backgammon positions and OCR). When doing this, it seems that a lot of the work involves trying out different configurations of the networks, in order to find the optimal configuration for learning. Oft... |
Can anyone suggest me some good books on cryptography? I have just starting studying cryptography but I know elementary number theory, abstract algebra and algorithms. Also please mention the difficulty level of the book.
|
Popular view tells us that any kind of information is just a collection of bits, that is zeroes and ones placed in a particular order. I was thus having this thought.
Suppose that I have some kind of file such as a text document, a PDF or anything else and that I also have a memory so perfect that I can remember the fi... |
Counting all possible paths, or all possible paths with a given length, between a couple of nodes in a directed or undirected graph is a classical problem. Attention should be given to what all means, due to the possibles cycles.
This question is slightly different, or at least I think.
INPUT: Be G a directed graph. G... |
Suppose we have a function based on two inputs of length $m,n$. Therefore the time complexity of the function is calculated by $T(m,n)$. Suppose that we have:
$T(m,c)\in O(m^2)$ for any constant $c$.
$T(c',n)\in O(n^2)$ for any constant $c'$.
What can we say about $T(m,n)$?
|
Can someone explain in plain English what "two's complement integer" means? I read this:
in Java long is a 64-bit signed two's complement integer
|
How can I sort a list of 5 integers such that in the worst case it takes 7 compares? I don't care about how many other operations are performed. I don't know anything particular about the integers.
I've tried a few different divide and conquer approaches which get me down to 8 compares, such as following a mergesort ... |
I have a problem similar to the interval scheduling algorithm. The differences are:
The jobs have the same length.
There are several categories of jobs and only one job from each category can be chosen.
There can be no overlap in time between different categories.
I have illustrated the problem with a picture:
Each l... |
I know every regular language is Turing-acceptable, but does that imply it is Turing-decidable?
|
The pumping lemma for regular languages can be used to prove that certain languages are not regular, and the pumping lemma for context-free languages (along with Ogden's lemma) can be used to prove that certain languages are not context-free.
Is there a pumping lemma for deterministic context-free languages? That is, ... |
I was wondering since randomness is embedded in genetic algorithms at almost every level, is there a really fine line between genetic algorithms and pure random search?
Ever since I finished my implementation of a GA , since randomness is present in the mutation function,the initialization part (as well as the reinitia... |
Following method is explained by my senior. I want to know whether I can use it in all cases or not. When I solve it manually, I come to same answer.
$T(n)= 4T(n/2) + \frac{n^2}{\lg n}$
In above recurrence master theorem fails. But he gave me this solution, when
for $T(n) = aT(n/b) + \Theta(n^d \lg^kn)$
if $d = \log... |
A graph $G$ is chordal if it doesn't have induced cycles of length $4$ or more. A clique tree $T$ of $G$ is a tree in which the vertices of the tree are the maximal cliques of $G$. An edge in $T$ corresponds to a minimal separator. The number of distinct clique trees can be exponential in the number of vertices in a ch... |
Wikipedia states the subset sum problem as finding a subset of a given multiset of integers, whose sum is zero. Further it states that it is equivalent to finding a subset with sum $s$ for any given $s$.
So I believe as they are equivalent, there must be a reduction in either side. The one from $s$ to zero is trivial... |
I have to write a regular expression that accepts any odd binary number not preceded by a 0. the best I can come up with is $1(0\cup1)^*1$, but that doesn't match just 1. The best it matches is 11.
|
This was given as a homework problem but I have already submitted the assignment. I'd like to resolve it at this point for my own satisfaction.
Given that $L_1$ is a linear language and $L_2$ is a regular language, show that $L=L_1L_2$ is a linear language.
Recall that a linear grammar $G=(\Sigma, V, P, \sigma)$ has p... |
A common interview question is to give an algorithm to determine if a given binary tree is height balanced (AVL tree definition).
I was wondering if we can do something similar with Red-Black trees.
Given an arbitrary uncoloured binary tree (with NULL nodes), is there a "fast" algorithm which can determine if we can c... |
Wiki has a good cheat sheet, but however it does not involve no. of comparisons or swaps. (though no. of swaps is usually decides its complexity). So I created the following. Is the following info is correct ? Please let me know if there is any error, I will correct it.
Insertion Sort:
Average Case / Worst Case : $\Th... |
If a TM(Turing Machine) accepts NO input string(even the blank), then its language is empty.
