instruction stringlengths 0 29.8k ⌀ |
|---|
null |
Over [here](http://cs.stackexchange.com/a/825/98), Dave Clarke proposed that in order to compare asymptotic growth you should plot the functions at hand. As a theoretically inclined computer scientist, I call(ed) this vodoo as a plot is never proof. On second thought, I have to agree that this is a very useful approach... |
How to fool the plot inspection heuristic? |
|asymptotics|didactics| |
Over [here](http://cs.stackexchange.com/a/825/98), Dave Clarke proposed that in order to compare asymptotic growth you should plot the functions at hand. As a theoretically inclined computer scientist, I call(ed) this vodoo as a plot is never proof. On second thought, I have to agree that this is a very useful approach... |
Didactic tools and methods particularly suitable for Computer Science education |
null |
General questions regarding learning computer science disciplines and CS education |
null |
[One time pad](https://en.wikipedia.org/wiki/One_time_pad) is an encryption method proven to have [perfect security](https://en.wikipedia.org/wiki/Information_theoretic_security) by Claude Shannon in 1948.
For a massage $m$ and a key ("pad") $k$ the encrypted ciphertext $c$ is
$$c = m \oplus k$$
The scheme is se... |
null |
Reduction is the process of solving one problem using a solution of another one.
Popular examples include:
* Proving [tag:undecidability] of $P$ by reducing the halting (or any undecidable) problem $\mathrm{HP}$ to $P$. This entails finding a computable function $f$ with $\mathrm{HP}(I) = \mathrm{true} \Longleftr... |
null |
An encryption method in which each message is encrypted by a XOR operation with a random key. The scheme has perfect security as long as the key used only once. |
null |
Tip: draw graphs of these functions using something like [Wolfram Alpha][1] to get a feeling for how they grow. Note that this is not very precise, but if you try it for sufficiently large numbers, you should see the comparative patterns of growth. This of course is no substitute for a proof.
E.g., try: [plot log(lo... |
An encryption method that encrypts messages by performing an XOR operation with a random key. The scheme has perfect security as long as each key is used only once. |
null |
The 3-SAT problem can be reduced to both the graph coloring and the directed hamiltonian cycle problem, but is there any chain of reductions which reduce directed hamiltonian cycle to graph coloring in polynomial time? |
Reducing directed hamiltonian cycle to graph coloring |
|reductions| |
I'm curious. I've been working on this datatype in *OCaml*:
type 'a exptree =
| Epsilon
| Delta of 'a exptree * 'a exptree
| Omicron of 'a
| Iota of 'a exptree exptree
Which can be manipulated using explicitly typed recursive functions (a feature that has been added quite recently)... |
Since @Pratik's answer covers good resources for algorithms, I just wanted to mention that since you asked about big-O notation, Peter Braß has written a book on the topic, which you can find [here](http://www-cs.ccny.cuny.edu/~peter/obook.letter.ps).
*Update:* In response to the comments, I recommend this book for ... |
The mathematical technique of [curve fitting][1] can be used to provide an infinite number of answers to your question. Given a curve and a range, one can readily find a polynomial that fits the curve to any degree of accuracy. This example from wikipedia shows how a sin wave can be fairly accurately fitted with a fort... |
null |
I am learning Automated Theorem Proving by myself and wanted to know what the different types of Automated Theorem Provers are. I found [A Review of Theorem Provers](http://www.google.com/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=6&ved=0CGgQFjAF&url=http%3A%2F%2Fwww.cs.cornell.edu%2FNuprl%2FPRLSeminar%2FPRLSeminar01... |
Types of Automated Theorm Provers |
|automated-theorem-proving| |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
I am learning Automated Theorem Proving by myself and wanted to know what the different types of Automated Theorem Provers are. I found [A Review of Theorem Provers](http://www.google.com/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=6&ved=0CGgQFjAF&url=http%3A%2F%2Fwww.cs.cornell.edu%2FNuprl%2FPRLSeminar%2FPRLSeminar01... |
Types of Automated Theorem Provers |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
null |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
If I understand correctly, all information about the game is available to both players. That is, all of the possible moves are known (mainly because both players can look at the cards of the other player) and this knowledge is available to both players. This makes game is a zero-sum game of perfect information. Thus th... |
Speaking from experience, when trying to figure out the growth rate for some observed function (say, Markov chain mixing time or algorithm running time), it is very difficult to tell factors of $(\log n)^a$ from $n^b$. For example, $O(\sqrt{n} \log n)$ looks a lot like $O(n^{.6})$ or so. |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
null |
|algorithms|education| |
Speaking from experience, when trying to figure out the growth rate for some observed function (say, Markov chain mixing time or algorithm running time), it is very difficult to tell factors of $(\log n)^a$ from $n^b$. For example, $O(\sqrt{n} \log n)$ looks a lot like $O(n^{.6})$ or so.
