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Given two regular languages $L_1$ and $L_2$, we define a new language
$$L=\{w_1w_2\mid \text{ there exist two words } x,y \text{ such that } xw_1\in L_1, w_2y\in L2\}$$
How do I show that $L$ is regular with equivalence classes?
My assignment allows the use of closure properties that all regular languages hold, but I ... |
Possible Duplicate:
Is the k-clique problem NP-complete?
I've been lately reading about the clique problem, specifically, the variety of the clique problem of deciding whether a given graph $G$ with $n$ nodes has a clique of at least size $k$.
Why is this problem $NP$-complete? Could one solve this problem in polyno... |
A BTree has a $k$ value that determines that every node has $k$ to $2k$ children. When a node has $2k$ keys it needs to be split into two nodes.
Let's say I want to create a $k/(2k-x)$ tree. (like a 2-3 tree that follows the BTree rules, but isnt $k/2k$)
What is the possible range of $x$? The tree must follow the behav... |
I am trying to create a DFA that can recognize strings with alphabet $\{a,b,c\}$ where $a$ and $c$ appear even number of times and where $b$ appears odd number of times.
I am wondering that this may only be expressed with other methods such as Turing machine or context-free languages.
You might find it fun to think of ... |
For a random undirected graph with $n$ nodes, where each node has $k$ incident edges ($nk/2$ edges in total), the vertex set is partitioned into two sets each having $n/2$ nodes.
What is the order of the number of edges that start in one partition and end in the other?
My back of the napkin calculation is half o... |
I'm reviewing for finals and have a sample problem that I think I understand, but would like someone to bless my understanding or smack me and tell me why I'm wrong.
I'm presented with a problem $\Pi$ of unknown complexity class. If I can transform $\Pi$ to some problem $X$, where $X \in {\sf P}$, what does that tel... |
It is well known that regular languages are characterized by the Myhill-Nerode equivalence. For language $L$ over $\Sigma^*$ define the equivalence $x\sim_L y$ over $\Sigma^*$ iff for all $z\in\Sigma^*$ we have $xz\in L \iff yz\in L$. Then $L$ is regular iff $\sim_L$ is of finite index, i.e., has a finite number of equ... |
Problems in NP have certificates which can be verified in polynomial time.
It seems conceivable that there could be problems in P which have certificates which can be verified in logarithmic time. (Such certificates would also have to be logarithmic in size, naturally.)
However, it is also conceivable that there are n... |
Say I have a context-free grammar defined by the following rule.
$$
\langle EXPR\rangle \rightarrow \langle EXPR\rangle + \langle EXPR\rangle~|~\langle EXPR\rangle \times \langle EXPR\rangle~|~(\langle EXPR \rangle)~|~x
$$
This grammar is ambiguous since, for instance, I can generate the string $x + x \times x$ via mor... |
I am trying to design an efficienct algorithm to color a unicyclic graph. I know if a graph does not contain any cycles (it's a tree) then it is 2-colorable. But cycles are either 2 (is even number of vertices) or 3 (is odd number of vertices) colorable. So if there contains just one cycle then the chromatic number of ... |
Given: $T(n) = T(\sqrt{n}) + 1$ (base case $T(x) = 1$ for $x<=2$)
How do you solve such a recurrence?
|
I am trying to understand why the modular exponentiation algorithm has a running time of about $\log(n)$ where $n$ is the exponent. Here is the algorithm:
function modular_pow(base, exponent, modulus)
result := 1
while exponent > 0
if (exponent mod 2 == 1):
result := (result * base) mod modul... |
I have a data structure described as following:
- It's a collection of trees.
- Each tree has the same structure.
- Each tree has information of diferent nature.
A example of this data structure:
4 - - - - - - - 'a' - - - - - - - 3.5
/ \ / \ / \
3 1 'f' 'y' 1.... |
Apparently, if ${\sf P}={\sf NP}$, all languages in ${\sf P}$ except for $\emptyset$ and $\Sigma^*$ would be ${\sf NP}$-complete.
