I want to write a program to do this, based on Soot's build-in Reaching-Definition analysis. Now I'm wondering is this the correct approach? I searched and found nobody seems to ever be interested in this direction.
Any suggestions?
What you probably want to do is combine a set of ranges using an iterative data flow solver. You want to combine range-values from inputs into range-values for the set of definitions that cross basic blocks.
For this you generally need a control flow graph and the transfer functions across the basic blocks. I suppose you can treat the reaching-definitions graph in a similar way.
You'll then need interprocedural range propagation to push the ranges across the code.
This is a really generic problem you are stating. Reaching Definitions does not have much to do with this. Global Value Numbering is more what you apparently want but it's too hard to tell from your description. Try the Soot mailing list with a more detailed problem statement.
Related
I want to make a Java program to help people with basic discrete mathematics (that is to say, checking the truth values of statements). To do this, I need to be able to detect how many variables the user inputs, what operators there are, and what quantifiers there are, if any (∃ and ∀). Is there a good algorithm for being able to do all these things?
Just so you know, I don't just want a result; I want full control over their input, so I can show them the logical proof. (so doing something like passing it to JavaScript won't work).
Okay, so, your question is a bit vague, but I think I understand what you'd like to do: an educational aid that processes first-order logic formulas, showing the user step by step how to work with such formulas, right? I think the idea has merit, and it's perfectly doable, even as a one-man project, but it's not terribly easily, and you'll have to learn a lot of new things -- but they're all very interesting things, so even if nothing at all comes out of it, you'd certainly get yourself some valuable knowledge.
I'd suggest you to start small. I'd start by building a recursive descent parser to recognize zero-order logic formulas (a machine that would decide if a formula is valid, i.e. it'd accept "A ^ B" but it'd reject "^ A ^"). Next up you'd have to devise a way to store the formula, and then you'd be able to actually work on it. Then again, start small: a little machine that accepts valid zero-order logic formulas like TRUE AND NOT (TRUE AND FALSE), and successfully reduces it step by step to true is already something that people can learn from, and it's not too hard to write. If you're feeling adventurous, add variables and make equations: A AND TRUE = TRUE -- it's easy to work these out with reductions and truth tables.
Things get tricky with quantifiers that bind variables, that's where the Automated theorem proving may come into play; but then, it all depends on exactly what you'd like to do: implementing transformations into the various normal forms, and showing the process step by step to the student would be fairly easy, and rather useful.
At any rate, I think it's a decent personal project, and you could learn a lot from it. If you're in a university, you could even get some credit for it eventually.
The technique I have used is to parse the input string using a context free grammar. There are many frameworks to help you do this, I have personally used ANTLR in the past to parse an input string into a descrete logic tree. ANTLR allows you to define a CFG which you can map to Java types. This allows you to map to a data structure to store and evaluate the truth value of the expression. Of course, you would also be able to pull out the variables contained in the data structure.
I thought of writing a piece of software which does Alpha Compositing. I didn't wanted ready made code off from internet so I tried to find research papers and other sources to understand the mathematical algorithms, and initiated to implement.
But, I got lost very quickly. So my question is,
How should I approach these papers to extract the necessary details from it in order to write algorithm based on it. Any specific set of steps which works well?
Desired answer :
Read ...
Extract ...
Understand ...
Implement ...
Note: This question is not limited to only Alpha Compositing, so more generalised approach will be helpful. I have tagged Java and C++, because thats my desired language to implement the image processing.
What I have done so far?
This is not a homework question but it is of course better to say what I know. I have read wiki of Alpha compositing, and few closely related Image compositing research papers. But, I stuck at the next step to take in order to go from understanding to implementation.
Wikipedia
Technical Memo, Image compositing
I'd recommend reading articles with complex formulas with a pencil and paper. Work through the math involved until you have a good grasp on it. Then, you'll be ready to code.
Start with identifying the steps needed to perform your algorithm on some image data. Include all of the steps from loading the image itself into memory all the way through the complex calculations that you may need to perform. Then structure that list into pseudocode. Once you have that, it should be rather easy to code up.
Write pseudocode. Ideally, the authors of the research papers would have done this, but often they don't. Write pseudocode for some simple language like Matlab or possibly Python, and hack away at writing a working implementation based on the psuedocode.
If you understand some parts of the algorithm but not others, then implement your pseudocode into real code for the parts you understand, and leaving comments for the places you don't.
The section from The Pragmatic Programmer on "Tracer Bullets" basically describes this idea. You want to quickly hack together something that takes your data into some form of an output, and then iterate on the body of the code to get it to slowly resemble the algorithm you're trying to produce.
My answer is necessarily somewhat vague. There's no magic bullet for something like this.