For example, in "Some unexpe... |
|logic|automated-theorem-proving| |
A nice example is Brzozowski's deeply magical minimal DFA algorithm. Given a finite automaton $N = (Q, S \subseteq Q, F \subseteq Q, R \subseteq Q \times \Sigma \times Q)$, we can compute a minimal deterministic finite automaton from it:
$$
\mathrm{Minimize} : \mathrm{NFA \to DFA} = \mathrm{Determinize\circ Rever... |
Speaking from experience, when trying to figure out the growth rate for some observed function (say, Markov chain mixing time or algorithm running time), it is very difficult to tell factors of $(\log n)^a$ from $n^b$. For example, $O(\sqrt{n} \log n)$ looks a lot like $O(n^{.6})$:
![enter image description here][1]... |
Over [here](http://cs.stackexchange.com/a/825/98), Dave Clarke proposed that in order to compare asymptotic growth you should plot the functions at hand. As a theoretically inclined computer scientist, I call(ed) this vodoo as a plot is never proof. On second thought, I have to agree that this is a very useful approach... |
Speaking from experience, when trying to figure out the growth rate for some observed function (say, Markov chain mixing time or algorithm running time), it is very difficult to tell factors of $(\log n)^a$ from $n^b$. For example, $O(\sqrt{n} \log n)$ looks a lot like $O(n^{.6})$:
![plot][1]
<sup>[[source](http:... |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
null |
I am learning automated theorem proving by myself and looked at [Coq][1] and did the first chapter of the intoduction to [Isabelle][2] amongst others; [Types of Automated Theorem Provers][3]
I have known Prolog for a few decades and am now learning F#, so ML, O'Caml and LISP are a bonus. Haskell is a different beast... |
null |
One thing that I think you'll find interesting is that the "theorem proving" term varies vastly depending on what field you're in. While they are -- in the abstract -- somewhat related, practical theorem proving (like the kind you see elaborated on in the Handbook of Automated Reasoning) has less to do with Coq or Isa... |
The categorization in that list is certainly still current.
Perhaps one new category has emerged, namely, _dependently-typed programming languages_. These are essentially automated theorem provers where the primary goal is not proving theorems, but programming. Due to the [Curry-Howard correspondence][1], these two... |
If I understand correctly, all information about the game is available to both players. That is, the starting configuration and all of the possible moves are known by both players (mainly because both players can look at the cards of the other player). This makes game is a zero-sum game of perfect information. Thus the... |
If I understand correctly, all information about the game is available to both players. That is, the starting configuration and all of the possible moves are known by both players (mainly because both players can look at the cards of the other player). This makes game is a zero-sum game of perfect information. Thus the... |
|coq|automated-theorem-proving|proof-assistants| |
|logic|automated-theorem-proving|proof-assistants| |
I am learning automated theorem proving / proof assistants by myself and looked at [Coq][1] and did the first chapter of the intoduction to [Isabelle][2] amongst others; [Types of Automated Theorem Provers][3]
I have known Prolog for a few decades and am now learning F#, so ML, O'Caml and LISP are a bonus. Haskell i... |
I am learning Automated Theorem Proving / Proof assisstants by myself and wanted to know what the different types of Automated Theorem Provers are. I found [A Review of Theorem Provers](http://www.google.com/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=6&ved=0CGgQFjAF&url=http%3A%2F%2Fwww.cs.cornell.edu%2FNuprl%2FPRLSe... |
|logic|coq|type-theory|recursion|proof-assistants| |
null |
I have designed a classifier M which recognizes gestures and classifies it under any category always. A gesture is classified based on the hamming distance between the sample time series y and the training time series x. The result of the classifier are probabilistic values. There are 3 classes/categories with labels A... |
Issue in comparing classifiers for pattern recognition |
|machine-learning|pattern-recognition| |
I am learning automated theorem proving, SMT solvers, and proof assistants. Why is it that automated theorem provers, i.e. ACL2, and SMT solvers don't need human assistance while proof assistants, i.e. Isabelle and Coq, do?
