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I have been reading some papers where I keep reading stuff like `first-order formula modulo a background theory`. Does anyone know what modulo means in this case ? Is it something like with respect to ? |
The meaning of modulo |
|untagged| |
You have left out a important step... The formula you have is for the pearson correlation. What makes it spearman is that x and y are the ranks for the two original variables. This ranking step must be taken into account for the complexity of the spearman correlation coefficient. Essentially you must sort each of t... |
I have been reading some papers where I keep reading stuff like “first-order formula modulo a background theory”. Does anyone know what modulo means in this case ? Is it something like “with respect to”? |
The meaning of modulo in “formula modulo a background theory” |
|terminology|logic|term-rewriting| |
There is a library called [SMAPO][1] (short for library of linear descriptions of SMAll problem instances of POlytopes in combinatorial optimization) for a lot of polytopes including the symmetric TVP as well as the graphical TVP.
For the STSP, this is the list of number of facets for small polytopes
Nodes ... |
For an assignment I have to program an application to schedule conversations.
There is an event where representatives of the elementary schools talks with the representatives of high schools. They will talk about the students that will be transferred to the highschool. There are approximately 200 elementary schools a... |
How to reduce a NP-problem? |
|np-hard|heuristics| |
Is it possible to design a compiler which optimizes a loop in which arrays are accessed in alternate fashion ?
For example:
for(int i = 0; i < n; i++)
{
// some operation on a[i] and b[i] where
// a and b are integer arrays
}
Now I think a good compiler optimization would be sto... |
|optimization|mathematical-programming| |
For asymptotic bounds, [Fiorini, Massar, Pokutta, Tiwari, and de Wolf][1] recently showed exponential lower bounds on the number of facets of *any polytope that projects to the TSP polytope* (the TSP polytope, being the convex hull of feasible TSP solutions). This is stronger than what you ask for, and implies that eve... |
[Garey & Johnson][1] outline the following four steps for proving NP-completeness results:
1. **Show that your problem is in NP.** Informally, this means that it's possible to verify the correctness of potential solutions to your problem in [polynomial time][2].
2. **Select a known NP-complete problem.** Again,... |
[Garey & Johnson][1] outline the following four steps for proving NP-completeness results:
1. **Show that your problem is in NP.** Informally, this means that it's possible to verify the correctness of potential solutions to your problem in [polynomial time][2].
2. **Select a known NP-complete problem.** Again,... |
[Garey & Johnson][1] outline the following four steps for proving NP-completeness results:
1. **Show that your problem is in NP.** Informally, this means that it's possible to verify the correctness of potential solutions to your problem "quickly" - i.e., in [polynomial time][2].
2. **Select a known NP-complete ... |
null |
nowadays this field is known as **big data** and its evolving very rapidly and quickly based on the strong connection with virtualization and relational database technology is only seen as a subset. also as comments note, key/value databases and NoSQL are where much new innovation and momentum is moving. but from your ... |
How to reduce to an NP-complete problem? |
null |
yes there did seem to be historically a strong connection between study of dynamical systems and advanced theoretical computer science thats shifted dramatically over time. some of this has become mainstream and incorporated into more "core CS" (for example the empirical study of algorithms running on the SAT transitio... |
Is it possible to design a compiler which optimizes a loop in which arrays are accessed in alternate fashion? For example like this:
// int[] a,b
int sum = 0;
for(int i = 0; i < n; i++)
{
sum += a[i] + b[i];
}
With the usual sequential array storage, `a[i]` and `b[i]` may be far awa... |
Are compilers able to detect alternating accesses to arrays and interleave them in memory? |
|compilers|arrays|program-optimization|memory-management| |
For an assignment I have to program an application to schedule conversations.
