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Is open adressing with prime steps bijective? |
|algorithms|hash-tables|hash| |
The idea is to decide nondeterministically at the beginning how much the word is cycled, and have a copy of the automaton for every case.
For every state $q \in Q$, separate $D$ into two parts $A_1$ and $A_2$. $A_1$ contains the states from which $q$ is reachable and $A_2$ the states that are reachable from $q$:
... |
Knowing that there is no surjection from $S$ to $\mathcal{P}(S)$.
Is it possible to show the existence of an undecidable language ?
or
There is a need about having infinite inputs, being $L\subseteq \Sigma^*$?
Let a language $L'$ be a bounded finite version of $L\subseteq \Sigma^*$ , with $L' \subset L$ ... |
Undecidability L for a finite set of programs S, a finite $\mathcal{P}(S)$, and finite inputs? |
|formal-languages|undecidability| |
I'm not sure I understand the question properly but every finite language is regular. There are no regular languages which are undecidable and therefore there are no finite languages which are undecidable. All of these statements are well-known and proofs can be found in <a href="http://www.amazon.com/Introduction-Auto... |
Undecidability Language for a finite set of programs S, a finite $\mathcal{P}(S)$, and finite inputs? |
Knowing that there is no surjection from $S$ to $\mathcal{P}(S)$.
Is there *a need* for L to be *infinite* to be undecidable, i.e. $L\subseteq \Sigma^*$?
I mean what if we choose a language $L'$ be a *bounded finite version of* $L\subseteq \Sigma^*$,
($N$ finite), $|L|\leq N$, with $L' \subset L$ , Is it po... |
Knowing that there is no surjection from $S$ to $\mathcal{P}(S)$.
Is there *a need* for L to be *infinite* to be undecidable, i.e. $L\subseteq \Sigma^*$?
I mean what if we choose a language $L'$ be a *bounded finite version of* $L\subseteq \Sigma^*$,
$|L'|\leq N$, ($N \in \mathbb{N}$), with $L' \subset L$ , ... |
If your language $L'$ is finite, you can perform [table lookup](https://en.wikipedia.org/wiki/Lookup_table) on a hardcoded table containing all words in $L'$. This is awkward to write down as Turing machine, but in other, equivalent models that is quite clear.
In fact, finite automata are sufficient. Construct an au... |
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 the... |
Is there an undecidable finite language of finite words? |
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 don't work with a *finite* set $B$ which also has no surjection onto $\mathcal{P}(B)$ ! (with $|B|=K$ and $K \in \ma... |
Why surjection with the power set isn't enough argument for undecidable language? |
|formal-languages|regular-languages|undecidability| |
This question on SO seems to be relevant: http://stackoverflow.com/questions/9589659/prevent-race-conditions-across-multiple-rows
Also, I would urge you to use SQL server locks instead of your own lock column (which it sounds like you're doing).
And it looks like doing hierarchical locks is kind of clumsy in SQL,... |
Let us first recapitulate in which context the cited statement makes sense.
1. Let us restrict ourselves to the domain of (decision) functions in $\mathbb{N} \to \{0,1\}$ (a subset of all functions).
2. Every such function corresponds to one element of $\mathcal{P}(\mathbb{N})$ (see [characteristic function](https:... |
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 \ma... |
Why absence of surjection with the power set is not enough to prove the existence of an undecidable language? |
|formal-languages|undecidability| |
The [Prevent race conditions across multiple rows](http://stackoverflow.com/questions/9589659/prevent-race-conditions-across-multiple-rows) on Stackoverflow seems to be relevant.
Also, I would urge you to use SQL server locks instead of your own lock column (which it sounds like you're doing).
And it looks like d... |
Let us first recapitulate in which context the cited statement makes sense.
1. Let us restrict ourselves to the domain of (decision) functions in $\mathbb{N} \to \{0,1\}$ (a subset of all functions).
2. Every such function corresponds to one element of $\mathcal{P}(\mathbb{N})$ (see [characteristic function](https:... |
null |
If you take any finite set $A$ of TMs, there is a language not decided by any TM in $A$ and the finite powerset would suffice for that. But this is not what we want. We want to show that there is an undecidable language, i.e. a language that *no* TM can decide it. The cardinality difference between a finite set and its... |
|formal-languages|computability|undecidability| |
Let G be a graph having n vertices, none of which are isolated, and n−1 edges, where n ≥ 2. Show that G contains at least two vertices of degree 1.
