## Search found 497 matches

Thu May 12, 2011 7:11 pm UTC
Forum: Mathematics
Topic: Formal mathematical definition of area
Replies: 10
Views: 2157

### Re: Formal mathematical definition of area

Note that it doesn't work on every subset of R^n (at least under certain standard axiomizations of the real numbers). Also note that it only allows you to determine the n-dimensional volume in R^n. There are measures that allow you to measure the volume of sets in arbitrary dimensions: http://en.wi...
Wed May 11, 2011 7:36 pm UTC
Forum: Mathematics
Topic: Formal mathematical definition of area
Replies: 10
Views: 2157

### Re: Formal mathematical definition of area

Of course, no one uses this in practice. Actually this is a powerful technique. Coordinate transformations and fubini's theorem allow you to calculate the integrals easily. The most general theory that allows you to define areas/volumes are volume forms on differentiable manifolds. Integrals over d...
Fri May 06, 2011 8:03 pm UTC
Forum: Coding
Topic: Passing a superclass into into a Generic Parameter (java)
Replies: 6
Views: 4011

### Re: Passing a superclass into into a Generic Parameter (java

What you are trying to do has to fail because sendCar(T) expects an object of class T (or one of its subclasses) and not an object of class Car. Obviously you cannot simply pass a super class to a method that expects a certain class. Otherwise all methods had to accept Object as parameters. If you w...
Wed May 04, 2011 7:25 pm UTC
Forum: Computer Science
Topic: Dual Implementation/Extension and recursion? Java.
Replies: 2
Views: 1938

### Re: Dual Implementation/Extension and recursion? Java.

Which method is called depends on the available method prototypes. Say you have a class class A { void compute(X param); void compute(Y param); } In this case the compiler will choose the correct method for you when you supply the correct type ie. final Object object; final A instance = new A(); // ...
Tue Apr 26, 2011 7:51 pm UTC
Forum: Coding
Replies: 24
Views: 3595

### Re: How bad are singletons?

Singletons (and global variables) are not that bad when you are the only person that will ever use your program/library/component. Singletons are incredibly bad when there is a chance that you will distribute your program/library sometime in the future. Other people might use multiple instances of y...
Sat Jul 10, 2010 12:00 pm UTC
Forum: Computer Science
Topic: I have an interesting question...
Replies: 13
Views: 2432

### Re: I have an interesting question...

Perhaps the many calculations per second might create subtle patterns, and with them, unique lines of code? They will but most of the output will just look like "asGFHs-.-df/hsreGG4\$3ztr". Constructing algorithms that extract "interesting" sequences out of random data don't seem...
Tue Jul 06, 2010 8:37 am UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

To be fair, it IS possible to achieve the general thing that OP is trying to do. That is, it is indeed possible to build a halting-checker that always returns "yes, no, and don't know", in finite time, and is always correct whenever it outputs something other than "don't know". ...
Mon Jul 05, 2010 7:13 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

And I would really like to see some example about your claim - some program, which actually has some other pattern in it and is still undecidable. I already posted such a program some posts before. Here is a non-recursive implementation: // let p be an array of pairs of strings containing a and b; ...
Mon Jul 05, 2010 6:48 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

⋅  Program calls something, which is identical to it. ⋅  It waits, at least some time, for the results of it, and uses those results in decisions of overall execution path. I told you several times: THAT IS A SPECIAL CASE. There is an infinite number of programs that don't behav...
Mon Jul 05, 2010 6:18 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

It's very real case that a program is waiting for something, which is topologically identical to it. But there are programs that do not do that and still the halting problem IS undecidable for them. I already gave you a _very_ simple example! My program computes a well-defined decision problem; the...
Mon Jul 05, 2010 3:11 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

My answer - my solver always returns. There is no "don't terminate otherwise" case. What does your solver return when "enumerate all sentences provable in ZFC" doesn't terminate? Does it return "This problem might be undecideable"? Building such a solver is trivial, to...
Mon Jul 05, 2010 2:39 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

There are many (infintly many) programs that do not depend on their own return value and are still undecideable. The program I gave is one example. Building an algorithm that computes the following: Given a turing machine x; Return true if x provably halts Return false if x provably doesn't halt Don...
Mon Jul 05, 2010 2:10 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

Yes, but then, how you build an unsolvable Post correspondence problem, which won't run into halting paradox? What do you mean by "halting paradox"? The halting problem is NOT a paradox. It can be proven in ZFC. It is consistent with ZFC (if ZFC is consistent itself). The program I gave m...
Mon Jul 05, 2010 12:53 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

heelium wrote:But, then, construct this case

See my post above. My program halts iff the Post correspondence problem has a solution. It is not decideable whether an instance of the Post correspondence problem has a solution.
Mon Jul 05, 2010 11:20 am UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

A program like: Given turing machine x; if(does_halt(x)) then dont_halt else halt; does not exist as the halting problem is undecideable. Consider this program: // let p be an array of pairs of strings containing a and b; e.g. //p = array({'aba', 'bab'}, {'aaa', 'bab'}, {'aba', 'bba'}, // {'abba', '...
Mon Jul 05, 2010 10:11 am UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

Each of these problems can be turned into a halting problem. What do you mean by this? In any case, there aren't uncountably many cases, because there are only countably many programs, and the original (unrelativized) halting problem is simply to determine for each program whether it halts or not, ...
Sun Jul 04, 2010 8:47 pm UTC
Forum: Computer Science
Topic: About solving halting problem on more general case
Replies: 128
Views: 13522

### Re: About solving halting problem on more general case

There are 4 class of programs: 1. Finish their job - they can be run and nothing more is needed to eventually know that. 2. Go into infinite repeating cycle - those are FSM's and could be detected by normal static analysis. 3. Go into growing cycle - those are infinite state machines and this text ...