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h2(n) dominates (or is more informed than) h1(n) if h2(n) >= h1(n) for every node n. How does this mean h2 will expand less nodes? |
Is it provable that using a more informed heuristic is guaranteed to expand fewer nodes of the search space? |
|artificial-intelligence|search-trees|heuristics| |
null |
The question is whether the following statement is true or false:
$A \leq_T B \implies A \leq_m B$
I know that if $A \leq_T B$ then there is an oracle which can decide A relative to B. I know that this is not enough to say that there is a computable function from A to B that can satisfy the reduction.
I don't ... |
|algorithms|probability-theory|randomness|random-number-generator| |
I often hear people talking about **parallel** computing and **distributed** computing, but I'm under the impression that there is no clear boundary between the 2, and people tend to confuse that pretty easily, while I believe it is very different:
- **Parallel** computing is more tightly coupled to multi-threading,... |
Distributed vs parallel computing |
|distributed-systems|parallel-computing| |
I'm reading through the [MIT course notes on state space search](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/).
Consider a state space $S$, a set of nodes in which we look for an element having a certain property.
A [heuristic function](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/07ImprovedMetho... |
Is using a more informed heuristic guaranteed to expand fewer nodes of the search space? |
I'm not sure I understand the question. The distinction between parallel and distributed processing is still there. The fact that you can take advantage of both in the same computation doesn't change what the concepts mean.
And I don't know what news are you following, but I'm quite sure parallel processing is not s... |
This is partly a matter of terminology, and as such, only requires that you and the person you're talking to clarify it beforehand. However, there are different topics that are more strongly associated with [parallelism](http://en.wikipedia.org/wiki/Parallel_computing), [concurrency](http://en.wikipedia.org/wiki/Concur... |
Historically, [Lisp](http://en.wikipedia.org/wiki/Lisp_%28programming_language%29) was the first major programming language to introduce metaprogramming facilities. Lisp's macro system allows the programmer to define new control structures, new data templates, etc. For example, the [Common Lisp Object System](http://en... |
The running time of the `InsertTerm` subroutine is $O(n)$ where $n$ is the number of terms in the polynomial, and this is the worst-case complexity as well as the average-case complexity absent any information about the monomial being inserted.
The outer loop of `PolynomialAdd` runs `MaxDegree(Poly1.head, Poly2.head... |
The question is whether the following statement is true or false:
$A \leq_T B \implies A \leq_m B$
I know that if $A \leq_T B$ then there is an oracle which can decide A relative to B. I know that this is not enough to say that there is a computable function from A to B that can satisfy the reduction.
I don't ... |
operations that aren't closed for undecidable languages |
null |
Yes, $A$ is a CFL. Use the context free language (with the notation $|x|_0$ meaning what you have as #0's in $x$):
$B=\{x\in \{0,1\}^*:3\cdot|x|_0=|x|_1\}$
and the morphism $f:\{a,b,c\}^*\rightarrow\{0,1\}^*:$ $ f(a)=0, f(b)=00, f(c)=1$
so that
$A=f^{-1}(B)$.
Since the CFL's are closed under inverse... |
One of the definitions of an c.e. set is the following:
> $A \subseteq \Sigma^*$ is c.e. iff there is a decidable language $V\subseteq \Sigma^*$ (called verifier) s.t.
> for all $x\in \Sigma^*$,
>
> $x\in A$ iff there exists a $y\in\Sigma^*$ s.t. $\langle x, y \rangle \in V$.
So one way to show that a langua... |
Can we show a language is not c.e. by showing there is not any verifier for it? |
|computability|proof-techniques|undecidability| |
I often hear people talking about *parallel* computing and *distributed* computing, but I'm under the impression that there is no clear boundary between the 2, and people tend to confuse that pretty easily, while I believe it is very different:
- *Parallel* computing is more tightly coupled to multi-threading, or ho... |
|terminology|distributed-systems|parallel-computing| |
One of the definitions of a computably enumerable (c.e., equivalent to recursively enumerable, equivalent to semidecidable) set is the following:
> $A \subseteq \Sigma^*$ is c.e. iff there is a decidable language $V\subseteq \Sigma^*$ (called verifier) s.t.
> for all $x\in \Sigma^*$,
>
> $x\in A$ iff there exis... |
Can we show a language is not c.e. by showing there is no verifier for it? |
Can we show a language is not computably enumerable by showing there is no verifier for it? |
In practice, a common method to show that a language is not semidecidable is to show it is not decidable and that it is co-semidecidable. You then make use of the fact that any language that is both semidecidable and co-semidecidable is also decidable to conclude that your language is not semidecidable.
As an exampl... |
To make the terminology I use clear: decidable = recursive = computable, semidecidable = recursively enumerable = computably enumerable, co-semidecidable = co-recursively enumerable = co-computably enumerable.
In practice, a common method to show that a language is not semidecidable is to show it is not decidable an... |
To make the terminology I use clear: decidable = recursive = computable, semidecidable = recursively enumerable = computably enumerable, co-semidecidable = co-recursively enumerable = co-computably enumerable.
