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In terms of references and their implementation on the heap and the stack, how is
equality testing for arrays different from that for integers?
This is to do with Java programming, if you have a stack and a heap, would equality testing for example j == i be the same for arrays and for integers? I understand that array... |
How do I build a random source that outputs the bits 0 and 1 with $prob(0) = prob(1) = 0.5$. We have access to another random source $S$ that outputs $a$ or $b$ with independent probabilities $prob(a)$ and $prob(b) = 1 - prob(a)$ that are unknown to us.
How do I state an algorithm that does the job and that does not co... |
Two processors $A, B$ with inputs $a \in \{0, 1\}^n$ (for $A$) and $b \in \{0, 1\}^n$
(for $B$) want to decide whether $a = b$. $A$ does not know $B$’s input and vice versa.
A can send a message $m(a) \in \{0, 1\}^n$ which $B$ can use to decide $a = b$. The communication and computation rules are called a protocol.
... |
A source provides a stream of items $x_1, x_2,\dots$ . At each step $n$ we want to save a random sample $S_n \subseteq \{ (x_i, i)|1 \le i \le n\}$ of size $k$, i.e. $S_n$ should be a uniformly chosen sample from all $\tbinom{n}{k}$ possible samples consisting of seen items. So at each step $n \ge k$ we must decide whe... |
I'm looking for some relatively simple examples of when structural hazards occur in a pipelined architecture.
The only scenario I can think of is when memory needs to be accessed during different stages of the pipeline (ie, the initial instruction fetch stage and the later memory read/write stage).
I'm thinking that th... |
I want to convert a user entered regular expression into an NFA so that I can then run the NFA against a string for matching purposes. What is the minimum machine that can be used to parse regular expresssions?
I assume it must be a push down automaton because the presense of brackets means the need to count and a DFA... |
The exercise is
Given a set of point $S$ and a point $p$. Decide in $O(n)$ time if $p$ is a vertex of convex polygon formed from points of $S$.
The problem is I am a little bit confused with time complexity $O(n)$. The more naive solution would be to construct convex polygon in $O(n\log n)$ and test if $p$ is one o... |
For the purpose of proving that they are not regular, what closure properties can I use to transform the languages
$L_a = \{ a^*cw \mid w \in \{a,b \}^* \land |w|_a = |w|_b \}$ and
$L_b = \{ab^{i_1}ab^{i_2}\ldots ab^{i_n} \mid i_j∈\mathbb N \land \exists j∈[1,n] \ i_j \not= j \}$
to $L := \{ a^nb^n \mid n\in \ma... |
As a university-level CS educator, the issue of which programming language to teach in the first programming course often comes up for discussion. There are thousands of languages to choose between, and lots of religious fever (or fevour) supporting one language camp over another. All of this subjective bias surroundin... |
Given the following recursive equation
$$ T(n) = 2T\left(\frac{n}{2}\right)+n\log n$$ we want to apply the Master theorem and note that
$$ n^{\log_2(2)} = n.$$
Now we check the first two cases for $\varepsilon > 0$, that is whether
$n\log n \in O(n^{1-\varepsilon})$ or
$n\log n \in \Theta(n)$.
The two cases are not s... |
I am reading "An Introduction to Formal Languages and Automata" written by Peter Linz and after reading the first five chapters I face below problem with
simple and regular (especially right linear) grammars which are very similar to each other.
What relation exists between these? What is the difference?
Can you create... |
I have an algorithm, shown below, that I need to analyze. Because it's recursive in nature I set up a recurrence relation.
//Input: Adjacency matrix A[1..n, 1..n]) of an undirected graph G
//Output: 1 (true) if G is complete and 0 (false) otherwise
GraphComplete(A[1..n, 1..n]) {
if ( n = 1 )
return 1 //one-... |
Is there a data structure to maintain an ordered list that supports the following operations in $O(1)$ amortized time?
GetElement(k): Return the $k$th element of the list.
InsertAfter(x,y): Insert the new element y into the list immediately after x.
Delete(x): Remove x from the list.