If a TM ONLY accepts the blank string(meaning that there is nothing on the tape except for the default blank characters), then its language has only one item and it is the blank string.
Are these definitions correct?
Could you ... |
I was learning about algorithms with polynomial time complexity. I found the following algorithms interesting.
Linear Search - with time complexity $O(n)$
Matrix Addition - with time complexity $O(n^2)$
Matrix Multiplication - with time complexity $O(n^3)$
Is there any algorithm with a higher complexity like $n^4$, ... |
I have read that optimization problems cannot be $\mathcal{NP}$-complete, but are always classified as $\mathcal{NP}$-hard. When a problem is NP-complete, I know it is contained in $\mathcal{NP}$P. This implies in particular that it is not hard for the second level of the polynomial time hierarchy, e.g. for $\Sigma_2^P... |
I need to give a PDA and CFG for a language that contains all binary strings that start and end with the same symbol. I've created the CFG with no problem, but I'm stuck with the PDA and don't quite know how to accomplish it.
The best I can figure is that I need to use non-determinism, but I don't quite know how to app... |
I am asked to construct a PDA to accept the language:
$\qquad \{w \in \{0, 1\}^* : \#_{0}(w) \ge \#_{1}(w)\}$
I am wondering how to interpret the $\#$ symbols and everything. Could someone please explain what exactly this means and how to construct it?
|
I have a heap where both child nodes of the root are 10, and I'd like to perform an operation to remove the min value 9.
I proceed to replacing the root with its next of kin, 18. However when I bubble down, I am unsure of which direction to take.
|
This question asks about NP-hard problems that are not NP-complete. I'm wondering if there exist any decision problems that are neither NP nor NP-hard.
In order to be in NP, problems have to have a verifier that runs in polynomial time on a deterministic Turing machine. Obviously, all problems in P meet that criteria, ... |
This question asks about a corner case of NP classes. From Wikipedia, NP is defined as:
the set of all decision problems for which the instances where the answer is "yes" have efficiently verifiable proofs of the fact that the answer is indeed "yes"
NP-Hard is defined informally as the set of problems that are
at le... |
I have given a post order & in order traversal a BST & I need to construct it. I want to know how to do this.
for eg.
Post Order : DCBGFEA
In Order : BDCAFGE
This is how I am trying to do :
From POST order it is clear that A is root. So in IN order, I consider everything right to A is at it's right sub tree & so fo... |
Let $L$ be a regular language.
Is the language $L_2 = \{y : \exists x,z\ \ s.t.|x|=|z|\ and\ xyz \in L \}$ regular?
I know it's very similar to the question here, but the catch is that it's not a simple substring of a word in a regular language, but rather an "exact middle" - we have to count the prefix and suffix leng... |
When clustering a set of data points, what exactly are the differences between Fuzzy C-Means (aka Soft K-Means) and Expectation Maximization?
In slide 30 and 32 of this lecture I found, it says that Soft K-Means is a special case of EM in Soft K-Means only the means are re-estimated and not the covariance matrix, why's... |
I have an exercise in my book to come up with a pushdown automaton accepting a language.
The exercise is to come up with a state diagram for the PDA accepting the language of all odd-length strings over $\{a, b\}$ with middle symbol $a$.
Here's what I have so far...
I wasn't sure how many states I needed, but I was th... |
I am trying to brush up on my regular grammar knowledge to prepare for an interview, and I just am not able to solve this problem at all. This is NOT for homework, it is merely me trying to solve this.
I want to give a regular grammar for the language of the finite automaton whose screenshot is below, please help me, a... |
I was thinking about how nature can efficiently compute ridiculous (i.e. NP) problems with ease. For example, a quantum system requires a $2^n$ element vector to represent the state, where $n$ is just the number of particles. Nature doesn't need any extra time despite the exponential nature of "solving" this $n$-partic... |
If I have a list of key values from 1 to 100 and I want to organize them in an array of 11 buckets, I've been taught to form a mod function
$$ H = k \bmod \ 11$$
Now all the values will be placed one after another in 9 rows. For example, in the first bucket there will be $0, 11, 22 \dots$. In the second, there will be ... |
In the context of database theory, what does semantic closure mean (linguistically speaking, i.e. not the mathematical definition)
If X is the set of attributes of $F$, then the semantic closure $F^+$ of $F$ is defined as follows:
$F^+=\{$ Y $\rightarrow$ Z $\ |\ $ Y $\cup$ Z $\subseteq$ X $\wedge\ F \models$ Y $\right... |
A simple question:
What would be the complexity of finding whether a hampath of length $k$ exists in a graph with $n$ vertexes where $k < n$?
