instruction stringlengths 35 29.1k |
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If $L_1$ is a regular language and $L_1 \cap L_2$ is a context-free language, does it mean that $L_2$ is a context-free language too?
I attempted to prove that $L_2$ was not required to be context-free by the following: If $L_1 = \{ a^n \}$ and $L_2 = \{ a^nb^nc^n \} $ then $L_1 \cap L_2 = \{ a^n \}$ which is context-f... |
When converting a CFG to a PDA I know that you get three main states, Qstart, Qloop and Qaccept. But Qloops will need a various amount of states, and my question is how many? Is there a way to find out the "worst case scenario" of how many states there can potentially be? I don't mean for one particular CFG, but in gen... |
I face this problem a lot while searching phone numbers and bank account numbers, when I do remember it partially.
I save a draft in gmail with the content I am mango. Then I search it, by entering just mango and it gets me to the draft.
But when I save a draft with some number such as 123987645 and try to search by ... |
I was just reading something about NP-hard problems and cryptosystems.
I was thinking: Every NP-complete problem can be reduced to another and every NP-complete problem has an equivalent (NP-hard) optimisation problem. A successful attack on one such NP-hard cryptosystem $A$ would mean that every other NP-hard cryptos... |
Are all Deterministic Finite Automatons also Non Deterministic Finite Automatons?
|
I have a friend working in wireless communications research. He told me that we can transmit more than one symbol in a given slot using one frequency (of course we can decode them at the receiver).
The technique as he said uses a new modulation scheme. Therefore if one transmitting node transmits to one receiving node ... |
This idea occurred to me as a kid learning to program and
on first encountering PRNG's. I still don't know how realistic
it is, but now there's stack exchange.
Here's a 14 year-old's scheme for an amazing compression algorithm:
Take a PRNG and seed it with seed s to get a long sequence
of pseudo-random bytes. To tran... |
I was solving a problem on topcoder http://community.topcoder.com/stat?c=problem_statement&pm=2402&rd=5009 .
There is one example :
{ 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 }
Returns: 16
So my question how its answer is 16 ?
|
Assume that $\mathrm{SAT} \in \mathrm{PSIZE}$, does it imply that $\mathrm{NP} = \mathrm{coNP}$ ?
I think that I've managed to show that if $\mathrm{SAT} \in \mathrm{PSIZE}$, then both $\mathrm{NP}$ and $\mathrm{coNP}$ are contained in $\mathrm{PSIZE}$, but I can't see how does help me. Any ideas ?
|
I'm interested in persistent catenable deques: deques that can be concatenated.
Kaplan and Tarjan came up with the first such data structure in 1995; Okasaki came up with a simpler, amortized version in 1997 using lazy evaluation (see Okasaki for references). Then a couple years later, Kaplan, Okasaki, and Tarjan came ... |
I have a found a small article [1] saying (the first paragraph of the introduction) that the minimum-weight independent dominating set is NP-complete in chordal graphs, but at the same time, seems to contradict that exact statement.
Moreover, I have found another reference [2] saying that in chordal graphs, it is polyn... |
How can we add n positive integers with binary expansion $l_1$, $l_2$,...$l_n$ bits so that the total complexity is $O (\sum l_i)$ for $i = {1,...,n}$ ? More importantly, how can show this complexity using amortized analysis (the potential method)?
I know the elementary school addition of 2 numbers of length $s$ and $r... |
I have been attempting to learn parameterized complexity on my own, and decided to go through all of the FPT race problems, and defining easy FPT algorithms for them, using concepts such as bounded search tree. I am stuck on figuring out an FPT algorithm for edge dominating set, defined as follows:
EdgeDominatingSet
In... |
I am reading the reduction given by Sipser in his textbook "Introduction to the Theory of Computation," on page 303. The reduction is:
\begin{equation} 3SAT \leq_p KCLIQUE \end{equation}
I am really trying to understand everything formally -- putting everything in a strict logical notation helps me learn Math. To clari... |
I have been trying to understand the difference between normal polynomial evaluation and horner's method. usually it takes 3n-1 operations while horner's method reduces it to 2n operations. I tried a couple of explanations but they were too theoritical. I would be glad if somebody comes up with a decent and simple expl... |
I have a list and want to select a random item from the list.