Why these two languages in particular? Can't we reduce any other language in ${\sf P}$ to them by outputting them when accepting or not accepting?
|
Consider an undirected graph with a source and a sink vertex. We would like to remove minimum number of vertices in that graph to disconnect any path between source and sink.
Can we do this using say a max-flow, min-cut algorithm?
|
I am trying to understand the distributed 6-color algorithm for vertex coloring (on page 10).
Here is a short description
Idea of the algorithm: We start with color labels that have $\log n$ bits. In each synchronous round we compute a new label with exponentially smaller size than the previous label, still guaranteed ... |
How is an arithmetic model defined?
What relations are between it and Turing machine? Are they equivalent in some sense?
Is it true that
in the arithmetic model of computation, the basic arithmetic operations (addition, subtraction, multiplication, division, and
comparison) take a constant unit time step to perform... |
Wikipedia defines it to be
An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm, i.e., $T(n) = O(n^k)$ for some constant k.
The algorithm runs in strongly polynomial time if [8]
the number of operations in the arithmet... |
Let $A$ and $B$ be Turing-recognizable languages. Must language $C = A \cap B$ be Turing-recognizable too?
I have a hunch that it should be because we can construct an enumerator for $C$ by enumerating all the languages in $A$ and then all the languages in $B$.
However, I also know that Turing-recognizable languages ar... |
From Bernhard Korte, Jens Vygen, Combinatorial Optimization,
Instances of LINEAR PROGRAMMING are vectors and matrices. Since no
strongly polynomial-time algorithm for LINEAR PROGRAMMING is known we
have to restrict attention to rational instances when analyzing the
running time of algorithms.
I was wondering wh... |
In other words, $L$ is the language of Turing machines that recognize the language consisting of only themselves.
Why is $L$ not Turing-recognizable? $L$ is clearly not decidable by Rice's Theorem, but how do I go one step further and also prove that no machine can enumerate $L$?
|
I am trying to figure out a greedy algorithm that finds the optimum (minimum) dominating set for any tree in linear time.
So a greedy algorithm to find a dominating set for a general graph is not optimum. It's an approximation of the optimum dominating set. But since this is a tree I am assuming that a greedy algorithm... |
I'm currently learning for an exam about compilers and found the following question:
(3 p.) Bootstrapping: Explain the concepts of rehosting and retargeting. Use T-diagrams.
As far as I understand, rehosting means to compile a compiler for another platform (host), so it should look like this:
-------------
| a ... |
For a given propositional formula f in DNF, one can decide in polynomial time, if the formula is satisfiable:
Just walk through all subformulas (l_1 and ... and l_k) and check, wheter it has NO complementary pair of literals. Formula f is satisfiable iff such subformula exists.
Is my approach above correct ?
If yes, I'... |
Applying a max-flow algorithm to the graph it's trivially possible to find one or two vertex covers, inverting source and sink and the directions of the flows. Is it possible to find more?
|
Summation of $O(n)$ from $1\le k\le n$.
I think it should be $O(n)$ only. Because we are addition $O(k)$ and maximum order will be $O(n)$. But answer is given as $O(n^2)$.
Correct me if I'm wrong.
|
How is asymptotic analysis (big o, little o, big theta, big theta etc.) defined for functions with multiple variables?
I know that the Wikipedia article has a section on it, but it uses a lot of mathematical notation which I am unfamiliar with it. I also found the following paper: http://people.cis.ksu.edu/~rhowell/asy... |
I have a DAG representing strict partial order where each node is an assignment of variables $V$ to their values $v$. Each arc $(u,w)$ represents a change in one variable value such that $u\succ w$.
So if I have $n$ binary variables, I will end up with $2^n$ nodes which is exponential to the size of variables $n$. is ... |
I went through a question asking me to categorize the following grammar.
$$S → AA, S → AB, A → a, A→BB, B → b, B → e$$
From the production rules, clearly it is Context-Free. But it accepts a finite set of strings.
