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Even this might be too basic for teenager, I nicely shows how to abstract problems, and is applicable for kids :
I highly recommend all CS people to take a look at: [Computer Science Unplugged](http://csunplugged.org/) , just to see how CS can look different :).
For young CS minded people I recommend to develop i... |
several favorite references which would be accessable to a highly motivated/advanced teenager
[1] <a href="http://www.amazon.com/The-New-Turing-Omnibus-Excursions/dp/0805071660">New Turing Omnibus</a> by AK Dewdney. has a grab bag of some of the more interesting/key concepts of CS. a very visual approach. AK Dewdney... |
What is a good beginner computer science book for a young adult, say, a 15 year old? I want to get started in CS, but have no idea where to start. I have limited experience in programming. |
Computer Science Book for Young Adults |
|soft-question| |
|soft-question|education| |
null |
The study of codes for error detection and correctoin, and codes for data-compression |
null |
Proof assistants such as Isabelle/HOL work on a syntactical level on a logical calculus. Imagine you have the [modus ponens rule](https://en.wikipedia.org/wiki/Modus_ponens) (MP)
$\qquad \displaystyle P\to Q, P\ \Longrightarrow\ Q$
and the proof goal
$\qquad \displaystyle (a \lor b) \to (c \land d), a \lor b \... |
Why is the Robinson Unification Algorithm so important to inference engines? |
null |
<sup>*I am learning [Automated Theorem Proving](http://en.wikipedia.org/wiki/Automated_theorem_proving) / [SMT solvers](http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories) / [Proof Assistants](http://en.wikipedia.org/wiki/Proof_assistant) by myself and post a series of questions about the process, starting [he... |
Why is unification so important to inference engines? |
<sup>*I am learning [Automated Theorem Proving](http://en.wikipedia.org/wiki/Automated_theorem_proving) / [SMT solvers](http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories) / [Proof Assistants](http://en.wikipedia.org/wiki/Proof_assistant) by myself and post a series of questions about the process, starting [he... |
<sup>*I am learning [Automated Theorem Proving](http://en.wikipedia.org/wiki/Automated_theorem_proving) / [SMT solvers](http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories) / [Proof Assistants](http://en.wikipedia.org/wiki/Proof_assistant) by myself and post a series of questions about the process, starting [he... |
<sup>*I am learning [Automated Theorem Proving](http://en.wikipedia.org/wiki/Automated_theorem_proving) / [SMT solvers](http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories) / [Proof Assistants](http://en.wikipedia.org/wiki/Proof_assistant) by myself and post a series of questions about the process, starting [he... |
|education| |
|complexity-theory|np-hard|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 $\mathrm{SAT}$ and ending wit... |
|asymptotics|didactics| |
The study of data representations that enable error detection, error correction and/or compression. |
null |
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... |
Why cannot I find any information about spanning tree for DAG ? I must be wrong somewhere. |
Does spanning tree make sense for DAG? |
|algorithms|graphs|trees| |
|graphs|spanning-trees| |
I often work with lexer/parsers, as opposed to a parser combinator and see people who never took a class in parsing, ask about parsing binary data. Typically the data is not only binary but also context sensitive. This basically leads to having only one type of token, a token for byte.
Can someone explain why pars... |
Why is using a lexer/parser on binary data so wrong? |
|parsers| |
Unification is such a fundamental concept in computer science that perhaps at time we even take it for granted. Any time we have a rule or equation or pattern and want to apply it to some data, unification is used to specialize the rule to the data. Or if we want to combine two general but overlapping rules, unificatio... |
null |
Proof assistants such as Isabelle/HOL work on a syntactical level on a logical calculus. Imagine you have the [modus ponens rule](https://en.wikipedia.org/wiki/Modus_ponens) (MP)
$\qquad \displaystyle P\to Q, P\ \Longrightarrow\ Q$
and the proof goal
$\qquad \displaystyle (a \lor b) \to (c \land d), a \lor b \... |
Proof assistants such as Isabelle/HOL work on a syntactical level on a logical calculus. Imagine you have the [modus ponens rule](https://en.wikipedia.org/wiki/Modus_ponens) (MP)
$\qquad \displaystyle P\to Q, P\ \Longrightarrow\ Q$
and the proof goal
$\qquad \displaystyle (a \lor b) \to (c \land d), a \lor b \... |
In principle, there is nothing wrong.
In practice,
- most non textual data formats I know aren't context-free and so aren't suitable for common parser generator. The most common reason for which they aren't context-free is that they have length fields giving the number of times a production has to be present.
... |
In principle, there is nothing wrong.
In practice,
- most non textual data formats I know aren't context-free and so aren't suitable for common parser generator. The most common reason for which they aren't context-free is that they have length fields giving the number of times a production has to be present.
... |
In principle, there is nothing wrong.
In practice,
- most non-textual data formats I know are not context-free and are therefore not suitable for common parser generators. The most common reason is that they have length fields giving the number of times a production has to be present.
Obviously, having a non ... |
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 $\mathrm{SAT}$ and ending wit... |
null |
|compilers|parsers| |
I often work with [lexer][1]/[parsers][2], as opposed to a parser combinator and see people who never took a class in parsing, ask about parsing binary data. Typically the data is not only binary but also context sensitive. This basically leads to having only one type of token, a token for byte.
Can someone explai... |
|programming-languages|compilers|parsers| |
In an attempt to offer a more objectively scientific answer to this question, I argue as follows. A dynamic language requires an interpreter, or runtime, to make decisions at run time. This interpreter, or runtime, is a computer program and, as such, was written in some programming language, either static or dynamic.