For the last two operations, y... |
Given a context-free grammar G, there exists a Nondeterministic Pushdown Automaton N that accepts exactly the language G accepts. (and visa versa)
There may also exist a Deterministic Pushdown Automaton D that accepts exactly the language G accepts too. It depends on the grammar.
By what algorithm on the productions o... |
I'm applying the Compare-and-Swap technique to a SQL database to create custom row-level locking in my dataset, allowing for safe READ UNCOMMITTED isolation at the database level.
The Resource table includes a LockOwner GUID and a IsLocked BIT field. To acquire a lock, a dirty-read query gets the ID, LockOwner, and Lo... |
I would like to use your help with the following problem:
$L=\{⟨M⟩ ∣ L(M) \mbox{ is context-free} \}$. Show that $L \notin RE \cup CoRE$.
I know that to prove $L\notin RE$, it is enough to find a language $L'$ such that $L'\notin RE$ and show that there is a reduction from $L'$ to $L$ $(L'\leq _M L)$.
I started to thi... |
Consider the following query:
SELECT Customer.Name FROM Customer
INNER JOIN Order on Order.CustomerId = Customer.Id
WHERE Customer.Preferred = True AND
Order.Complete = False
Let's suppose all of the relevant attributes (Customer.Preferred, Order.Complete, Order.CustomerId and Customer.Id) are indexed. How can I... |
I'm learning for the exam and have problems with this task:
Describe an algorithm that transforms a given NFA $A = (Q, \Sigma, \delta, q_0, F)$ (which may have $\epsilon$-transitions) into an equivalent NFA without $\epsilon$-transitions with the same condition number. And then determine the maturity of the algorithm.... |
As follows from my previous question, I've been playing with the Riemann hypothesis as a matter of recreational mathematics. In the process, I've come to a rather interesting recurrence, and I'm curious as to its name, its reductions, and its tractability towards the solvability of the gap between prime numbers.
Tersel... |
I've got in a few days an exam and have problems to solve this task.
Let $L$ be a regular language over the alphabet $\Sigma$. We have the operation
$\operatorname{cycle}(L) = \{ xy \mid x,y\in \Sigma^* \text{ and } yx\in L\}$
And now we should show that $\operatorname{cycle}(L)$ is also regular.
The reference is that... |
Who can help me with this topic: Probing with a step width that is a prime number.
I am struggling with this question about defining a hashing function $h(k, i)$ for open addressing on a table of length m, that is, with slots numbers $0, 1, 2, \dots ,m − 1$.
We know that a function $h(k, i) = h_1(k) + i \cdot h_2(k) \m... |
Is there a need for $L\subseteq \Sigma^*$ to be infinite to be undecidable?
I mean what if we choose a language $L'$ be a bounded finite version of $L\subseteq \Sigma^*$, that is $|L'|\leq N$, ($N \in \mathbb{N}$), with $L' \subset L$. Is it possible for $L'$ to be an undecidable language?
I see that there is a prob... |
From this statement
As there is no surjection from $\mathbb{N}$ onto $\mathcal{P}(\mathbb{N})$, thus there must exist an undecidable language.
I would like to understand why similar reasoning does not work with a finite set $B$ which also has no surjection onto $\mathcal{P}(B)$! (with $|B|=K$ and $K \in \mathbb{N}$... |
Let $G = (V,E)$ be a graph having $n$ vertices, none of which are isolated, and $n−1$ edges, where $n \geq 2$. Show that $G$ contains at least two vertices of degree one.
I have tried to solve this problem by using the property $\sum_{v \in V} \operatorname{deg}(v) = 2|E|$. Can this problem be solved by using pigeon h... |
Is the set of LL(*) grammars the same as the set of context-free grammars?
|
I am new and I have to develop an algorithm with a 2d integer array as input to compute the best career path.
Lets consider a network with n nodes, which are numbered from $1$ to $n$.
All are connected one to the other.
To move from node $i$ to node $j$ can have different costs (classical example job changing):
posit... |
Which machine learning algorithms (besides SVM's) use the principle of structural risk minimization?
|
I read that testing the length of the input string is in DLOGTIME.
The question is how can testing the length of the input string be in DLOGTIME?