An algorithm which is said to be random:
When you see the first item in the list, you set it as the selected item.
When you see the second item, you pick a random integer in the range [1,2]. If it's 1, then the new item becomes the selected item. Otherwise ... |
Let $G$ be a "hypergraph", a collection of vertices $V=\{v_1,v_2,\ldots,v_n\}$ and a collection of "hyperedges" $E=\{e_1,e_2,\ldots,e_m\}$, where $e_i\subseteq V$ and unlike normal edges, an edge may contain more than two vertices.
An "independent set" (http://en.wikipedia.org/wiki/Independent_set_(graph_theory)) is a ... |
Let's say we have the following simple transaction-schedule:
T1 | T2 | T3
-----+------+-----
w(x)| |
| w(x) |
| | w(x)
T1 comes before T2, so in the precedence graph, we draw an arrow from T1 to T2. T2 comes before T3, so we draw an arrow from T2 to T3.
My question is: is it also necessary to... |
Kadane Algorithm is used to solve the maximum subarray problem which in simpler terms is to find the highest possible value of a continuous sub array in an array.
One often cited application of Kadane Algorithm is that given the prices of the stock over X days , on which days should we buy and sell the stock in order ... |
Is there a way to take the interection of two NPDAs?
I can't seem to find anything that can make that happen, but it seems like the type of thing that is should be relatively trival.
|
We have a 0-1 knapsack in which the increasing order of items by weight is the same as the decreasing order of items by value. Design a greedy algorithm and prove that the greedy choice guarantees an optimal solution.
Given the two orders I imagined that we could just choose the first k elements from either sequence an... |
I want to show that for any language $L \subseteq \{ a \}^* $, $L$ satisfies the pumping lemma for context free languages if and only if it satisfies the pumping lemma for regular languages.
I know that every regular language is also a context free language so I tried to show that direction of the proof first but ran i... |
Today we discussed in a lecture a very simple algorithm for finding an element in a sorted array using binary search. We were asked to determine its asymptotic complexity for an array of $n$ elements.
My idea was, that it is obvisously $O(\log n)$, or $O(\log_2 n)$ to be more specific because $\log_2 n$ is the number o... |
I am having trouble in understanding order-statistics tree .
Definition :
Every node in tree stores the number of descendants of itself .
Can you please explain the Algorithm or pseudocode how to Insert and Delete a node in the tree when tree is to be balanced .
Basically i want to find the rank of an element in t... |
Ok before I start I realise this is on the fringe of on-topic (I have read the Questions help for this site), particularly as this is not a real-world problem. However:
I cannot find anything relevant on Google
From a purist point of view surely it must fall within Computer Science?
In any case, if I have overstepped... |
The derivatives of iterated functions at a fixed point $z_0$ are useful in constructing a Taylors series of iterated analytic functions - in other words, the Taylors series of a dynamical system $f^t(z_0)$.
A simpler version of the problem casts light on possible approaches. Instead of iterated functions, consider com... |
I have read that TSP and Subset Sum problems are NPC problems which are also NP Hard. There are also problems like Halting Problem which is NP Hard, but not NP Complete
And Wikipedia defines this as
A problem $H$ is NP-hard if and only if there is an NP-complete problem
$L$ that is polynomial time Turing-reducible t... |
I'm a freshman CS student at my university and i'm struggling with understanding my professor through his thick accent. I've asked him to explain the proof for this multiple times and still have trouble comprehending what he's trying to tell me.