Would this be in NP-complete or just NP?
|
Small introduction. We have a task that consists of sub-tasks. Each sub-task can be implemented by some set of web-services. We want to find the best implementation of this task. "Best" means it has best values of QoS (availability, latency, cost etc.).
So there are plenty of works:
Canfora G. и др. An approach for Qo... |
Say I have two functions $f(x) = O(1)$ and $g(x) = o(1)$. Let $h(x) = f(x)g(x)$. Is $h(x) = o(1)$?
By definition of small-o $g(x)$ must approach 0 as $x \rightarrow \infty$, so I think yes. However, how can I formally prove it? Is my intuition correct?
|
I have the following question, but don't have answer for this. I would appreciate if my method is correct :
Q. When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70, 80, 90 are traversed, not necessarily in the order given. How many different orders are possible... |
In college we have been learning about theory of computation in general and Turing machines more specifically. One of the great theoretical results is that at the cost of a potentially large alphabet (symbols), you can reduce the number of states down to only 2.
I was looking for examples of different Turing Machines a... |
I am given a list of $n>1$ arrays, where each array has fairly small number of elements (rarely above $5$). Also $n$ is quite small in practice (around $6$).
My problem is that I would like to efficiently map each element product to unique integer. Also, I would like to efficiently compute the integer, when I change th... |
Note: This is a part of a homework question
Were asked to construct a multi-tape Turing Machine for language {$a^n b^n c^n \mid n \geq 0$}
Then it says "Discuss how much time your machines saves over a one-tape DTM using the same algorithm"
Any hint?
Here's my algorithm:
(1) Cut-and-paste c's to tape 3
(2) Cut-and-past... |
I mean Dijkstra's algorithm for the shortest path.
In all descriptions that I saw (including wikipedia),
on every step,
it always selects the nearest neighbor based on examining their weights.
Imagine that we have following paths from source A to destination B
(I will list weights of different paths, not full graph - f... |
I was reading an answer to a recent question, and sort of a strange, ephemeral thought came to mind. My asking this might betray either that my theory chops are seriously lacking (mostly true) or that it's just too early for me to read this site. Now, with the disclaimer out of the way...
It is a well-known result it c... |
How would you algorithmically detect for any given photo whether the sun was shining when the picture was taken?
Examples
A sample from this webcam at a mountain top:
Clearly the sun is shining.
In this other sample it's far less obvious:
One could probably detect fairly easy whether it's foggy by trying to identify... |
I'm a bit confused as to how to represent the Chomsky form for the language L that generates all strings with the alphabet {a}
My approach was
S -> AB | e
A -> a
Now here's the part I'm confused, how do I represent B? If B -> a then I get only even strings, if B -> e then it's not in normal form. :| Any help would be ... |
Prove if a oracle machine $K$ is given with $\mathsf{P^k}=\mathsf{NP}$ then $\mathsf{NP}=\mathsf{co\text{-}NP}$.
Lets assume that $\mathsf{P^k}=\mathsf{NP}$ then $\mathsf{co\text{-}P^k}=\mathsf{co\text{-}NP}$. I am stuck here, I don't know how to prove this. Can someone help?
I know that $\mathsf{P}=\mathsf{co\text{-... |
I am running some experiments with a maze, and trying different variations of A*. Based on my experiments, I have been able to form some opinion (that at least in those cases, graph checking is better than IDA).
I am looking for online articles that have done similar experiments, comparing variations of A* with respec... |
I'm reading about the prize collecting steiner tree problem and an approximation algorithm that uses randomization to set a lower bound on the optimal solution (see Chapter 5.7 in The Design of Approximation Algorithms by Williamson and Shmoys). I don't understand the second line in the proof for Lemma 5.16: .
It see... |
In the field of Cryptography and Computation Complexity there is a notion of negligible function.