$\text{DLOGTIME} = O(\log n)$, so what number would be in $n$? (as it seems that $n$ is definitely not the length of the input string..... or is it?)
So, to summarize, can an... |
Converting regular expressions into (minimal) NFA that accept the same language is easy with standard algorithms, e.g. Thompson's algorithm. The other direction seems to be more tedious, though, and sometimes the resulting expressions are messy.
What algorithms are there for converting NFA into equivalent regular expre... |
I am trying to solve the following computational geometry problem.
Let $S$ be a set of $n$ axis-parallel rectangles in the plane, so that the bottom edge of each rectangle in $S$ lies on the $x$-axis.
What is (an upper bound on) the combinatorial complexity of the union $K$ of the rectangles in $S$?
Give an efficient... |
Possible Duplicate:
Construction of a regular expression
can someone help me with the following exercise?
In the formation of a regular expression from a finite automaton $A$ with three states they have been calculated the following parts, in which 1,2 and 3 been renamed, 1 is the start state and 2,3 are accepting s... |
I need help with the following exercise:
Construct an $\varepsilon$-NFA for the following regular expression $(a|\varepsilon)(ba)^*(c^*a|bc)^*$.
i already tried this exercise with nerode but i didnt come to a solution please help me
thank you guys
Source wiki
Nerode : (Given a language L, and a pair of strings x and y,... |
In a directed graph with a starting node and an ending node, how to find a small (doesn't have to be smallest. <10 for example) set S of nodes such that every possible path from the starting node to the ending node contains at least one member of set S. The graph may have loops. This may be NP hard. Is there an approxi... |
If an encryption algorithm is meant to convert a string to another string which can then be decrypted back to the original, how could this process involve any randomness?
Surely it has to be deterministic, otherwise how could the decryption function know what factors were involved in creating the encrypted string?
|
Is "party attendance" type of problems solvable in Prolog? For example:
Burdock Muldoon and Carlotta Pinkstone both said they would come if Albus Dumbledore came. Albus Dumbledore and Daisy Dodderidge both said they would come if Carlotta Pinkstone came. Albus Dumbledore, Burdock Muldoon, and Carlotta Pinkstone all sa... |
I have a "smarter" version of Bellman-Ford here; this version is more clever about choosing the edges to relax.
//Queue Q; source s; vertices u, v; distance to v d(v)
Q ← s // Q holds vertices whose d(v) values have been updated recently.
While (Q !empty) {
u ← Dequeue(Q)
for each neighbor v of u {
Relax(u, v)
... |
Most of the computers available today are designed to work with binary system. It comes from the fact that information comes in two natural form, true or false.
We humans accept another form of information called "maybe" :)
I know there are ternary processing computers but not much information about them.
What is the ... |
I'm trying to prove that every well-balanced orientation of an Eulerian graph is Eulerian.
I want to prove it by showing that for any two vertices $u$ and $v$, their local arc connectivities coincide, that is
$\qquad \displaystyle P_D'(u,v)=P_D'(v,u)$
for every well-balanced orientation of an Eulerian graph. How can I... |
In the usual definition of probabilistic poly-time machine it is said that the machine halts in polynomial time for all inputs.
Is the intention really to say that the machine halts for all inputs, or that if it halts it must be in polynomial time?
|
Are there any advantages of having more than 2 hidden layers in a Neural Network?
I've seen some places that recommend it, others prove that there is no advantage.
Which one is right?
|
Solving the maximum flow problem yields one qualified minimal cut. But I want several (maybe hundreds) small cuts as candidates. The cuts don't have to be minimum cuts, as long as they are small (in weight). How do I do that?
|
Preface: This question was originally asked on Theoretical Computer Science, and the kind people there referred me to this web site. It is being repeated here in an attempt to find a satisfying answer.
Over the years, two novel encryption techniques have come to mind and been implemented as programming libraries that ... |
Dynamic programming can reduce the time needed to perform a recursive algorithm. I know that dynamic programming can help reduce the time complexity of algorithms. Are the general conditions such that if satisfied by a recursive algorithm would imply that using dynamic programming will reduce the time complexity of the... |
How do you check if two algorithms (say, Merge sort and Naïve sort) return the same result for any input, when the set of all inputs is infinite?