There is an event where representatives of the elementary schools talks with the representatives of high schools. They will talk about the students that will be transferred to the highschool. There are approximately 200 elementary schools a... |
How to reduce to an NP-hard problem? |
|complexity-theory|reductions|np-hard| |
|algorithms|memory-management| |
computer scientists generally are of the consensus that the Church Turing thesis[1] is correct and definitive, ie that Turing machines describe computation, and that _more powerful forms do not really exist,_ and take assertions that some model is "more powerful" than Turing machines with extreme skepticism, even near ... |
null |
computer scientists generally are of the consensus that the Church Turing thesis[1] is correct and definitive, ie that Turing machines describe computation, and that _more powerful forms do not really exist,_ and take assertions that some model is "more powerful" than Turing machines with extreme skepticism, even near ... |
there is much interesting research in this area that is ongoing. see eg
- using search engines to estimate size based on pages counted eg [How Large is the WWW](http://www.stat.washington.edu/adobra/Files/Papers/Webpaper.pdf) by Dobra and Fienberg
- theoretical models of networks that model the growth of the web... |
null |
In first order logic there are formulae that are not necessarily valid. The equality
$x + y = y + x$
does not hold for arbitrary interpretations of equality and the addition symbol. It does hold for the interpretation of $+$ and $=$ in standard arithmetic. So if we assume the theory of Peano arithmetic (or first ... |
null |
Just an extended comment.
I think that before trying to find a reduction, you should try to better formalize the problem:
* define exactly what the *parameters* of the problem are, formalize their constraints, and formalize the question;
* try to simplify (or remove) the details;
For example:
* *If a grou... |
For an assignment I have to program an application to schedule conversations.
There is an event where representatives of the elementary schools talks with the representatives of high schools. They will talk about the students that will be transferred to the highschool. There are approximately 200 elementary schools a... |
We collect most of the information about possible compiler optimizations during forward pass. Is it possible to utilize the information collected in forward pass in a backward pass so as to perform better optimizations ?
Note: I have been going through the patent at http://www.google.com/patents/US7765534 and was wo... |
Benefit of Backward Pass at compiler time |
|optimization|compilers| |
Is there any book or tutorial that teaches us how to efficiently apply the common algorithms (sorting, searching, etc.) on large data (i.e. data that cannot be fully loaded into main memory) and how to efficiently apply those algorithms considering the cost of block transfer from external memory ? For example, almost a... |
For an assignment I have to program an application to schedule conversations.
There is an event where representatives of the elementary schools talks with the representatives of high schools. They will talk about the students that will be transferred to the highschool. There are approximately 200 elementary schools a... |
We collect most of the information about possible compiler optimizations during forward pass. Is it possible to utilize the information collected in forward pass in a backward pass so as to perform better optimizations ?
Note: I have been going through the patent [Compiler with cache utilization optimizations](http:... |
|compilers|program-optimization| |
|algorithms|efficiency|memory-management| |
Questions about how to optimise a program's performance, both manually and automatically, e.g. in compilers. |
null |
If you don't have distinct variables in your clauses, resolution will give you too weak conclusions.
For example, let's have 4 clauses:
1. $A\lor B(x)$
2. $\lnot A\lor C(x)$
3. $\lnot B(c)$
4. $\lnot C(d)$
where $x, y$ are variables and $c, d$ constants. If we perform resolution on the first two without ren... |
Many major compiler optimizations use backward passes. For example, computing liveness information, which is used to do dead code elimination, usually requires a backwards pass over the CFG of a program in order to identify unnecessary statements. Partial redundancy elimination, a powerful algorithm for eliminating r... |
null |
null |
Benefit of Backward Pass at compile time |
How exactly [Loop Dependence Analysis] helps in [vectorization] ? Are there any standard rules of safety criterias for parallizing such loops ?
[Loop Dependence Analysis]:http://en.wikipedia.org/wiki/Loop_dependence_analysis
[vectorization]:http://en.wikipedia.org/wiki/Vectorization_(parallel_computing) |
Using Loop Dependence analysis for vectorization |
|compilers|program-optimization| |
As the new semester starts soon, I am interested in reasearch regarding the teaching of introductory programming courses. I would like to improve my university course and I am looking for scientific papers on that topic.
One trend I have seen is that some students (a smaller group) are interested in computers or the... |
References on teaching introductory programming courses |
|reference-request| |
null |
Im looking for a major in Theoretical Compiter Science, especificaly im interested on complexity theory and probabilistic automata theory, as Im still graduating in one year, what advanced courses in Math (like Galois theory or Armonic analysis for example) do you think would be usefull to take in this 2 semesters and ... |
Math for TCS major |
|complexity-theory|automata| |
To show that a grammar is unambiguous, it is enough to show that for any expression E, there is only one "last step" possible in any derivation of E. It is the case here : the last rule is given by the last symbol of the expression (either +, *, or a terminal a), and the parentheses will prevent any ambiguity.