In practice, a common method to show that a language is not semidecidable is to show it is not decidable an... |
null |
I'm reading through the [MIT course notes on state space search](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/).
Consider a state space $S$, a set of nodes in which we look for an element having a certain property.
A [heuristic function](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/07ImprovedMetho... |
I'm reading through the [RMIT course notes on state space search](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/).
Consider a state space $S$, a set of nodes in which we look for an element having a certain property.
A [heuristic function](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/07ImprovedMeth... |
**Hint:** A generic simple polygon is monotone with respect to the $x$-axis if and only if it has exactly one vertex whose $x$-coordinate is smaller than its neighbors. This observation immediately suggests an $O(n)$-time algorithm, at least if no edge of your polygon is vertical.
**Spoilers ahoy:**
>!<pre>IsMonot... |
1.I'm trying to find the best algorithm for
converting an "ordinary" linked list
into an `ideal skip list`
.
Where the definition of an `ideal skip list` is that in the first level we'll have all
the elements , in the level above - half of them , the one after - quarter of them ... and so on .
... |
Building an ideal skip list ? and merging two skip lists into a new one? |
|algorithms|lists| |
As pointed out by @Raphael, Distributed Computing is a subset of Parallel Computing; in turn, Parallel Computing is a subset of Concurrent Computing.
*Concurrency* refers to the *sharing* of resources in the same time frame.
For instance, several processes share the same CPU (or CPU cores) or share memory or an I/O... |
1.I'm trying to find the best algorithm for
converting an "ordinary" linked list
into an `ideal skip list`
.
Where the definition of an `ideal skip list` is that in the first level we'll have all
the elements , in the level above - half of them , the one after - quarter of them ... and so on .
... |
As pointed out by @Raphael, Distributed Computing is a subset of Parallel Computing; in turn, Parallel Computing is a subset of Concurrent Computing.
*Concurrency* refers to the *sharing* of resources in the same time frame.
For instance, several processes share the same CPU (or CPU cores) or share memory or an I/O... |
null |
I am trying to search for an algorithm that can tell me that which node has the highest download/or upload capacity given a directed graph. Now, I looked at the maximal flow problem and at the edmond-karp algorithm. My questions;
1) Edmond-karp just tells us that how much throughput we can get (at the sink) from sou... |
Find the maximum bandwidth throughput in a directed graph |
|algorithms|graphs| |
1. I'm trying to find the best algorithm for converting an “ordinary” linked list into an “ideal skip list”.
Where the definition of an “ideal skip list” is that in the first level we'll have all
the elements, in the level above - half of them , the one after - quarter of them ... and so on.
I'm thinking abo... |
Building an ideal skip list? And merging two skip lists into a new one? |
null |
I'm reading through the [RMIT course notes on state space search](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/).
Consider a state space $S$, a set of nodes in which we look for an element having a certain property.
A [heuristic function](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/07ImprovedMeth... |
I have two closely related questions:
1. I'm trying to find the best algorithm for converting an “ordinary” linked list into an “ideal" skip list.
The definition of an “ideal skip list” is that in the first level we'll have all the elements, half of them in the next level, a quarter of them in the level after t... |
Building and merging skip lists |
I am trying to search for an algorithm that can tell me which node has the highest download (or upload) capacity given a weighted directed graph, where weights correspond to individual link bandwidths. I have looked at the maximal flow problem and at the Edmond-Karp algorithm. My questions are the following:
1. Edm... |
Finding the maximum bandwidth along a single path in a network |
the set of languages (equivalently) accepted by finite automata, generated by left- and right-linear grammars and described by regular expressions. |
How can I prove that the language that the operator $A$ defines for regular language $L$ is a context free language.
$A(L)= \{ w_1w_2: |w_1|=|w_2|$ and $w_1, w_2^R \in L \}$, where $x^R$ is the reversed form of $x$.
I understand that since $L$ is regular so does $L^R$ and a so a context free grammar, for making ... |
Why does $A(L)= \{ w_1w_2: |w_1|=|w_2|$ and $w_1, w_2^R \in L \}$ generate a context free language for regular $L$? |
|formal-languages|regular-languages|context-free|formal-grammars| |
I'm reading through the [RMIT course notes on state space search](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/).
Consider a state space $S$, a set of nodes in which we look for an element having a certain property.
A [heuristic function](http://www.cs.rmit.edu.au/AI-Search/Courseware/Slides1/07ImprovedMeth... |
the science and art of determining properties of algorithms, very often including correctness, runtime and space usage. |
the amount of time resources (number of atomic operations or machine steps)
required to solve a problem or run an algorithm with respect to the input size. |
the set of languages (equivalently) described by context-free grammars or accepted by (non-deterministic) pushdown automata. |
How can I prove that the language that the operator $A$ defines for regular language $L$ is a context free language.
$A(L)= \{ w_1w_2: |w_1|=|w_2|$ and $w_1, w_2^R \in L \}$, where $x^R$ is the reversed form of $x$.