Update: Thank you Ben for describing how this is impossible to do algorithmically in the general case. Dave's answer is a great summary of both algorithmic and manual (subjec... |
I need to recover a data block from a repeated stream of data. I'm looking to see what algorithms may already exist for this as it does not feel like a novel situation.
Here are the specifics:
There is an N-length block of data contained in a stream
The block is repeated many times in the stream
the data is highly cor... |
I have to make a quick clustering program but the following formula is gibberish to me:
$\operatorname{Perf}(X,C) = \sum\limits_{i=1}^n\min\{||X_i-C_l||^2 \mid l = 1,...,K\}$
where $X$ is a set of multi-dimensional data and $C$ is a set of centroids for each data cluster.
This formula is a fitness function for an a... |
I try to solve the following coverage problem.
There are $n$ transmitters with coverage area of 1km and $n$ receivers. Decide in $O(n\log n)$ that all receivers are covered by any transmitter. All reveivers and transmiters are represented by their $x$ and $y$ coordinates.
The most advanced solution I can come with t... |
For my pet project I need to cluster some data which could be easily represented as graph, so I want to use this as an opportunity to educate myself and play with various algorithms. I'd prefer the book on graph clustering as it often more self contained but articles are fine too. Back in the days I used to work in the... |
We receive a stream of $n-1$ pairwise different numbers from the set $\left\{1,\dots,n\right\}$.
How can I determine the missing number with an algorithm that reads the stream once and uses a memory of only $O(\log_2 n)$ bits?
|
I know that there are non-regular languages, so that $L^*$ is regular, but all examples I can find are context-sensitive but not context free.
In case there are none how do you prove it?
|
I've been looking around for an algorithm that would optimize the distance between 2 list of coordinates and choose which coordinate should go together.
Say I have List 1:
205|200
220|210
200|220
200|180
List 2:
210|200
207|190
230|200
234|190
Calculated Distance between Coords:
205|200 to 210|200 == 5.00
205|200 to ... |
We know that the $polyL$-hierarchy doesn't have complete problems, as it would conflict with the space hierarchy theorem. But: Are there complete problems for each level of this hierarchy?
To be precise: Does the class $DSPACE(\log(n)^k)$ have complete problems under $L$-reductions for each $k > 0$?
|
Reading the paper An Introduction to the Lambda Calculus, I came across a paragraph I didn't really understand, on page 34 (my italics):
Within each of the two paradigms there are several versions of typed
lambda calculus. In many important systems, especially those a la
Church, it is the case that terms that do h... |
I'm looking for a data structure that supports efficient approximate lookups of keys (e.g., Levenshtein distance for strings), returning the closest possible match for the input key. The best suited data structure I've found so far are Burkhard-Keller trees, but I was wondering if there are other/better data structures... |
Has anyone seen this problem before? It's suppose to be NP-complete.
We are given vertices $V_1,\dots ,V_n$ and possible parent sets for each vertex. Each parent set has an associated cost. Let $O$ be an ordering (a permutation) of the vertices. We say that a parent set of a vertex $V_i$ is consistent with an ordering... |
I have problem with solving the following exercise
Given the set $P$ on $n$ points in two dimensions, build in time $O(n\log n)$ a data structure of $P$ such that given a horizontal segment $s$ find the first point that $s$ touches when moving upwards from the x-axis in time $O(\log^2n)$.
The preprocessing time is eq... |
It is well-known that every boolean function $f:\{0,1\}^n\to \{0,1\}$ can be realized using a boolean circuit of depth 2 (over the variables, their negation and constant values) containing AND gates in the first level and one single OR gate in the upper level; this is simply the DNF representation of $f$.
Another type ... |
I have the following question from Computational Complexity - A modern Approach by Sanjeev Arora and Boaz Barak:
[Q 4.1]
Prove the existence of a universal TM for space bounded computation (analogously to the deterministic universal TM of Theorem 1.9).