Of cour... |
Lets say I have given following grammar which generates arithmetic expressions in reverse polish notation:
$G=({E},{a,+,*},P,E)$
$P={ E \rightarrow EE+ | EE* | a }$
I know this grammar is unambiguous.
What I do not understand is how I can prove this.
I already searched a lot to in google, etc. but eve... |
Unambiguity of Reverse Polish Notation |
|formal-languages|formal-grammars| |
null |
|compilers|parallel-computing|program-optimization| |
|reference-request|education| |
|complexity-theory|automata|education| |
There is (at least) one way to prove unambiguity of a grammar $G = (N,T,\delta,S)$ for language $L$. It consists of two steps:
1. Prove $L \subseteq \mathcal{L}(G)$.
2. Prove $[z^n]S_G(z) = |L_n|$.
The first step is pretty clear: show that the grammar generates (at least) the words you want, that is correctn... |
Here's a [survey paper](http://www.seas.upenn.edu/~eas285/Readings/Pears_SurveyTeachingIntroProgramming.pdf) and [another](http://londonmet-163-167-082-061.londonmet.ac.uk/library/a98362_3.pdf).
You might want to consider the [inverted method](http://se.inf.ethz.ch/old/projects/michela_pedroni/Report.pdf) also known... |
I try to teach myself the usage of bison. The manpage bison(1) says about bison:
> Generate a deterministic LR or generalized LR (GLR) parser employing LALR(1), IELR(1), or canonical LR(1) parser tables.
What is an IELR-parser? All relevant articles I found on the world wide web are paywalled. |
What is an IELR(1)-parser? |
|parsers| |
I'm looking for a major in Theoretical Computer Science; specifically, I'm interested on complexity theory and probabilistic automata theory. As I'm graduating in one year, what advanced courses in math (like Galois theory or Harmonic analysis, for example) do you think would be useful to take over the next two semeste... |
I'm reading through `"Computers and Intractability: A guide to the Theory of NP-Completeness" by Michael R. Garey and David S. Johnsonand, p. 20` and I came across this concept of a function that is polynomially related to input lengths obtained using some encoding scheme. Let $Len:D_p\rightarrow \mathbb Z^+$ be a func... |
Polynomially related lengths under two different encodings |
|polynomial-time|encoding-scheme| |
I'm reading through `"Computers and Intractability: A guide to the Theory of NP-Completeness" by Michael R. Garey and David S. Johnsonand, p. 20` and I came across this concept of a function that is polynomially related to input lengths obtained using some encoding scheme. Let $$Len:D_p\rightarrow \mathbb Z^+$$ be a fu... |
I'm reading through `"Computers and Intractability: A guide to the Theory of NP-Completeness" by Michael R. Garey and David S. Johnsonand, p. 20` and I came across this concept of a function that is polynomially related to input lengths obtained using some encoding scheme. Let $$Len:D_p\rightarrow \mathbb Z^+$$ be a fu... |
null |
The problem is:
∃x∀y(x ≥ y)
With a domain of all real positive integers.
The negation is:
∀x∃y(x < y)
so, if y = x + 1
the negation is true.
That means the negation of the negation (or, the original problem) is false.
My question is, that if the original problem is ∃x∀y(x ≥ y), why can't x = y a... |
Predicate Logic Paradox |
|discrete-mathematics| |
I'll start with your last question (in the comments); namely "Why doesn't x = y satisfy the initial problem".
The answer is in the quantifiers. Read from left to right. It starts with "there exists" X. So pick an X in your head. Say X = 5. We can not pick Y here because it doesn't have a value yet and we MUST pick ... |
|logic| |
|algorithms|optimization|linear-programming|mathematical-programming| |
|complexity-theory|polynomial-time|encoding-scheme| |
|formal-languages|formal-grammars|parsers| |
|algorithms|randomness| |
I found a few resources which helped me to understand the more complex algorithms for use of loop dependence analysis.
The basic way in which the result from Loop Dependence Analysis is utilized is through various tests such as
[Dependence Test] of various types such as GCD Test, Conservative Test etc. help in d... |
I keep coming across references to [fixed point][1] in questions and answers at stackexchange and I look up the meaning on the web obviously finding reference at sites such as Wikipedia. However none of the references really answer my question of what is a fixed point and what does it mean in the world of computer scie... |
Fixed point, what does it mean in the world of computer science |
|terminology| |
null |
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