The question is:
Prove that: $P\rightarrow(Q\rightarrow R)$ is equivalen... |
Is there a good general paper about the interpretation or compilation
of REGEXP in programming languages for pattern matching, with or
without variables? I am not looking for a quick explanation about the
construction of DFAs, but for a real paper on how it is actually done
in programming languages implementation, and ... |
I have come up with a type of simulation "game" but I cannot find anything describing it online.
The simulation has a 2D "world" with a number of automatons on a discrete grid, similar to the game GNU Robots, although for an interesting game, their behavioral rules should be much more complex:
#.......
#...#...
...#...... |
so I am a bit confused here. I read a memory-map ranging from certain hex values and I'm trying to find out how large RAM is by it. Here's the code:
const char *memorybottom = 0x00000000;
const char *memorytop = 0xAA55D0AB;
The bottom is 0, and the top is AA55D0AB. I tried to convert that to binary and increased each ... |
I am looking for more information/references on how graph search is utilized in social media. Papers, books , anything really.
|
The question is as follows:
True or False: For every non-directed connected non-weighted graph and for every spanning tree T of the graph there exists a vertex v such that T is a DFS tree with the root v.
What about if instead of DFS I used BFS?
I have no clue where to begin with this one. I feel like I'm overlooking s... |
Help would be much appreciated.
"Receive a number and reorder it from the largest to the smallest.
Input: 13252
Output: 53221
Cant use arrays...
Only while, for, if/else ...
any idea? i'm clueless.
Thanks for the help.
|
Let's say I can solve problem $A$ in polynomial time using only $\log n$ bits of randomness, with a $\ge \frac{2}{3}$ chance of a correct answer. Then surely I can solve $A$ determistically by running my algorithm for $A$ over all random strings of length $\log n$ (of which there are a polynomial number) and take a po... |
Apropois to Raphael's suggestion on Intersection of two NPDAs:
Let $A_1$ and $A_2$ NPDA for context-free languages $L_1$ and $L_2$, respectively. Assuming that we know that $L = L_1 \cap L_2$ is context-free, can we (effectively) construct NPDA $A$ for $L$?
Any type of algorithm would be acceptable, but the more practi... |
Does music stop for a short interval while listening into it,maybe a milliseconds that we just doesnt sense it cause by interrupts for operating system to run other programs
|
From the property of Red-Black Trees we know that:
All leaves (NIL) are black. (All leaves are same color as the root.)(Comren et al "Introduction to Algorithms")
But what is the reason that we should enforce them as Black, even though they're NILL's?
|
I know I can use a Bayes classifier to determine if something is one of N classes, but can I also determine if something is NOT in any of the predefined classes? Or will a Bayes classifier only find the closest class?
|
Could I construct (for some wired reason) a DFA that has a state that is not connected to anything, and it would still be legal?
I'm studying for a test, and I found a question that asks if an infinite DFA could represent a regular language, and I want to use a regular DFA and add all the infinite states not connected ... |
I was trying to find info about this Finite Automata type FAB (Finite Automata Bowl) and wasn't able to find a lot. It is basically the rules that apply to PDA apply to FAB except you drop the temporal order of the stack. So instead of being restricted to only removing the top symbol of the stack, you can remove any sy... |
I'm studying threads in C and I have this theoretical question in mind that is driving me crazy.
Assume the following code:
1) void main() {
2) createThread(...); // create a new thread that does "something"
3) }
After line 2 is executed, two paths of execution are created. However I believe that immediately after... |
My question is that I'm trying to find the sparsest cut in a connected, undirected graph (all weights are = 1). Basically, I am looking trying to find the smallest cut (i.e., number of edges cut since all weights = 1) while maximizing the number of vertices in the resulting subgraph. How do I approach this problem with... |
Given an array $A$ of integers in ascending order, how efficiently can it be decided whether there exists an integer $i$ such that $A[i] = i$? How would an optimal algorithm for this problem work?
|
I have points of self-intersecting polygon, its edges and also I am able to find points where it intersects itself using Bentley–Ottmann algorithm.