$\{e, a, aa, ab, abb, ba, bba, b, bb, bbb, bbbb\}$
which is regular language.
So, is the above grammar reg... |
Trivially decidable problem is one in which the problem is a known property of the language/grammar. So intersection of two regular languages is regular should be trivially decidable? But it is given as not trivially decidable.
|
Using python need to code a recursive function with one input and no global integers that calculates the number of options to get $x$ using $a*1+b*2+c*3$.
Say $x=3$, there are four options: $\lbrace (1,1,1),(1,2),(2,1),(3)\rbrace$.
|
I am trying to create an isochrone based on the OpenStreetMap data set. Everything works fine, I extracted data, processed it into a DAG, ran a Dijkstra algorithm over it. The result is a subset of the complete graph. This is an impression of the covered parts of the subset displayed over Google Maps:
However, when th... |
Strips –Stands for STanford Research Institute Problem Solver (1971).
STRIPS Pseudo code -
STRIPS(stateListstart, stateListgoals)
1.Set state = start
2.Set plan = []
3.Set stack = goals
4.while stack is not empty do
1.STRIPS-Step()
5.Return plan
STRIPS-Step()
switch top of stack t:
1.case this a goal that match... |
In Fibonacci heaps, we keep a mark field for every node in the heap. Initially all the nodes are unmarked. Once a node is deleted, its parent is marked. If a node is deleted and its parent is already marked, the parent will be cut and inserted into the root list. I just wonder what the purpose of marking is? What happe... |
For 2D polygonal meshes, the QuadEdge and HalfEdge data structure representations are sufficient to store and enable efficient query of all topological and incidence information. Are there compact and efficient data structures for 3D polyhedral meshes? I know there has been some recent work on compact representations f... |
I try to solve exercise "on the power of double - logarithmic space" from the great textbook Computational Complexity by Oded Goldreich.
The goal is to show that the given set $S=\left \{ w_k \mid k \in \mathbb{N} \right \}$, where $w_k$ - concatenation of all $k$-bit long strings separated by *'s is not regular and y... |
I've been reading a lot of computer science literature in the recent past but haven't ran across an explanation of Turing machines, the different types, and why they seem to come up so often (I understand they are a sort of a basis for CS topics).
I've also seen comments by some members mentioning turing-completeness... |
Given following grammar:
$$
\begin{align}
S \rightarrow &A1B \\
A \rightarrow & 0A \mid \varepsilon \\
B \rightarrow & 0B \mid 1B \mid \varepsilon \\
\end{align}
$$
How can I show that this grammar is unambiguous? I need to find a grammar for the same language that is ambiguous, and demonstrate it.
I know if I was aske... |
Given $n$ jobs, schedule them such that the weighted sum is minimum.
weighted minimum sum S for the schedule $\sigma = \{ J_1, J_2, ... J_n \}$ is given by :
$S = \sum_{1\leqq i \leqq n} w_i C_i$ where $C_i\ = \sum_{1\leqq j \leqq i} t_j$ and $w_i$ is the weight of job $J_i$, $t_i$ is the time $J_i$ takes to complete... |
Let $L_\epsilon$ be the language of all $2$-CNF formulas $\varphi$, such that at least $(\frac{1}{2}+\epsilon)$ of $\varphi$'s clauses can be satisfied.
I need to prove that there exists $\epsilon'$ s.t $L_\epsilon$ is $\mathsf{NP}$-hard for any $\epsilon<\epsilon'$.
We know that $\text{Max}2\text{Sat}$ can be approxim... |
Assume i have 2 numbers in binary form (or, more precisely, assume to know the number of their digits, DF1, DF2):
101010101001010101010101010111111111111111111111010101
10101111111111111111010101
Is there a formula for the exact number of binary digits (DP) of the product?