I understand that since $L$ is regular so does $L^R$ and a so a context free grammar, for making ... |
a tree in which each node has no more than two children |
Questions about asymptotic notations and analysis |
the defining property of those formal languages which cannot be decided by any Turing machine |
You can show that it is decided by a PDA.
Check if the input string up to $i$th symbol is in $L$ while pushing them to the stack. Then check if the rest of the string is also in $L$ while poping one symbol from the stack for each symbol you read.
You can guess $i$ nondeterministically.
|
You can prove it's context-free by providing a PDA that accepts it (and proving the PDA works, typically by construction).
A PDA could work as follows. Read symbols and count them using the stack. Nondeterministically determine when you've read half the symbols. If what you've seen so far isn't in the regular langua... |
Will there be a need to change the definitions of security if we have quantum computers? What cryptographic constructions will break? Do you know a survey or an article that explains what will be needed to change? |
What is the difference between classical crypto and post-quantom crypto? |
|cryptography|quantum-computing| |
null |
What is the difference between classical crypto and post-quantum crypto? |
|reference-request|cryptography|quantum-computing| |
a particular kind of mathematically-based technique for the specification, development and verification of software and hardware systems. |
the analytic study of ways in which data are efficiently and effectively stored to and retrieved from computer systems. |
the algorithmic problem of ordering a set of elements with respect to some ordering relation. |
A computation model which relies on quantum-mechanic phenomena, such as entanglement and superposition. This generalizes the probabilistic model of computation. |
Research on methods and techniques to ensure the quality of software systems through design and development processes. |
state machines with stacks, capable of accepting the set of context-free languages. |
the study of relations (i.e., database tables) and relational operators (join, selection, projection, etc.) as a kind of algebraic structure. |
You can show that it is decided by a PDA.
Check if the input string up to $i$th symbol is in $L$ while pushing them to the stack. Then check if the rest of the string is also in $L^R$ while poping one symbol from the stack for each symbol you read. (Note that if $L$ is a regular language so is $L^R$ and memberships ... |
Let $A'(L)= \{ w_1 \sharp w_2: |w_1|=|w_2|$ and $w_1, w_2^R \in L \}$ where $\sharp$ is a new symbol.
$A'(L)$ is the intersection of context-free language $\{ w_1 \sharp w_2: |w_1|=|w_2|\}$ and regular $L\sharp L^R$, therefore it is context-free. $A(L)$ is a homomorphic image of $A'(L)$, so it is context-free as wel... |
A [question was posted on Stack Overflow][1] asking for an algorithm to solve this problem:
> I have a matrix (call it A) which is nxn. I wish to select a subset
> (call it B) of points from matrix A. The subset will consist of n
> elements, where one and only one element is taken from each row and
> from each co... |
Maximise sum of "non-overlapping" numbers in square array - help with proof |
|dynamic-programming| |
I'm by no means an expert (or even close to that) on the topic, but from what I know:
Classical cryptography depends on the intractability of factoring (or the discrete log problem). However, factoring is not believed to be NP-complete, and it is indeed solvable in polynomial time by quantum computers. So any crypto... |
Summary of this [paper][1] providing a (partial) answer.
There are two kinds of traditional public-key cryptographic methods: those based on integer factorization, and those based on the discrete logarithm, including elliptic-curve-based methods. These models are believed to be hard in the classical models, but have... |
A [question was posted on Stack Overflow][1] asking for an algorithm to solve this problem:
> I have a matrix (call it A) which is nxn. I wish to select a subset
> (call it B) of points from matrix A. The subset will consist of n
> elements, where one and only one element is taken from each row and
> from each co... |
null |
null |
A [question was posted on Stack Overflow][1] asking for an algorithm to solve this problem:
> I have a matrix (call it A) which is nxn. I wish to select a subset
> (call it B) of points from matrix A. The subset will consist of n
> elements, where one and only one element is taken from each row and
> from each co... |
null |
|algorithms|dynamic-programming|check-my-algorithm| |
|algorithms|computability|graphs|undecidability| |
|data-structures|machine-learning| |
Actually, I don't believe your proposed solution is correct. An example where you might need this case
| # |
| # # #|
| # # #|
| # # #|
might be
| 1 2 1 1|
| 2 1 1 1|
| 1 1 1 2|
| 1 1 2 1|
The optimal solution consists of all 2s, while there are only 1s in ... |
I'm trying to find the best algorithm for converting an “ordinary” linked list into an “ideal" skip list.
The definition of an “ideal skip list” is that in the first level we'll have all the elements, half of them in the next level, a quarter of them in the level after that, and so on.
I'm thinking about a $\m... |
Building ideal skip lists |
My organization wants to maintain multiple copies of data in order to preserve access in the case of localized disasters as well as for the purpose of long term preservation. Are there accepted formal models for determining the appropriate variety of media and their placement in the network? Are an currently operating ... |
Distributed Storage for Access and Preservation |
|digital-preservation|distributed-systems|storage| |
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