That is, prove that there exists a Turing Machine $SU$ such th... |
There is a family of random graphs $G(n, p)$ with $n$ nodes (due to Gilbert). Each possible edge is independently inserted into $G(n, p)$ with probability $p$. Let $X_k$ be the number of cliques of size $k$ in $G(n, p)$.
I know that $\mathbb{E}(X_k)=\tbinom{n}{k}\cdot p^{\tbinom{k}{2}}$, but how do I prove it?
How to s... |
If I were to let the variables be the propositions and, constraint be all clauses being satisfied, which technique would be more effective in solving 3-SAT? Forward checking or arc consistency? From what I gathered forward-checking is $O(n)$, while Arc consistency is about $O(8c)$ where c is the number of constraints (... |
As discussed in this question, I drafted a spec algorithm that hinges on finding a specific root of a system of trigonometric equations satisfying the following recurrence:
$\qquad f_{p_0} = 0\\
\qquad p_0 = 2\\
\qquad \displaystyle
f_{p_n}(x) = f_{p_{n-1}}(x) + \prod_{k=2}^{p_{n-1}} (-\cos(2\pi(x+k-1)/p_{n-1}) + 1)\... |
My problem is how can I transform a regular grammar into a linear grammar?
I know that a linear grammar has the form
$\begin{align} A &\to w_1Bw_2 \\
A &\to w \end{align}$
where $A,B \in N$ and $w,w_1,w_2 \in \Sigma^*$.
|
I've got a problem with this task. I should declare a context-free grammar for this language:
$\qquad \displaystyle L := \{\, a^nb^ma^{n+m} : n,m \in \mathbb{N}\,\}$
My idea is: We need a start symbol, for example $S$. I know that I can generate the first $a$ and the last $a$ by $S \to a a$. I don't know what is the ne... |
It is a trivial exercise in finite automata to show that there is no algorithm that can detect all the viruses, yet there are many software companies selling Anti Virus Software.
Is there any part of CS that deals with Viruses and Anti Viruses ?
PS : I am not asking about non CS related justification of to have AV or n... |
I'd like to understand the Baum-Welch algorithm. I liked this video on the Forward-Backward algorithm so I'd like a similar one for Baum-Welch.
I'm having trouble coming up with good resources for Baum-Welch. Any ideas?
|
I need to prove that $\mathsf{NP}$ is a subset of the union of $\mathsf{DTIME}(2^{n^c})$ for all $c > 1$.
Let $L$ be a language/decision problem in $\mathsf{NP}$. Then $L$ can be decided given a polynomial-size certificate in polynomial time with a turing machine $M$. So then we enumerate all possible certificates of p... |
I have two ways of producing a list of items in a random order and would like to determine if they are equally fair (unbiased).
The first method I use is to construct the entire list of elements and then do a shuffle on it (say a Fisher-Yates shuffle). The second method is more of an iterative method which keeps the li... |
The following is a doubt that I came across while doing a OS home assignment - however, it seems more concept-based than a straightforward coding question, so IMHO I don't think the homework tag is appropriate for this.
In a pure demand paging scheme for multiple processes running at the same time, given a fixed amount... |
I started reading more and more language research papers. I find it very interesting and a good way to learn more about programming in general. However, there usually comes a section where I always struggle with (take for instance part three of this) since I lack the theoretical background in computer science: Type Rul... |
Alternative Formulation
I came up with an alternative formulation to the below problem. The alternative formulation is actually a special case of the problem bellow and uses bipartite graphs to describe the problem. However, I believe that the alternative formulation is still NP-hard. The alternative formulation uses a... |
i have the following regular grammar :
$$S \rightarrow aS | cS | bQ_1$$
$$Q_1 \rightarrow bQ_2$$
$$Q_2 \rightarrow aQ_3 | cQ_3 | bQ_1$$
$$Q_3 \rightarrow aQ_4 | cQ_4$$
$$Q_4 \rightarrow \varepsilon$$
The question is to transform that into a linear grammar with less nonterminals than the regular grammar and my idea was... |
We have the following linear grammar:
$$E \rightarrow aO | bO | bbE | bb$$
$$O \rightarrow aE | bE | abaE | aba$$
Does the linear grammar generate a regular language, if yes why ?