DP = F (DF1, DF2)
[I need this, in a practi... |
There are polynomial time algorithms to find maximum weighted matching in a general graph. Is there any algorithm that also handles negative weights in the general graph and find maximum weighted matching for that graph with negative weights ?
|
I just started reading a book called Introduction to Data Compression, by Guy E. Blelloch. On page one, he states:
The truth is that if any one message is shortened by an algorithm, then some other message needs to be lengthened. You can verify this in practice by running GZIP on a GIF file. It is, in fact, possible t... |
I am unable to understand that what the characteristic path length (CPL) of a graph is.
In one of its definitions, it is written that
it is defined as the median of the means
of the shortest path lengths connecting each vertex to all other vertices.
This is what I understand. Is it right?
Suppose we have 3 nodes A,... |
In [1] strongly-polynomial is defined as either:
The algorithm runs in strongly polynomial time if the algorithm is a polynmomial space algorithm and performs a number of elementary arithmetic operations which is bounded by a polynomial in the number of input numbers.
A polynomial algorithm is a polynomial space algor... |
I have a question about the stable marriage algorithm, for what I know it can only be used when I have arrays with the same number of elements for building the preference and the ranking matrices.
For example if we have 10 students that should be assigned to 10 dorms, then I can build the preference and ranking matrix ... |
I wrote a function to check equality between integers a and b using bitwise shift operators. Return value of 1 means both are Equal and 0 means unequal inputs.
int foo(int a, int b)
{
return ((a>>= b<<= a) ? 1 : 0);
}
How can I prove theoretically that function foo() works for all values in subset of integer r... |
I had an interview today, and the interviewer has told me about a theorem (of someone called Hill- or Hell-something) which states that for a non-deterministic algorithm there exists a deterministic algorithm of some time complexity and a space complexity of no more than the original space complexity times log(n).
I am... |
$S \rightarrow S$, $L(G) = \{\}$
LL(1) analysis:
We estabilish $FIRST(S)$ to be empty and $FOLLOW(S)$ to be $\{\$\}$.
$FIRST(S)$ doesn't contain ε, so the parse table looks like this:
+---+---+
| | $ |
+---+---+
| S | |
+---+---+
and correctly rejects any input including ε.
LR(1) analysis:
We start with the initia... |
I have a language which is made out of and has a grammar only operating on well parenthesized words or words of one symbol. I want to know if the problem of belonging to this language is decidable.
Example. Consider the following grammar:
$$a \to a(aa) \\ a \to b \\a (a(a(ab))) \to b$$
I'll denote by $L(x)$ the languag... |
I am particularly interested in solutions to the problem that encapsulated search can depend on the order of evaluation.
According to [1], encapsulated search in PAKCS depends on the order of evaluation, while in MCC, it does not, but using it requires knowledge of the compiler implementation and it does not follow the... |
I found the algorithm for finding the negative cycle in a graph after running Bellman-Ford algorithm.
The algorithm is to perform another relax iteration over all the edges. Than if we find an edge to relax we stop and start to follow it parent vertex starting from $V$ that $u$ is its parent until we close a cycle.
I'... |
How can someone find what type of grammar for a given programming language?
Formerly I'm looking for a grammar type for most popular programming languages: C, C++, C#, Java, List, OCaml, Haskell etc.
|
Prove that the problem of determining if graph is bipartite is computationally equivalent under log-space reductions to $s$-$t$ undirected connectivity.
Problem of $s$-$t$ undirected connectivity is the following given an undirected graph $G = (V, E)$ and two designated vertices, $s$ and $t$, determine whether there i... |
Given a directed graph $G$, edge weights for each edge, source vertex $s$ and $d[v]$ for each vertex in the graph (the distance from $s$ to $v$), I need to find an algorithm that builds the shortest paths graph.
I was thinking of going on edges by BFS, but then how can I know which edge should be in the tree and how to... |
Counter machines with two or more counters are typically shown to be equivalent to Turing machines in courses on the theory of computation. However, I have not seen a formal analysis of which languages can be recognized by a one-counter machine. Are these languages equivalent to the context-free languages (perhaps by... |
A multiset is an unordered collection of elements where elements may repeat any
number of times. The size of a multiset is the number of elements in it counting
repetitions.