I have tried this problem by using the property summation degree = 2|E| . Can this problem be solved by using pigeon hole principle? |
Graph Algorithms |
|graphs| |
|algorithms|formal-languages|finite-automata| |
|complexity-theory|reference-request|recurrence-relation|mathematical-analysis| |
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 [pige... |
Low-degree nodes in sparse graphs |
|algorithms|time-complexity|algorithm-analysis|runtime-analysis| |
|formal-languages|computability|undecidability| |
Yes, it can.
You have $n-1$ edges, which means $2n-2$ holes for node-pigeons. If every node is supposed to have degree two (or more), we have to place (at least) two pigeons for each node, that makes a total of $2n$ pigeons.
By said principle, (at least) two pigeons do not find a solitary hole, which means (at le... |
|graphs|proof-techniques| |
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 [pige... |
Static LL(\*) grammar analysis is undecidable. In other words, there are some grammars that are LL(\*) but we can't figure this out statically. ANTLR v3 fails over to backtracking in this case and therefore can exhibit the PEG A->a/ab problem where ab is dead code in the cases where grammar analysis failed.
In ANTLR... |
No, since no `LL(*)` grammar can be left-recursive and obviously there are context-free grammars which are left-recursive. |
Is the set of LL(*) grammars the same as the set of context-free grammars?
Thank you. |
Is the set of LL(*) grammars the same as the set of CFG grammars? |
|formal-languages|formal-grammars| |
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):
- posi... |
Optimal path - best career |
|algorithms| |
|algorithms|automata|finite-automata| |
|algorithms| |
Which machine learning algorithms (besides SVM's) use the "structural risk minimization" principle? |
ML algos based on "structural risk minimization"? |
|machine-learning| |
No, since no `LL(*)` grammar can be left-recursive and obviously there are context-free grammars which are left-recursive.
As requested: A sample of a left-recursive, context-free grammar (which is therefore not `LL(*)`) :
S -> S x
| ɛ
The language this grammar describes is _one or more times the c... |
null |
I'm looking for intuition about when a language is regular and when it is not. For example, consider:
$$ L = \{ 0^n 1^n \mid n \geq 1 \} = \{ 01, 0011, 000111, \ldots \}$$
which is not a regular language. Intuitively it seems a very simple language, there doesn't seem to be anything complicated going on. What is ... |
{"Voters":[{"Id":39,"DisplayName":"Gilles"}]} |
I'm looking for intuition about when a language is regular and when it is not. For example, consider:
$$ L = \{ 0^n 1^n \mid n \geq 1 \} = \{ 01, 0011, 000111, \ldots \}$$
which is not a regular language. Intuitively it seems a very simple language, there doesn't seem to be anything complicated going on. What is ... |
The structural risk minimization principle is a principle that is at least partly 'used' in all machine learning methods, since overfitting is often to be taken into account: reducing the complexity of the model is (supposedly and in practice) a good way to limit overfitting.
- SVMs explicitly have a parameter for t... |
Be sure to complete the first task before reading below.
Hint 1:
>! What are the conditions necessary to use the Floyd-Warshall's algorithm? Does it match those of your exercise?
Hint 2:
>! Well, I think you are ready to write the corresponding pseudo-code :-) |
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):
... |
null |
1. $L_a = \{ a^*cw \mid w \in \{a,b \}^* \land |w|_a = |w|_b \}$
>! $L_a \cup d^* = L_a'$
$L_a' = \{ \{a,d\}^*cw \mid w \in \{a,b,d \}^* \land |w|_a + |w|_d = |w|_b \}$ (union?)
>! $L_a' \cap a^*cw = L_a''$
$L_a'' = \{ d^*cw \mid w \in \{a,b \}^* \land |w|_a = |w|_b \}$
>! homomorphism $ h(... |
|complexity-theory|computability|reductions| |
null |
null |
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 summariz... |
DLOGTIME complexity class and testing the length of the input string |
|complexity-theory| |
If I got your question right, this is a matter of definition.
Assume that the input to your TM is the number $n$ (say, $n=1000$).