... |
An algorithm is a finite description of a computational process that transforms input data into output data.
Questions tagged with [tag:algorithms] are typically asking an [algorithm](http://en.wikipedia.org/wiki/Algorithm) for a specific task, or asking to analyze some specific algorithm. In the former case, it is ... |
null |
Questions related to design and analysis of algorithms |
null |
Complexity theory classifies problems with respect to their computational hardness, i.e. which machine models can solve them under which restrictions, and the relations between these classes like the famous $\sf{P}$ and $\sf{NP}$ classes.
[Computational complexity][1] is about the inherent difficulty of computationa... |
null |
Questions related to (computational) complexity of solving problems |
null |
The theory of computability studies which functions can be computed using which machine models.
[Computability theory](http://en.wikipedia.org/wiki/Computability_theory) (also known as recursion theory) is a branch of mathematical logic and computer science. It is mainly concerned with [computability](http://en.wiki... |
null |
Computability theory a.k.a. recursion theory. |
null |
Formal languages are sets of strings, i.e. sequences over symbols from some alphabet.
In general, the field of formal languages studies mathematical and logical properties of and relationships between languages (or sets) of strings (or sequences of symbols) over alphabets (or sets of symbols). Commonly encountered v... |
null |
Questions related to formal languages, grammars, and automata theory |
null |
null |
null |
In an attempt to offer a more objectively scientific answer to this question, I argue as follows. A dynamic language requires an interpreter, or runtime, to make decisions at run time. This interpreter, or runtime, is a computer program and, as such, was written in some programming language, either static or dynamic.
... |
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... |
Applications that allow to create formal proofs. They assist the user by finding partial and checking complete proofs. |
null |
Why focusing on dags and not general directed graphs? I think you should have a look [the directed minimum spanning tree problem][1]. The problem can be solved using the [Chu-Liu/Edmonds algorithm][2]. The wikipedia entry is not as clear as I was expecting, but it does have links to the original papers.
[1]: htt... |
Why focusing on dags and not general directed graphs? I think you should have a look at [the directed minimum spanning tree problem][1]. The problem can be solved using the [Chu-Liu/Edmonds algorithm][2]. The wikipedia entry is not as clear as I was expecting, but it does have links to the original papers.
[1]: ... |
null |
If you like, take one of the online courses following these links:
[MIT OpenCourseWare][1]
[Coursera 2012][2]
[1]: http://ocw.mit.edu
[2]: http://www.coursera.org |
One generalization of a tree in a directed graph is an arborescence. It's a directed tree with all edges directed from parent to child. |
null |
Knapsack problems are known to be easily solved in polynomial time using Dynamic Programming. But why do people say that this is actually an NP-Complete problem, which means that solving the problem in polynomial problem is no-way? |
Why is knapsack problem NP-C? |
|complexity-theory| |
[Knapsack problem][1] is $\sf{NP\text{-}complete}$ when the numbers are given as *binary* numbers. In this case, the dynamic programming will take exponentially many steps (in the size of the input, i.e. the number of bits in the input) to finish. (Another good example is considering the usual algorithms to see if a nu... |
[Knapsack problem][1] is $\sf{NP\text{-}complete}$ when the numbers are given as *binary* numbers. In this case, the dynamic programming will take exponentially many steps (in the size of the input, i.e. the number of bits in the input) to finish $\dagger$.
On the other hand, if the numbers in the input are given i... |
The [Knapsack problem](https://en.wikipedia.org/wiki/Knapsack_problem) as defined in [Karp's paper](https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems) is NP-Complete since there is a reduction from other NPC problem (Exact Cover, in this case) to Knapsack. This means that there is **no** polynomial algorit... |
Why is knapsack problem NP-Complete? |
|complexity-theory|np-complete| |
The [Knapsack problem](https://en.wikipedia.org/wiki/Knapsack_problem) as defined in [Karp's paper](https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems) is NP-Complete since there is a reduction from other NPC problem (Exact Cover, in this case) to Knapsack. This means that there is **no** polynomial algorit... |
The [Knapsack problem](https://en.wikipedia.org/wiki/Knapsack_problem) as defined in [Karp's paper](https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems) is NP-Complete since there is a reduction from other NPC problem (Exact Cover, in this case) to Knapsack. This means that there is **no** polynomial algorit... |
|complexity-theory|graphs|np-complete| |
|complexity-theory|reductions|np-complete| |
|complexity-theory|np-complete|approximation| |
|complexity-theory|np-complete| |
|complexity-theory|np-complete|reductions| |
null |
[Knapsack problem][1] is $\sf{NP\text{-}complete}$ when the numbers are given as *binary* numbers. In this case, the dynamic programming will take exponentially many steps (in the size of the input, i.e. the number of bits in the input) to finish $\dagger$.
On the other hand, if the numbers in the input are given i... |
The [Knapsack problem](https://en.wikipedia.org/wiki/Knapsack_problem) as defined in [Karp's paper](https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems) is NP-Complete since there is a reduction from other NPC problem (Exact Cover, in this case) to Knapsack. This means that there is **no** polynomial algorit... |
Knapsack problems are easily solved by dynamic programming. Dynamic programming runs in polynomial time; that is why we do it, right?
I have read it is actually an NP-complete problem, though, which would mean that solving the problem in polynomial problem is probably impossible.
Where is my mistake? |
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