(a) What is the number of multisets of size $4$ that can be constructed from $n$
distinct elements so that at least one element occurs exactly twi... |
In their book Randomized Algorithms, Motwani and Raghavan open the introduction with a description of their RandQS function -- Randomized quicksort -- where the pivot, used for partitioning the set into two parts, is chosen at random.
I have been racking my (admittedly somewhat underpowered) brains over this for some t... |
I've come across many definitions of recursive and recursively enumerable languages. But I couldn't quite understand what they are .
Can some one please tell me what they are in simple words?
|
I have read a few algorithms for $LR(k)$ parser, in which there is a frequent mention of selecting a handle from the grammar given.
For example, one document said - "the essence of LR parsing is identifying the handle on top of stack"
Please help me understand, what are handles in parsing?
|
I need some help with the following problem. Let $L \subseteq \Sigma^*$ be a regular language. I have to prove that the language $P = \{\alpha \mid \beta\alpha\gamma \in L, \beta,\gamma \in \Sigma^*\}$ is regular, where $\Sigma$ is the alphabet. In other words $P$ is the language of all substrings of words from $L$. H... |
$$\text{maximize } f(\mathbf{x}) \quad\text{subject to } \mathbf{Ax} = \mathbf{b}$$
where
$$f(\mathbf{x}) = \sum_{i=1}^N\sqrt{1+\frac{x_i^4}{\left(\sum_{i=1}^{N}x_i^2\right)^2}},$$
$\mathbf{x} = [x_1,x_2,...,x_N]^T \in \mathbb{R}^{N\times 1}$ and $\mathbf{A} \in \mathbb{R}^{M\times N}$.
We can see that $f$ is convex ... |
I received the following assignment:
$\text{EXACT-TRIPLE} = \{ \phi \mid \phi \text{ is a boolean formula that has exactly 3 satisfying assignments} \}$.
I need to decide whether this problem belongs to NP or not. I assume it does not. How do I prove that?
|
I try to provide a strict and mathematical rigorous proof to the following problem in Distributed Algorithms.
Prove or make a contradiction: if to vertices $a$ and $b$ on the network $G$ are located on the distance $k$ from each other, and there are $k^2$ different paths on different edges, so it is possible to transf... |
Consider a sequence of $n$ flips of an unbiased coin. Let $H_i$ denote the absolute value of the excess of the number of heads over tails seen in the first $i$ flips. Define $H=\text{max}_i H_i$. Show that $E[H_i]=\Theta ( \sqrt{i} )$ and $E[H]=\Theta( \sqrt{n} )$.
This problem appears in the first chapter of `Randomi... |
I am interested in the stateless k-armed bandit problem, where an agent repeatedly chooses one of k independent arms, each with a different distribution of rewards, and tries to maximize its total reward.
I read many papers about this subject, but I am still confused, as there are two types of solutions:
A. It has been... |
I try to solve an exercise in Distributed Algorithm described as follow.
Let's define a label assignment problem as follow. There is a anonymous network (vertices don't have unique ID's , nodes don't have any clue about $n$ - number of vertices nor about network topology ). The labels assigned to vertices must be disti... |
A function in $\Theta(m + n^2)$ and $0 < m < n^2$, is in $\Theta(n^2)$. Does a function in $\Theta(m\log n)$ and $0 < m < n^2$, imply that it is $\Theta(n^2\log n)$?
|
First of all sorry, if this question already exists, in that case, pointing to the right direction will be appreciated.
Secondly, sorry, if the question is below the expected level of Niveau, but all help appreciated.
In the textbook by J. Hromkovic, named "Theoretical Computer Science, Introduction to Automata, Comput... |
XOR is not the correct name, but I am looking for some kind of exclusive behavior.