I planned to build non-self intersecting polygons by editing edges around intersection points, but problem is when you have two edges that intersect, you don't know which t... |
I am reading The Design of Approximation Algorithms (Williamson and Schmoys; page 50 of this PDF) about solving the minimum-degree spanning tree problem of maximum degree 2 in polynomial time. The text states that we are going to find a tree $T$ with maximum degree at most $2\mathrm{OPT} +\lceil\log_{2} n\rceil$ in pol... |
Context
In a 2-dimensional space, suppose $p_0$ is the origin - the lowest point of the Convex Hull (CH), and suppose $p_1, ..., p_{n-1}$ are sorted by their polar angles. When applying Graham scam, I always observe that $p_1$ and $p_{n-1}$ are vertices of the Convex Hull (CH). For instance, consider the graph, for whi... |
For a class project we're developing a software that solves a common optimisation problem. After some research we've found out that our problem is called QAP (Quadratic Asssignment Problem) and the algorithm that is commonly used is Branch and Bound. I understand the basics of the problem and I see the need of a lower ... |
Assuming that a stack data structure is available, how can this data structure be used to compute a representation of an integer in base three? For example, the algorithm for printBase3 would return 12020 on input 141.
|
I was reading the following FDS paper:
https://www.usenix.org/system/files/conference/osdi12/osdi12-final-75.pdf
and it says that the the following hash function does not distribute things uniformly (instead it creates a binomial distribution):
$$i = (hash(g + t)) \pmod n$$
while the following did distribute things uni... |
I was reading the following FDS paper:
https://www.usenix.org/system/files/conference/osdi12/osdi12-final-75.pdf
The paper has a TLT (tract locator table) for identifying where to write in each server. The table is basically a hash table where the index i maps to some (tract) server to do writes to or reads to.
Say tha... |
How can any Constraint satisfaction problem be converted to an instance of Satisfiability? I have a CSP and i know its NP hard to solve it, but i would like to convert to an instance of k-SAT, but im not sure of any algorithm for transformation
|
In class last week, my professor commented and said that Turing machines are used as a standard measure/model of what is computable and are a helpful basis of discussion for that subject. She also said that all variants of Turing machines are proven to be computationally equivalent -- read, just as powerful -- as one a... |
I was reading the following computer systems paper:
https://www.usenix.org/system/files/conference/osdi12/osdi12-final-75.pdf
And I was trying to understand why it claims that it does not need data locality for it be perform well.
Basically, in the abstract it says:
"...FDS multiplexes an application's large scale I/O ... |
Recall that Paxos is a distributed system algorithm with the goal that the processes participating in its protocol will reach consensus on one of the valid values.
I was studying Paxos from:
http://research.microsoft.com/en-us/um/people/lamport/pubs/paxos-simple.pdf
and I was wondering, what is so special about a major... |
If you resize an 1000x1000 raster image to 10x10 and resize it back to 1000x1000 is this considered to be an example of aliasing?
|
I thought the Gibbs phenomenom is the result of Fourier analysis estimation (but was it Fourier Series estimation or can it also be Fourier Transform estimation?)
JPEG uses the Discrete cosines Transform. A DCT is similar to a Fourier transform in the sense that it produces a kind of spatial frequency spectrum.
But ... |
I need to find a context-free grammar for the following language which uses the alphabet $\{a, b\}$
$$L=\{a^nb^m\mid 2n<m<3n\}$$
|
This is my problem:
There are n collections of M geometric shapes (not necessarily disjoint).
Pick a single shape from each collection,
such that the n selected shapes are pairwise interior-disjoint.
This problem is NP-complete even when the shapes are restricted to axis-parallel squares (see this cstheory.SE que... |
If given that all edges in a graph $G$ are of equal weight $c$, can one use breadth-first search (BFS) in order to produce a minimal spanning tree in linear time?