I have some difficulties in understanding intuition behind this notion. The following are some definitions from Chapter 9. Cryptography from the textbook Computation Complexity. A modern approach by Arora and Barak with ex... |
So I have a question:
Give a CFG for $\{a^i b^j : 2 i<j\}$
And this is my approach:
$S\to AB$
$A\to aAb\mid \varepsilon$
$B\to b \mid bB$
A confirmation, or correction, along with how you tested(and tips for testing future of my problems) will be greatly appreciated thanks.
|
The usual statement of the fair cake-cutting problem assumes that all $n$ players get their share at the same time. However, in many cases the players arrive incrementally. For example, we may divide a cake over $n$ players, but then a new player arrives and wants a share.
Usually, fair cake division requires a lot of ... |
How to represent the calculation in this image mathematically?
For example: With the discrete convolution
$(f * g)[n]\ \stackrel{\mathrm{}}{=}\ \sum_{m=-\infty}^\infty f[m]\, g[n - m]$
and Fourier transform.
|
I (will, at the end) have a connected, undirected graph with N nodes and 2N-3 edges. You can consider the graph as it is built onto an existing initial graph , which has 3 nodes and 3 edges, iteratively. Every node added onto the graph and has 2 connections with the existing nodes (not necessarily with the initial 3 on... |
For this term:
$\lambda x.(f (g x))$, what are the free and bound variables?
I'm confused as to how to expand this so it will be easier to see.
If I expand this will it be $\lambda x. \lambda f. \lambda g$?
|
I have read many solutions for the minimum cost of triangulation problem and intuitively get the idea , however I am struggling to figure out how to prove it formally. I kind of feel that it has to be proven by induction but I struggle at choosing the right quantity to look at and also at the inductive step portion of ... |
I have been reading about AVL trees, at the moment I'm trying to figure out how to determine the height of a tree and how to draw an AVL tree of some height with minimum number of elements.
In a tutorial I found that this: would be a AVL tree of height 7
And this AVL tree with the height 4
This is really confusing ... |
An intelligent 15-year-old I know is interested in both computer science and genetics. I told her that these fields make an excellent combination. I'd like to give her a book on bioinformatics or computational genomics. I'm looking for a fun book, not a textbook. Specifically, it should inspire people to want to st... |
From what I have understood :
A Flip Flop is a clocked latch i.e. flip flop = latch + clock
Latch continuously checks for inputs & changes the output whenever there is a change in input
Flip Flop also continuously checks input, but changes the output time determined by clock. [so, even though if inputs are changed, it... |
Input:
A list $A=a_1,\ldots,a_n$, with $\oplus$ a associative operation on $M$, and $A\subset M$.
pairs $(s_i,t_i)$ for all $1\leq i\leq m$.
Output:
The list $b_1,\ldots,b_m$, where $b_i = \bigoplus_{j=s_i}^{t_i} a_j$.
We want an efficient algorithm to compute the output, such that it uses minimum number of $\oplus... |
My task is to compare templates of two websites. I am ready with my algorithm. But it takes too much time to give a final answer.
Here, "template" means the way any page presents its contents.
Example:
Any shopping website have page of any Shoes, that contains,
Images in the left.
Price and Size in the right.
Reviews ... |
I'm looking for an algorithm which would find a minimal spanning tree given certain constraints (CSP) about importance of some nodes, e.g. consider a graph with next distance matrix:
$$
\left[ \begin{array}{c}
- & A & B & C & D & E & F \\
A & 0 & 120 & 100 & inf & inf & 30 \\
B & 120 & 0 & 70 & inf & 150 & inf \\
C & 1... |
I'm studying Turing Machines and I've already showed how Turing-Decidable is closed for the operations of Union, Intersection, Concatenation, Complement and Kleene Star. Next I did some demonstrations to show how T-Recognizable languages are closed for Union, Intersection, Concatenation and Kleene Star.
Now I'm trying ... |
$L = \{a^n b^m | m \not= n^2 \}$
I guess I need to use Pumping Lemma for CFL in order to prove this. But I'm stuck.
Assuming that $ a^n b^m = uvxyz$, we know that $v$ or $y$ can not have both $a$ and $b$ symbols in them. Otherwise pumping would generate strings not of the form $a^i b^j$.
Hence both $v$ and $y$ must co... |
I'd appreciate hints for this problem
I'm trying to design a Turing Machine which calculates $\max \{x_1, x_2,..,x_k \}$.
Assuming $1 = 1^1; 2=1^2; n=1^n$ and all numbers/strings are separated by a blank character $B$.
|
The context-free languages are not closed under complement, we know that.