I am currently solving a set of different (assignment) problems by modeling flow networks and running a min-cost-max-flow algorithm. Flow networks are quite handy because a lot of problems can be reduced to them in an easy and understand... |
G=({S,A,B},{0,1},P,S)
Where P:
S→A1B
A→0A|ε
B→0B|1B|ε
I have to list the first 25 strings from L(G). So far I've made the tree, but I'm not sure that it's correct.
|
I have to solve system of linear algebraic equations $AX=B$, where $A$ is a two-dimensional matrix with all elements of main diagonal equal to zero.
How to solve this problem? Iterational methods are not applied in this case.
One way is LU Decomposition method with reordering rows of $A$ to get entries in the main diag... |
In a bridge game, a deck of 52 cards (13 spades , 13 clubs, 13 diamonds, 13 spades) are dealt to 4 players (13 cards each) then game starts.Game session ends after 13 tricks each having 4 cards.There are 28561 possible non repeated 4 card groups.
What is the best method of generating and storing all possible trick comb... |
Given an integer array (maximum size 50000), I have to find the minimum and maximum $X$ such that $X = a_p \oplus a_{p+1} \oplus \dots \oplus a_q$ for some $p$, $q$ with $p \leq q$.
I have tried this process: $\text{sum}_i = a_0 \oplus a_1 \oplus \dots \oplus a_i$ for all $i$. I pre-calculated it in $O(n)$ and then th... |
I saw in this video that computing clustering coefficient of central node of a star graph using the following algorithm is $\Theta(n^2)$ and for a clique it is $\Theta(n^3)$. is that correct?
def clustering_coefficient(G,v):
neighbors = G[v].keys()
if len(neighbors) == 1: return 0.0
links = 0.0
for w i... |
Using the Shortest-Seek-Time-First (SSTF) disk scheduling algorithm (where we select a request with a minimum seek time from the current head position), what happens if the requests in both directions from the current head position are equal?
For example, if the head position is at 25, and the nearest positions are 5 ... |
my assumption:
- we have an undirected graph with only positive edges
- the edges are sorted alphabetically:
e.g A-B, A-C, B-D
and e.g not C-A, D-B, A-B
I do not understand, why we need the first loop (line 1) here.
I executed the algorithm on paper on 3-4 different undirected graphs.
And everytime the first... |
When we say that in random graph we add an edge with a certain fixed probability, what do we actually mean?
For example if probability is 0.5, does that mean that we can just add two edges in a graph because 0.5+0.5=1.
|
my question is simple.
Is it possible to use plants as a medium to store data?
My opinion is: Possible, but we need to solve, how to distinguish 2 states.
Duplication and CRC of stored DATA is quiet simple. Growing new plants is easiest possibility, but we need to create unit, which will take care about raid and dupli... |
I'm trying to practice myself with random algorithms.
Lets call a CNF formula over n variables s-formula if it is either unsatisable or it has at
least $\frac{2^n}{n^{10}}$ satisfying assignments.
I would like your help with show a randomized algorithm for checking the
satisfiability of s-formulas, that outputs the cor... |
In an unweighted, undirected graph with $V$ vertices and $E$ edges such that $2V \gt E$, what is the fastest way to find all shortest paths in a graph? Can it be done in faster than Floyd-Warshall which is $O(V^3)$ but very fast per iteration?
How about if the graph is weighted?
|
Computer Networking:
A Top Down Approach
Featuring the Internet,
Jim Kurose, Keith Ross
Addison-Wesley 4nd edition , page -223.
Also here slide 60 .
RDT2.1 (Reliable data transfer) -
Sender(s):
state=ready; i=0;
On rdt_send(d,m):
if state=ready
then
{ p=<s,d,m,i,
EDC(s||d||m||i)>;
udt_send... |
INPUT: "an undirected, weighted graph (negative weights allowed)"
Could someone give an example for an undirected graph with negative edges where Dijkstra's algorithm doesn't work?
As far as i understood it only fails by directed graphs in case of negative edges.
Am i right ?
|
As I know, there are several upper bounds on the generalization error of hypothesis set with respect to sample complexity. For hypothesis space $V$, if the learning algorithm output the set of hypotheses that are consistent with the training data, i.e., $\sum\limits_{1 \leq i \leq n}{\frac{I[h(x_i) \not= y_i]}{n}} = 0$... |
Why are computable numbers (in Turing's sense) enumerable?