Intuitively this sounds correct, as BFS does not visit a node twice, and it only traverses from vertex $v$ to vertex $u$ iff it hasn't visited $u$ before, su... |
I was studying Paxos from the paper by Lamport called "Paxos Made Simple".
Recall that Paxos is a distributed system algorithm with the goal that the processes participating in its protocol will reach consensus on one of the valid values.
On page 3, it says
Since all numbers are totally ordered, condition P2 guarante... |
I was studying Paxos from:
http://research.microsoft.com/en-us/um/people/lamport/pubs/paxos-simple.pdf
Recall that Paxos is a distributed system algorithm with the goal that the processes participating in its protocol will reach consensus on one of the valid values.
I was reading page 4 of the paper where it says condi... |
I was studying Paxos from:
http://research.microsoft.com/en-us/um/people/lamport/pubs/paxos-simple.pdf
Recall that Paxos is a distributed system algorithm with the goal that the processes participating in its protocol will reach consensus on one of the valid values.
On page 4 of the paper, at the bottom where they outl... |
I believe I understand the concepts of algorithm analysis. However, I'm not fully confident in applying those concepts. I'd appreciate help in bridging the gap between concept and application.
I understand that if $f(n) \in O(g(n))$ and $f(n) \in \Omega(g(n))$ then $f(n) \in \Theta(g(n))$
Essentially, when Big-O and B... |
Context
Consider this algorithm. If the set $\{\angle p_ip_{i+1}p_{i+2} : i=0,...,n-1\}$ does not contain left and right turns, output "yes the polygon is convex"; otherwise, "no".
My answer
Consider this nonsimple polygon having 4 vertices; the algorithm above will output "yes" as the set of points does not contain ... |
I'm writing a balanced $n_d$-Hyperoctree data structure in which the only fundamental operations I provide are edge traversals between parent and child nodes. I'm storing the nodes using a Morton z-curve.
Using only this information:
The level of a node can be computed by traversing to the root of the tree.
Neighbor ... |
Suppose I have two vectors $V_1, V_2 \in R^l$. Can they be converted into bit vectors $B_1,B_2 \in \{0,1\}^l $ such that if $V_1, V_2$ is close in Euclidean distance, $B_1,B_2$ is close in hamming distance?
Please note that this is a little different from locality sensitive hashing, where each vector will be hashed ... |
I am trying to prove this following theorem, can someone help please?
Let $L$ be a language over the alphabet $\Sigma = \{ a,b \}$.
If $L' = \{ w\$w^R \mid w \in L\}$ is context-free, then $L$ is regular.
|
I've read that subset sum is NP-complete. What happens when I change the decision problem to look for a constant number? So the decision problem would look like this:
Input:
A collection of nonnegative integers A and a nonnegative integer b,
Output:
Boolean value indicating whether some subset of
the collecti... |
First off I am new to computer science (first semester) and do not know anything about physics, so I am appologizing up front for this not very scientific question.
I've been wondering how data is processed at the LHC. I am sure CERN doesn't just use one programming language to write code but I am curious what the fast... |
Consider, for example, the definition for $\Sigma_2^p$ complexity class.
$$ x \in L \Leftrightarrow \exists u_1 \forall u_2 \;M(x, u_1, u_2) = 1, $$
where $u_1, u_2 \in \{0,1\}^{p(|x|)}$, for some polynomial $p$. Here, $M$ must be polynomial time. But polynomial in the size of what exactly? For example, if we choose (g... |
I was studying Paxos from:
http://research.microsoft.com/en-us/um/people/lamport/pubs/paxos-simple.pdf
and was wondering, what guarantees Paxos to converge and not run forever without a consensus/agreement on a value? Is it guaranteed to converge always or is it a probabilistic bound that the probability that it does n... |
My neural net is having trouble switching the sign of a weight. The issue is that the deltas applied to the weight are proportional to that weight, so when it gets closer to zero, the deltas become smaller and are never sufficient to get it past that point. I tried adding a momentum term with 5% of the previous iterati... |
For example,
Let the Grammar be:
S->Sa|B
Thus, S->Sa->Saa->...->Saa...aaa->Baa...aaa
What's wrong with this?