Have you implemented any image processing algorithms? Maybe start with something a little simpler, like desaturation/color intensification, reversal (side to side and upside down), rotating, scaling, and compositing images through a mask.
Once you have those figured out, you will be in a very good position to do an alpha composite.
I agree that academic papers seem to go out of their way to make implementation details muddy and uncertain. I find that large amounts of simplification to what is written is needed to begin to perform a practical implementation. In their haste to be general, writers excessively parameterize every aspect. To build useful, reliable software, it is necessary to start with something simple which actually works so that it can be a framework to add features. To do that, it is necessary to throw away 80–90 percent of the academic generality. Often much can be done with a raft of symbolic constants, but abandoning generality (say for four and five dimensional images) doesn't really lose anything in practice.
My suggestion is to first write the algorithm using Matlab to make sure that you understood all the steps and then try to implement using C++ or java.
To add to the good suggestions above, try to write your pseudocode in simple module (Object oriented style ) so has to have a deep understanding of each part of your code while not loosing the big picture. Writing everything in a procedural way is good a the beginning but as the code grow, it might get become hard to keep up will all you are trying to do.
This example cites one of the seminal works on the topic: Compositing Digital Images by Porter & Duff. The class java.awt.AlphaComposite implements the same rules.
I now have an idea, that I use the function as a string, and I calculate the real integral by hand, and ask a question to the user what the definite integral is, but that isn't a real solution.
I was wondering if there was a way to input a function and output an integral/derivative (depending on user choice). My initial step was to put it into an array somehow, but given the many types of functions, this wasn't happening.
I researched everywhere, and I haven't found a method that actually does this with no additional code, nor any code that actually does this, period.
Also, I want to see if there was a way to make a GUI interface and plot inputted functions on to that, if that's possible too.
Thanks :)
What you're describing is known as symbolic integration. There's currently no fully general way to implement it, but there are some techniques available. One such is the Risch algorithm.
Alternatively, an easier problem than symbolic integration is [symbolic differentiation -- and, if the differential of the user's input is equivalent* to the expression which they were asked to integrate, then their integral is probably correct.
You may also want to consider using an existing CAS**, such as Mathematica, to implement this. They've already implemented most of the tools you're after.
*: Keep in mind, though, that two mathematical expressions may be equivalent without being identical, either in trivial ways (e.g, terms in a different order), more complex ones (e.g, large expressions factored differently), or fundamentally (e.g, trig functions replaced with complex exponentials or vice versa).
**: Computer algebra system
Javacalculus is what you are looking for.
Good luck!
I have as an input a 2D polygon with holes, and I need to find it's straight skeleton, like in the picture:
(source: cgal.org)
Maybe there is a good Java library for it?
And if not, can you point me to the good explanation of the algorithm, so I could implement it myself? (I haven't found good resources on Google)
I wrote this a little while back. Not sure if it's robust enough.
https://github.com/twak/campskeleton
(edited for 2018...)
See http://www.sable.mcgill.ca/~dbelan2/roofs/roofs.html which contains an applet.
You may be able to use the JTS Topology Suite. It is a very capable library that I've used on a number of projects - never for straight skeleton, but it may be possible.
Edit:
Ah. I see that "Straight Skeleton" is a technical term. The wikipedia article references several algorithms. Have you looked at those?
As I understand it, you have a (convex?) polygon. From it, you subtract 1 or more (potentially non-convex) polygons. You want to turn the result into a set of polygons without holes. Are there extra rules that you're trying to apply?
I have a hard time coming up with a set of rules from the example that you provided. The outer polygons are non-convex; so it doesn't seem like you're trying to find a convex set to represent the result (which is a relatively common task).
If you could use the breakdown shown below, the algorithm is pretty simple. Can you clarify?
Can I ask u what is your purpose for finding Straight skeleton? Is it personal or commercial? I would be interested in knowing how you r using it to solve real time problems? I do have a java library that does that. My algorithm is listed here http://web.stcloudstate.edu/rsarnath/skeleton/definition.htm
Given the source code of a program, how do I analyze it and count the function points within it?
Thanks!
You might find this tutorial on FPA of interest. Personally, I don't put much stock in this estimation method. From my perspective it attempts to provide a precise estimate in for things that have been shown repeatedly to not be precisely measurable. I much prefer planning poker or something similar that tries to group things within a similar order of magnitude and provide an estimate based on your previous estimations for similarly sized stories.
If you're doing this for a class, simply follow the rules given in the text book and crank out the answer. If you're really intending to try this as a software development estimation method, my advice is to simplify the process rather than make it more complex. I would imagine that members of the International Function Point User Group (yes, there is one), will disagree.
With a code analysis tool. If you want to write one yourself, you might want to start with cglib or ASM.