$n$ appears on the tape as a binary sequence, and it's length is at most $\lceil \log_2 n\rceil = O(\log n)$. So in order to test the length of the input you need check only $O(\log n)... |
If I got your question right, this is a matter of definition.
Assume that the input to your TM is the number $n$ (say, $n=1000$).
$n$ appears on the tape as a binary sequence, and it's length is at most $\lceil \log_2 n\rceil = O(\log n)$. So in order to test the length of the input you need check only $O(\log n)... |
It is hard to answer the question without further context.
Complexity is typically defined in terms of the size of the input (the number of bits needed to represent the input) and therefor depends on the representation you choose for the inputs. (More formally, a language or a formal computational problem is defined... |
Yes, there is a need for $L$ to be infinite in order to be undecidable.
To add up on the answers of Raphael and Sam, you should think about "decidable" as things that a computer-program can solve. The program required is very simple, it just needs to output "Yes" for elements in $L$, or otherwise, say no.
So the ... |
null |
To be at all interesting (for the purpose of thinking about computability) a decision problem has to have infinitely many "yes" answers and infinitely many "no" answers. Such decision problems correspond exactly to languages contain infinitely many strings over their alphabet and also exclude infinitely many strings ov... |
As follows [from my previous question][1], I've been playing with the [Riemann hypothesis][2] 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 numbe... |
As follows [from my previous question][1], I've been playing with the [Riemann hypothesis][2] 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 numbe... |
ML algorithms based on "structural risk minimization"? |
As follows [from my previous question][1], I've been playing with the [Riemann hypothesis][2] 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 numbe... |
If your language $L'$ is finite, you can perform [table lookup](https://en.wikipedia.org/wiki/Lookup_table) on a hardcoded table containing all words in $L'$. This is awkward to write down as Turing machine, but in other, equivalent models that is quite clear.
In fact, finite automata are sufficient. Construct an au... |
I'm studying for my final in theory of computation, and I'm struggling with the proper way of answering whether this statement is true of false.
By the [definition](https://en.wikipedia.org/wiki/Mapping_reducibility) of $\leq_m$ we can construct the following statement,
$w \in A \iff f(w) \in B \rightarrow w \no... |
Which machine learning algorithms (besides SVM's) use the principle of [structural risk minimization](https://en.wikipedia.org/wiki/Structural_risk_minimization)? |
|reference-request|machine-learning| |
null |
Converting regular expressions into (minimal) NFA is easy with standard algorithms. The other direction seems to be more tedious, though, and sometimes the resulting expressions are messy.
What algorithms are there for converting NFA into regular expressions? Are there advantages regarding time complexity or result ... |
How to convert finite automata to regular expressions? |
|automata|finite-automata|regular-expressions| |
###Method###
The nicest method I have seen is one that expresses the automaton as equation system of (regular) languages which can be solved. It is in particular nice as it seems to yield more concise expressions than other methods.
Let $A= (Q,\Sigma,\delta,q_0,F)$ an NFA without $\varepsilon$-transitions. For ev... |
###Method###
The nicest method I have seen is one that expresses the automaton as equation system of (regular) languages which can be solved. It is in particular nice as it seems to yield more concise expressions than other methods.
Let $A= (Q,\Sigma,\delta,q_0,F)$ an NFA without $\varepsilon$-transitions. For ev... |
|formal-languages|automata|finite-automata|regular-expressions| |
Converting regular expressions into (minimal) NFA that accept the same language is easy with standard algorithms. 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 expressions? Are there advant... |
[{"Id":98,"DisplayName":"Raphael"}] |
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 summariz... |
|algorithms|formal-languages|automata|finite-automata|regular-expressions| |
###Method###
The nicest method I have seen is one that expresses the automaton as equation system of (regular) languages which can be solved. It is in particular nice as it seems to yield more concise expressions than other methods.
Let $A= (Q,\Sigma,\delta,q_0,F)$ an NFA without $\varepsilon$-transitions. For ev... |
I try to solve the following computational geometry problem.
>Let S be a set if $n$ axis-parallel rectangles in the plane, so that the bottom edge of each rectangle in $S$ lies on the $x$-axis.
>1. What is (an upper bound on) the combinatorial complexity of the union K of the rectangles in S?
>2. Give an effici... |
An Area of Intersection of Rectangles |
|algorithms|computational-geometry| |
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