Our alphabet is $\Sigma$ = {a,b} and our nonterminals are E and O. We begin by E.
|
In thinking about how to approach this problem I think several things will be required, some tivial:
An expression tree where non-leaf node is an operation (not sure if that part is redundant), but not every node has just two children.
All nodes for operations have a defined number of children that they must have (som... |
Alexia Massalin's Dissertation on Synthesis was a Phd thesis on Operating Systems that contained a concept called 'Quajects' (see Chapter 4).
This is some additional commentary on the Phd Thesis.
Best I can work out - a Quaject is construct that generates Assembler customised for the function being used at the time. ... |
I have a directed acyclic graph where edge (A,B) means that vertex A depends on vertex B.
Vertex deletions have the following restrictions:
When vertex B is removed, all dependent vertexes should also be removed.
When vertex A is removed and vertex A was the only vertex that depends on B, vertex B should also be re... |
You are given n integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ between $0$ and $l$ with the requirement that the $b_i$'s form a non-decreasing sequence. Define the deviation of such a sequence to be $\max(|a_1-b_1|, \ldots, |a_n-b_n|)$. Design an algorith... |
For a given undirected graph $G$, a Gomory-Hu tree is a graph which has the same nodes as $G$, but its edges represent the minimal cut between each pair of nodes in $G$. The Gomory-Hu algorithm finds such a tree for a graph. A representant pair of nodes is defined as follows: if $R$ and $S$ are two components of the Go... |
Suppose I have a recurrence like $T(n)=2T(n/4)+\log(n)$ with $a=2, b=4$ and $f(n)=\log(n)$.
That should be case 1 of the Master theorem because $n^{1/2}>\log(n)$. There is also a lambda in case 1: $f(n)=O(n^{(1/2)-\lambda})$. Is this correct? And how can I find this lambda?
|
Given a complete binary tree with $n$ nodes. I'm trying to prove that a complete binary tree has exactly $\lceil n/2 \rceil$ leaves.
I think I can do this by induction.
For $h(t)=0$, the tree is empty. So there are no leaves and the claim holds for an empty tree.
For $h(t)=1$, the tree has 1 node, that also is a leaf, ... |
Definition: A polygon $P$ in the plane is called monotone with respect to a straight line $L$, if every line orthogonal to $L$ intersects $P$ at most twice.
Given a polygon $P$, is it possible to determine if there exists any line $L$ such that the polygon $P$ is monotone with respect to $L$? If yes, how?
Previously,... |
Languages like Java, C#, Eiffel, and C++ have subtype hierarchies which are directed acyclic graphs, due to interfaces in Java and C# and multiple inheritance in Eiffel and C++. An obvious way to check whether type $A$ is a subtype of type $B$ is to traverse the graph of the subtype hierarchy starting at $A$ to see whe... |
Consider an array $X$ of $n$ cells, each containing a number from $\{1,..., n\}$. There is at least
one duplicate number, i.e., a number that appears at least twice. I want output some duplicate number. When streaming we may pass over $X$ more than once. The inspection of a cell generates cost $1$. The cost of a run of... |
Given an integer sequence $\{ a_1, a_2, \ldots, a_N \}$ that has length $N$ and a fixed integer $M\leq N$, the problem is to find a subset $A =\{i_1, \dots, i_M\} \subseteq [N]$ with $1 \leq i_1 \lt i_1 \lt \dots \lt i_M \leq N$ such that
$\qquad \displaystyle \sum_{j=1}^M j \cdot a_{i_j}$
is maximized.
For instance... |
I was fooling around with Google Blocky's Maze demo, and remembered the old rule that if you want to solve a maze, just keep your left hand to the wall. This works for any simple-connected maze and can be implemented by a finite transducer.
Let our robot be represented by a transducer with the following actions, and ob... |
If a weighted graph $G$ has two different minimum spanning trees $T_1 = (V_1, E_1)$ and $T_2 = (V_2, E_2)$, then is it true that for any edge $e$ in $E_1$, the number of edges in $E_1$ with the same weight as $e$ (including $e$ itself) is the same as the number of edges in $E_2$ with the same weight as $e$? If the stat... |
What would be the standard topics covered in an 'Advanced Placement Computer Science A' test? Is there any good study reference someone can share?