Why is right recursion a solution to the problem?
S->BS'
S->aS'|e
|
I've a subset of the simple paths in a graph. The length of the paths is bounded by $d$.
What's the most compact way (memory-wise) I can represent the paths such that no other paths apart from the selected ones are represented?
Note that I want to use this representation in an algorithm that will iterate through this... |
I'm trying to work through various exercises in Skiena's "Algorithm Design Manual." One problem that I am stuck on is as follows:
What value is returned by the following function? Express your answer as a function of n. Give the worst-case running time using Big Oh notation.
function conundrum(n)
r:=0
for i:=1... |
I am now preparing for a test in my algorithms course and I have stumbled upon a question about a data structure which seems too trivial for me, but is probably not trivial at all.
The question is:
Let a "minimum stack" be a data structure that supports the following functions:
Creating a new empty data structure.
I... |
It seems like the proof that $A_{DFA}$ is decidable in Sipser (2nd ed.) assumes the computation will halt... and hence only really proves that $A_{DFA}$ is recognizable.
The language $A_{DFA}$ is defined by $A_{DFA} = \{\langle B, w \rangle \mid B \text{ is a } \mathsf{DFA} \text{ that accepts input string } w \}$.
Her... |
I want to prove that a language is not $\omega$-regular.
The language I'm working with can be defined as:
$$L = \{ a_1 \dots a_n x^\omega ~ | ~ n > 0, a_1 \dots a_n \in L^\prime \}$$
where $L^\prime$ is a specific non regular language (I omit the definition $L^\prime$ because I think it is of no help for my problem), ... |
In proofs of decidability, we often want to simulate another model of computation by a Turing machine. But if I can simulate a $\mathsf{DFA}$ by, say, a C program, then is there some result which says that the $\mathsf{DFA}$ can be simulated by some $\mathsf{TM}$? Could a program be used in place of a $\mathsf{TM}$ in ... |
Given an integer $n$, calculate $n!=n\times(n-1)\times(n-2)\dotsc 3\times2\times1$.
What is the best time and space complexity of calculating $n!$?
P.S. I do not have any idea about this topic. I was using MATLAB and I needed to compute $200!$ but it said "Out of memory"!! That's why I am asking.
|
In a programming book that I'm currently reading it's stated that
$$\sum\limits_{i=1}^{n}i^2$$ is $O(n^3)$. My understanding was that $i\times i$ is a primitive operation and the complexity would be $O(n)$. What am I missing?
|
Say that for a particular problem, e.g., the independent set problem, it has been shown that no polynomial-time algorithm exists to solve it.
Could we get around this by finding an algorithm which approximates the solution to a certain accuracy?
That is, would the result above bar the existence of an algorithm which fi... |
a few days ago I asked a question about the limits of compression:
Can PRNGs be used to magically compress-stuff?
The idea common to all the answers was that if you consider all programs
of length < k (Let's call this set $C_k$), then there is only a finite number of possible outputs generated by programs in $C_k$ (let... |
I am learning 2-phase locking and its unclear to me how it achieves/guarantees before-or-after atomicity (i.e. serilizability).
I went to the following notes
http://ocw.mit.edu/resources/res-6-004-principles-of-computer-system-design-an-introduction-spring-2009/online-textbook/atomicity_open_5_0.pdf
on page 9-73 it ar... |
While familiarizing myself with polynomial hierarchy, I have come across a problem
of showing $NP^{\Sigma_{k}^{p} \cap \Pi_{k}^{p}} \subseteq \Sigma_{k}^{p}$. By looking at the proof for $NP^{SAT} \subseteq \Sigma_{2}^{p}$, I got the concept
where we can guess the choices of the NTM and answers to SAT call and then enc... |
I have searched on Google, but I can't quite understand what is pass-by-value-result. What is the advantage and disadvantage of using pass-by-value-result?