|
Why do some inference engines need human assistance while others don't? |
|logic|proof-assistants|automated-theorem-proving|smt-solvers| |
A [Fibonnaci Heap][1] supports the following operations:
- `insert(key, data)` : adds a new element to the data structure
- `find-min()` : returns a pointer to the element with minimum key
- `delete-min()` : removes the element with minimum key
- `delete(node)` : deletes the element pointed to by `node`
... |
Priority queue with both decrease-key and increase-key operations |
|data-structures|priority-queues| |
null |
Validity of higher order formulae is in general not decidable and search spaces are *huge*, so all you can hope to do is to *try* to find a proof -- assuming it exists -- by cleverly enumerating the proof space (think [sledgehammer](http://www.cl.cam.ac.uk/research/hvg/Isabelle/sledgehammer.html), aptly named) but that... |
I am learning [Automated Theorem Proving][1] / [SMT solvers][2] / [Proof Assistants][3] by myself and keep reading about the [Unification Algorithm][4].
- What is it and why is so important to [Inference Engines][5]?
- Why is it so important to Computer Science?
- Why should every computer science student lear... |
Why is the Robinson Unification Algorithm so import to inference engines? |
|logic|proof-assistants|automated-theorem-proving|smt-solvers|unification| |
There isn't an easy way to do this. In fact [a recent paper by Charles Parker][1] explains some of the problems with using ROC curve measurements (there's a friendly overview at [my blog][2] - self promotion alert!!). His paper does make some recommendations on the best ways to compare different classifiers, so you wil... |
I don't think it is important to _inference engines_. The unification algorithm is however very helpful for [_type inference_][1]. These are two very different kinds of inference.
Type inference is important to computer science because _types_ are important in the theory of programming languages, which is a signific... |
I don't think it is important to _inference engines_. The unification algorithm is however very helpful for [_type inference_][1]. These are two very different kinds of inference.
Type inference is important to computer science because _types_ are important in the theory of programming languages, which is a signific... |
I am learning [Automated Theorem Proving][1] / [SMT solvers][2] / [Proof Assistants][3] by myself and keep reading about the [Unification Algorithm][4].
- What is it and why is so important to [Inference Engines][5]?
- Why is it so important to Computer Science?
[1]: http://en.wikipedia.org/wiki/Automate... |
I don't think it is important to _inference engines_. The unification algorithm is however very helpful for [_type inference_][1]. These are two very different kinds of inference.
Type inference is important to computer science because _types_ are important in the theory of programming languages, which is a signific... |
This has come up on the Coq mailing list several times, but I never saw a conclusive answer. Coq isn't as general as it could be; the rules in (Coquand, 1990) and (Giménez, 1998) (and his PhD thesis) are more general and do not require strict positivity. Positivity enough is not enough, however, when you go outside `Se... |
null |
|complexity-theory|reductions| |
Let $Q \in \sf{NP}$ and $Q' \in \sf{NP\text{-}hard}$. Then, by definition, $Q$ is (many-one) reducible to $Q'$ in polynomial time.
The exact chain of the reductions will depend on the $\sf{NP\text{-}hard}$ness proof of $Q'$. Typically, it is proven by a chain of reductions starting from $SAT$ and ending with $Q'$ an... |
|algorithms|asymptotics|didactics|benchmarking| |
|data-structures|binary-trees|combinatorics|graphs|proof-techniques| |
|logic|proof-assistants|automated-theorem-proving|coq| |
I am learning [automated theorem proving][1], [SMT][2] solvers, and [proof assistants][3]. Why is it that automated theorem provers, i.e. [ACL2][4], and SMT solvers don't need human assistance while proof assistants, i.e. [Isabelle][5] and [Coq][6], do?
[1]: http://en.wikipedia.org/wiki/Automated_theorem_proving... |
|logic|programming-languages|coq|inductive-datatypes| |
Assume you have a priority queue that has $O(1)$ `find-min`, `increase-key`, and `insert`. Then the following is a sorting algorithm that takes $O(n)$ time:
vector<T>
fast_sort(const vector<T> & in) {
vector<T> ans;
pq<T> out;
for (auto x : in) {
out.insert(x);
}
... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.