Edit: Answer
An adjustment for my search term returned a Wikipedia page just for this type of exam and the AB version.
|
Is it possible to show that the minimum vertex cover in a bipartite graph can be reduced to a maximum flow problem? Or to the minimum cut problem (then follow max-flow min-cut theorem, the claim holds).
Intuitively: for each flow, pick one endpoint, then it is a minimum vertex cover in bipartite graph. But can it be sh... |
$L=\{<\!M,x\!>\, \mid M's \text{ transition function can only move right and } M\text{ halts on } x \}$. I need to show that $L$ is recursive/decidable.
I thought of checking the encoding of $M$ first and determine whether its transition function moves only right (Can I do that?). If so then try to simulate $M$ on $x... |
I have a game I'm building some ai for that has 2 players making simultaneous moves. In this game there is exactly one move where, if they both make it at the same time, the outcome is different than if they'd made it separately (all other moves are pretty independent).
Anyway, I'm trying to find a good algorithm to t... |
Possible Duplicate:
How to prove that a language is not regular?
Given a language $L = \{a^pb^{2p} \mid p \ge 1\}$, how could I show, using the Pumping Lemma that $L$ is not regular?
|
The document I am reading is here: Turing Machines
Before getting into the question, here is the notation used on the picture:
Here $\Delta$ denotes the blank and R, L and S denote move the head right, left
and do not move it, respectively. A transition diagram can also be
drawn for a Turing machine. The states ar... |
Is there any decision problem that is in a complexity class properly included in DLOGTIME? (except $O(1)$, of course)
If there is, can we create complete problems for DLOGTIME? So, can there be reduction by $O(\log(\log n))$ or smaller?
|
I know that the complexity class $\mathsf{P}$ has complete problems w.r.t. $\mathsf{NC}$ and $\mathsf{L}$ reductions.
Are these two classes the only possible classes of reductions under which $\mathsf{P}$ has complete problems?
Also, what classes of reduction can be used for $\mathsf{NP}$ beside polynomial-time reduc... |
I consider Point Location Problem in Polygon in repetitive mode in the case of simple polygon.
In computational geometry,Point Location Problem in Polygon problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon.
There are few method that work in Single-Shot approach, where ... |
Suppose we have a graph G. How can we find a spanning tree that minimizes the maximum weight of all the edges in the tree? I am convinced that by simply finding an MST of G would suffice, but I am having a lot of trouble proving that my idea is actually correct. Can anyone show me a proof sketch or give me some hints a... |
EDIT: ad hoc speed-ups are excluded.
We have the result that propositional resolution requires exponential time. The resolution result uses the proof of the pigeonhole principle as an example of a proof that takes exponential time.
Let's also say we have a hypothetical algorithm M for SAT that runs in polynomial time.... |
This is an automata theory homework question.
I need to create DFA that meets the following criteria:
Alphabet $\Sigma = \{ a, b, c \}$
Machine accepts empty string and strings of length that is a multiple of three, with every block of three containing one $a$, one $b$ and one $c$.
So far, I came up with this machi... |
Suppose we want to join two relations on a predicate. Is this in NC?
I realize that a proof of it not being in NC would amount to a proof that $P\not=NC$, so I'd accept evidence of it being an open problem as an answer.
I'm interested in the general case as well as specific cases (e.g. perhaps with some specific data s... |
I think that in Peterson's algorithm for mutual exclusion, if the process first to enter the critical section were to die or be cancelled, the other process would loop forever, waiting to enter the critical section.
In the picture, if process 1 is stopped, the rest of the processes behind process 1 will execute up to w... |
I get the proof of going from an enumerator to a Turing Machine (keep running enumerator and see if it matches input) but I don't see how the other way works.
According to my notes and the book (Intro to the Theory of Computation - Sipser), to get Turing enumerator from a Turing machine, we basically write all combinat... |
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