If I have a program code like this, what will be the result when parameters are passed by value-result?
#include <stdio.h>
int a=2;
int b=1;
void fun(int x, int y... |
Recall that Paxos is a distributed system algorithm with the goal that the processes participating in its protocol will reach consensus on one of the valid values.
I was studying Paxos from:
http://research.microsoft.com/en-us/um/people/lamport/pubs/paxos-simple.pdf
and I was confused about one specific part. How does ... |
I'm wondering if there is a way to extend Hinley-Milner's type system to allow polymorphic types without the need of a let construct, by adding an intersection type (as Dan pointed out) that represents the possible types of a function type.
Say I have this expression:
$\lambda x.\lambda y.(x\ (x\ y))$
While running the... |
For an assignment in my university, we have to answer multiple choice questions about theoretical computer science. This particular one I find very hard to understand. I wonder if some of you could explain it to me.
In this question, L1, L2, L3, L4 refer to languages and M, M1, M2 refer to Turing machines.
Let
L1 ... |
When given the length of a source array, I want to generate the array of swaps that need to be performed in order to sort the source array. I want to make this array as small as possible. Swaps will be performed only if necessary for sorting, as defined by the following function.
def compare_swap(array, a, b):
if ... |
What are the possible ways to calculate $(x^y) \bmod z$ quickly for very large integers?
Integers $x,y \lt 10^{10000}$ and $z \lt 10^6$.
|
I have to craft up a number made of 19 digits so that, after some mathematical operations made 11 times, the resulting sum of the remainders of the first ten operations is equal to the the remainder of the eleventh operation. The eleven calculations are as follows. I need to reverse them in order to be able to craft up... |
I am trying to get an idea of how the AKS primality test should be interpreted as I learn about it, e.g. a corollary for proving that PRIMES ⊆ P, or an actually practical algorithm for primality testing on computers.
The test has polynomial runtime but with high degree and possible high constants. So, in practive, at w... |
Every proof I can find of this result is by way of regular expressions. Is there any "constructive" proof that defines the corresponding DFA (probably NFA)? For instance the proof of concatenation closure is most often presented by demonstrating the NFA. I'm just curious whether this is out there somewhere
|
I've read the wikipedia article, but I don't speak category theory (and I'm not sure how to start so I'm just picking something that sounds interesting). So, can someone give me a simple, possibly incorrect (for learning/clarity), pragmatic (if it applies to programming, which I'm pretty sure it does) explanation of wh... |
I am trying to figure out a reduction to prove $W[1]$-hardness for this, but I am having significant trouble. Here is the problem:
Bag Automaton:
A non deterministic finite state automaton $M=(Q,I,s,F,d)$. $Q$ is the set of states, $I$ is the set of items, $s\in Q$ is the start state, $F\subseteq Q$ is the set of acce... |
Let's suppose I have an NP-complete problem A.
Can there be $A_1$, $A_2$ such that $A_1$ and $A_2$ are disjoint, $A = A_1 \cup A_2$, and $A_1$ and $A_2$ are NP-complete?
My guess would be yes. For example, just partition SAT into formulas with an even number of variables and formulas with an odd number.
Follow up: ... |
I am curious what is the difference between diameter of a graph vs longest path of a graph. I just read diameter of a graph can be solved using Floyd warshall in O(V^3) while longest path can be calculated in O(V + E) using topological sort.
|
I am interested to know whether that language $$
L = \{ a^pb^q \mid p, q \text{ are prime} \}
$$ is regular. How do you prove that it is not regular?
|
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