It must be very obvious, but I'm currently just not seeing it.
|
Is it possible that $\mathsf{P} \not = \mathsf{NP}$ and the cardinality of $\mathsf{P}$ is the same as the cardinality of $\mathsf{NP}$? Or does $\mathsf{P} \not = \mathsf{NP}$ mean that $\mathsf{P}$ and $\mathsf{NP}$ must have different cardinalities?
|
I have a question that I still struggle with.
It would be really appreciated if you guys could give me some hints.
Here is the problem :
Assume that $a[1\dots n]$ is an array of $n$ positive real numbers.
Let $\alpha >0$ and $\beta >0$
a subarray $a_1$ with $m$ elements of $a[1 \dots n]$ is called increasing if $\fra... |
3-Coloring problem can be proved NP-Complete making use of the reduction from 3SAT Graph Coloring (from 3SAT). As a consequence, 4-Coloring problem is NP-Complete using the reduction from 3-Coloring:
Reduction from 3-Coloring instance: adding an extra vertex to the graph of 3-Coloring problem, and making it adjacent t... |
We commonly create sub-groups of strings in one particular algorithm implementation. I just want to know in CS literature is there any standard name for such kind of grouping. For e.g.
Hello World! This is May from the dairy farm.
Strings with sub-groups of two:
Hello World!
World! This
This is
is May
...
|
Is there an undecidable problem which is not NP-hard?
|
Which tools or softwares are mostly used for the purpose of modeling a computer network?
|
I need help with the following question:
Order the following formalisms according to their expressive power:
placing A before B means that any language definable by A is definable
by B. Also state which, if any, of them are equivalent.
• Turing Machines (TM)
• Regular expressions (reg.exp.)
• Turing Machines with multi... |
I have a background in computer architecture and only cursory understanding of process networks. For a paper I am writing I need to understand prefix monotonicity properly.
For now I have "a stream transformer is prefix monotonic if its output for a given input record r is dependent only on the input stream up to and ... |
The universal Turing machine $U_{TM}$ is a TM that takes in as input an encoding of a TM and a string, then runs the TM on the string and does whatever the simulated TM does. The language of the universal TM is the set of all encodings of a TM/string pair as a string for which the TM accepts the string.
I have seen se... |
What are the key differences between these three terms isomorphism, automorphism and homomorphism in simple layman language and why we do isomorphism, automorphism and homomorphism ?
|
I have a recursive algorithm with time complexity equivalent to choosing k elements from n with repetition, and I was wondering whether I could get a more simplified big-O expression. In my case, $k$ may be greater than $n$ and they grow independently.
Specifically, I'd expect some explicit exponential expression.
The... |
Suppose we have a function on GPU which calculates elements of array from which we need to select top K elements. The number of elements can be quite big so we can't store them in memory and our algorithm should be online. Another requirement for algorithm is its good parallelization so it could be effectively run on G... |
I’m trying to make a photo mosaic web application. I split the main picture in to a number of squares. I split this square up in to 9 squares.
Then I calculate the mean color (RGB) of the entire square and the mean color of the 9 little squares. So I will get the following vector.
Vector: Mean R; mean G; mean B; cell... |
Suppose I have a set of sets of integers $A$, is there an efficient algorithm/data structure that will allow me to query for all sets of integers that include a given input set? That is, given input $I\subset \mathbb Z$, find $C$, the sets in $A$ that include all of $I$, that is $C=\left\{ B \in A \mid I\subseteq B\rig... |
Applicative order: Always fully evaluate the arguments of a function
before evaluating the function itself , like -
$(\lambda x. x^2(\lambda x.(x+1) \ \ 2))) \rightarrow (\lambda x.
x^2(2+1))\rightarrow \ (\lambda x. x^2(3)) \rightarrow \ 3^2 \
\rightarrow \ 9$
Normal order: The expression would be reduced from ... |
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