As far as I understand, context-free languages that are a subset of $a^*b^*$ for some letters $a,b$ are closed under complement(!?)
Here is my argument. Each CF language $L$ has a semi-linear Parikh image $\pi(L) = \{ (m,n) \mid a^mb^n \in L \}$.... |
Let's say I have two equations for a geometric object (a rectangle):
$\left\{
\begin{array}{l}
x \ge 0 \\
y \ge 0 \\
A \ge 0 \\
P \ge 0 \\
A = x*y \\
P = 2*x + 2*y
\end{array}
\right.$
Now I would like to set the values of some variables, and compute the values of the other ones.... |
Some sets of ordered binary trees can be represented as a CFG with rules of the form
A -> aBC
A -> b
Where A,B,C are nonterminals and a and b are terminals representing internal nodes and leaf nodes respectively. The tree can be recovered from any word in the language by a preorder traversal.
The set of all such gramm... |
In a depth first tree, there are the edges define the tree (i.e the edges that were used in the traversal).
There are some leftover edges connecting some of the other nodes. What is the difference between a cross edge and a forward edge?
From wikipedia:
Based on this spanning tree, the edges of the original graph can ... |
I wish to understand why P is a subset of PSCPACE, that is why a polynomial-time langauge does have a polynomial-sized circuit. I read many proofs like this one here on page 2-3, but all the proofs use the same technique used in the Cook-Levin theorem to convert the computation of M on an n-bit input x to a polynomial ... |
I'm a bit confused about the definition of BPP. The way BPP is defined in typical text books (Arora/Barak for example) is that if M(x) is a Probabilistic Turing Machine (PTM) that recognizes a language $L(x)$, then $Pr[M(x)=L(x)]> 2/3$. My question is, what is the probability taken over? Arora/Barak remark (7.2) that t... |
In the paper Complexity of the Frobenius Problem by Ramírez-Alfonsín, a problem was proved to be NP-complete using Turing reductions.
Is that possible? How exactly? I thought this was only possible by a polynomial time many one reduction. Are there any references about this?
Are there two different notions of NP-hardne... |
I've done some testing of different initial temperatures in my simulating annealing algorithm and noticed the starting temperature has an affect on the performance of the algorithm.
Is there any way of calculating a good initial temperature?
|
I am having hard times learning Dynamic Programming.
I looked around the web and found many tutorials with examples.
Each time I tried to figure out how to solve a new problem before looking at the solution my mind locked up and I could not continue trying...
I do not where to start!! For example, in divide and conquer... |
An independent set (IS) in a graph is a set $V' \subseteq V(G)$ of pairwise non-adjacent vertices.
I am interested in the generalization $c$-IS where two nodes in $V' \subseteq V(G)$ need to have distance at least $c$ to any other vertex in $V'$.
Has this problem been studied before?
|
Consider an array A[100] & each element occupies 4 word. A 32 word cache is used and divided into 8 word blocks. What is the hit ratio for the following statement. Assume one block is read into cache in case of miss:
for(i=0;i<100;i++)
A[i]=A[i]+10
each array element is of 4 word & each cache block size is 8 words, ... |
I have an exam coming up soon and I need help with this. Consider the problem:
Given a Turing machine $M$, determine if $M$ halts in at most ten steps on every input.
Is this decidable? Prove your answer.
|
I have having trouble with the following question:
Given an NFA $A$ and a regular expression $B$, consider the problem of determining if $L(A) = L(B)$. Is this decidable? Prove your answer.
|
The problem I have is like this bin packing problem, but instead I have $n$ bins and a collection of items with discrete masses. I need to put at least $m$ kg of stuff in each bin.
Is there an efficient way of doing this? Is there a way that will assure there is approximately the same amount in each bin? Does having a ... |
Given the fact that $s$-$t$ path enumeration is a #P-complete problem, could there be efficient methods that compute (or at least approximate) the average length of $s$-$t$ path without enumerating them? What if paths are allowed to revisit vertices?
Relevant results on special graphs could also be helpful.
|
I have a problem that can be viewed in two different ways:
Compute an $n$-dimensional integral, numerical context. The domain of integration is an $n$-dimensional hyper-cube of side $L$.
Count (just count) the roots of an $n$-dimensional function (not a polynomial).
Solving just one of them is sufficient for solving ... |
I am trying to understand Tarjan's strongly connected component algorithm and I have a few questions (the line numbers I am referring to are from Algoritmy.net):
On line 33 why is node.lowlink = min(node.lowlink, n.index) — shouldn't it be same as line 31: node.lowlink = min(node.lowlink, **n.lowlink**)?
Do we have to... |
When talking about Constraint Satisfaction Problems (CSP), what does the term extensional constraint mean?
|
This may be a silly question. It seem clear that an FSA, since it is finite, can only count the number of symbols in its input string up to a number bounded by the number of its states. But now suppose we equip the FSA with output (e.g. printing) capabilities. It would then be very easy to construct a machine capable o... |
In writing a decider for a machine to see if it has made a left move or not on an input of w, it is said that if we continue the computation for $|w|+N+1$ ($N$ : number of states) number of steps, we can make a decision for this decide.
I didn't get why $|w|+N+1$ number of steps. Could someone explain this in more deta... |
This may be basic to some of you, but excuse my inexperience with comp. geometry:
Given a set of $n$ circles with centers $(x_i, y_i)$ for $1 \leq i \leq n$ and each having radii $r$. Also given a rectangle. All objects are on a plane. How to verify that every point inside the rectangle (including its edges) is fully... |
Considering this FSM:
Can someone explain me why the grammar is not:
$S \rightarrow aA$
$A \rightarrow aA \mid bB \mid \varepsilon$
$B \rightarrow bB \mid \varepsilon$
Why does A not have a transition to $\varepsilon$?
|
When Savitch's famous theorem is stated, one often sees the requirement that $S(n)$ be space constructible (interestingly, it is omitted in Wikipedia). My simple question is: Why do we need this? I understand the requirement for $S(n)$ being in $\Omega(\log n)$, which is clear from the proof. But no proof I have seen s... |
I just learned PDAs in class today, but am having problems understanding the syntax of the transition function. Could someone please explain to me the meaning of this syntax:
$\delta(q, \lambda, S) = \{(q, aaB), (q, bbA)\}$
This is one of the rules for my language. I am unsure of what the meanings of this syntax exact... |
According to my understanding, a Turing machine that's valid has to have finite steps to finish a certain step. If this is right, what else determines the validity of a turing machine?
|
We are given an (unsorted) list $L=(a_1,\dots,a_n)$ of numbers of size $n$, where $a_i\in \{ 1,\dots,B\}$.
We want to find the minimum number $x$ from $\{ 1,\dots,B\} \backslash L$.
What is the space complexity of this problem ? (The space to store the input, $L$, does not count.) What if the input $L$ is in a strea... |
I have to solve the following problem:
Consider the problem Connected:
Input: An unweighted, undirected graph $G$.
Output: True if and only if $G$ is connected.
Show that Connected can be decided in polynomial time.
I have been at this for hours, and I can't seem to find a way to prove this.
Any hints?
|
I know that there exists a Turing Machine, if a function is computable. Then how to show that the function is not computable or there aren't any Turing Machine for that. Is there anything like a Pumping lemma?
Similarly, how can we show a language is not recursively enumerable?
|
Is there any set of rules or methods to convert any context free grammar to a push down automata?
I already found some slides online but I wasn't able to understand them.
In slide 10 he speaks about some rules could anyone explain that?
|
Please help me understand, and if possible, tips, to determine a pumping length $p$.
Suppose I have the example :
Let $G$ be a Context-Free-Grammar with a set of variables $\{S,A,B,C\}$, set of terminals $\{0,1\}$, start variable $S$, and rules
$S \to ABA \mid SS$
$A \to S0 \mid 1C1$
$B \to S1 \mid 0$
$C \to 0$
Now g... |
I am a little bit confused by the definition of dominant strategy and winning strategy, what's the difference between them.
Following are the definitions taken from wikipedia, below every definition I added some thoughts. If you fell that my thoughts are not correct or ambigues please let me know.
Dominant strategy.In... |
PIC16F887 Block Diagram
According to the block diagram above, since we already have Program Memory, which may be used to store our program, why should we still need EEPROM? What is it for?
|
Is there a formal definition for a size of a context-free grammar? The only definition I have seen so far is on this wiki page:
The size of a grammar is the sum of the sizes of its production rules, where the size of a rule is one plus the length of its right-hand side.
So, how does one define the size of a producti... |
If there is a Turing Machine $M_e$ (computing some partially computable function $f$), is there an algorithm to decide if $f$ diverges for all possible inputs?
|
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