I am really confuse with the statement coverage. I did some search on the Internet. Some say the statement coverage only go through the true condition, which in this case is 1-2-3-4-12. However, others say the statement coverage should cover as many statements as possible, which I believe in this case will be 1-2-3-5-6-7-8-9-10-11-12. Which one is correct?
For the branch coverage, I believe I should test both the true/false conditions without considering the loop, which I will use the value 1)x=-1 and 2)x=0
For the path coverage, I think I should test all the paths so compared to branch coverage I will need to test the loop also. So I am going to use the value 1) x= -1, 2)x = 0 and 3) x = 10.
Is my answers correct?
Thank you in advance
I think "statement coverage" refers to "meaningful/useful/normal".
The nubmer of statement may vary by breaking one statement into two.
The "true" condition may not be useful for us just like the example you gave. Normally we want a positive number to get its factorial. You can switch the "true" and "false" conditions whatever you like.
To calculate Statement Coverage, find out the shortest number of paths following which all the nodes will be covered.
So in your case :
1-2-3-5-6-7-8-9-10-11-12
This path is the shortest and covering maximum number of nodes but not all
so we have to take one more path , which is :
1-2-3-4-12
So in this exercise , the value of SC=2
Related
In Z3 (Python) my SAT queries inside a loop are slowing down, can I use incremental SAT to overcome this problem?
The problem is the following: I am performing a concrete SAT search inside a loop. On each iteration, I get a model (of course, I store the negation of the model in order not to explore the same model again). And also, if that model satisfies a certain property, then I also add a subquery of it and add other restrictions to the formula. And iterate again, until UNSAT (i.e. "no more models") is obtained.
I offer an orientative snapshot of the code:
...
s = Solver()
s.add(True)
while s.check() == sat:
s.check()
m = s.model()
phi = add_modelNegation(m)
s.add(phi) #in order not to explore the same model again
if holds_property(m): #if the model holds a property
s = add_moreConstraints(s,m) #add other constrains to the formula
...
The question is that, as the formula that s has to solve gets greater, Z3 is starting to have more trouble to find those models. That is okay: this should happen, since finding a model is now more difficult because of the added restrictions. However, in my case, it is happening too much: the computation speed has been even halved; i.e. the time that the solver needs to find a new model is the double after some iterations.
Thus, I would like to implement some kind of incremental solving and wondered whether there are native methods in Z3 to do so.
I have been reading about this in many pages (see, for instance, How incremental solving works in Z3?), but only found this response in How to use incremental solving with z3py interesting:
The Python API is automatically "incremental". This simply means the ability to call the command check() multiple times, without the solver forgetting what it has seen before (i.e., call check(), assert more facts, call check() again; the second check() will take into account all the assertions from the very beginning).
I am not sure I understand, thus I make a simple question: that the response mean that the incremental SAT is indeed used in Z3's SAT? The point I think I am looking for another incrementality; for example: if in the SAT iteration number 230 it is inevitable that a variable (say b1) is true, then that is a fact that will not change afterwards, you can set it to 1, simplify the formula and not re-reason anything to do with b1, because all models if any will have b1. Is this incremental SAT of Z3 considering these kind of cases?
In case not, how could I implement this?
I know there are some implementations in PySat or in MiniSat, but I would like to do it in Z3.
As with anything related to performance of z3 solving, there's no one size fits all. Each specific problem can benefit from different ideas.
Incremental Solving The term "incremental solving" has a very specific meaning in the SAT/SMT context. It means that you can continue to add assertions to the system after a call to check, without it forgetting the assertions you added before hand. This is what makes it incremental. Additionally, you can set jump-points; i.e., you can tell the solver to "forget" the assertions you put in after a certain point in your program, essentially moving through a stack of assertions. For details, see Section 3.9 of https://smtlib.cs.uiowa.edu/papers/smt-lib-reference-v2.6-r2021-05-12.pdf, specifically the part where it talks about the "Assertion Stack."
And, as noted before, you don't have to do anything specific for z3 to be incremental. It is incremental by default, i.e., you can simply add new assertions after calling check, or use push/pop calls etc. (Compare this to, for instance, CVC4; which is by default not incremental. If you want to use CVC4 in incremental mode, you have to pass a specific command line argument.) The main reason for this is that incremental mode requires extra bookkeeping, which CVC4 isn't willing to pay for unless you explicitly ask it to do so. For z3, the developers decided to always make it incremental without any command line switches.
Regarding your particular question about what happens if b1 is true: Well, if you somehow determined b1 is always true, simply assert it. And the solver will automatically take advantage of this; nothing special needs to be done. Note that z3 learns a ton of lemmas as it works through your program such as these and adds them to its internal database anyhow. But if you have some external mechanism that lets you deduce a particular constraint, just go ahead and add it. (Of course, the soundness of this will be on you, not on z3; but that's a different question.)
One specific "trick" in speeding up enumerating "find me all-solutions" loops like you are doing is to do a divide-and-conquer approach, instead of the "add the negation of the previous model and iterate." In practice this can make a significant difference in performance. I think you should try this idea. It's explained here: https://theory.stanford.edu/~nikolaj/programmingz3.html#sec-blocking-evaluations As you can see, the all_smt function defined at the end of that section takes specific advantage of incrementality (note the calls to push/pop) to speed up the model-search process, by carefully dividing the search space into disjoint segments, instead of doing a random-walk. Using this might give you the speed-up you need. But, again, as with anything performance specific, you'll need to tell us more about exactly what problem you are solving: None of these methods can avoid performance problems caused by modeling issues. (For instance, using integers to model booleans is one common pitfall.) See this answer for some generic advice: https://stackoverflow.com/a/57661441/936310
I should check existence of values based on some conditions.
i.e. i have 3 variables, varA, varB and varC. varC should not be empty only if varA>varB (condition).
i normally use some syntax to check any of the variables and run a frequency of any of them to see if there are errors:
if missing(varC) and (varA>varB) ck_varC=1.
if not(missing(varC)) and not(varA>varB) ck_varC=2.
exe.
fre ck_varC.
exe.
I had some errors when the condition became complex and when in the condition there are missing() or other functions but i could have made a mistake.
do you think there is an easier way of doing this checks?
thanks in advance
EDIT: here an example of what i mean, think at a questionnaire with some routing, you ask age to anyone, if they are between 17 and 44 ask them if they work, if they work ask them how many hours.
i have an excel tool where i put down all variables with all conditions, then it will generate the syntax in the example, all with the same structure for all variables, considering both situations, we have a value that shouldn't be there or we don't have a value that should be there.
is there an easier way of doing that? is this structure always valid no matter what is the condition?
In SPSS, missing values are not numbers. You need to explicitly program those scenarios as well. you got varC covered (partially), but no scenario where varA or varB have missing data is covered.
(As good practice, maybe you should initialize your check variable as sysmis or 0, using syntax):
numeric ck_varC (f1.0).
compute ck_varC=0.
if missing(varC) and (varA>varB) ck_varC=1.
if not(missing(varC)) and not(varA>varB) ck_varC=2.
***additional conditional scenarios go here:.
if missing(varA) or missing(varB) ck_varC=3.
...
fre ck_varC.
By the way - you do not need any of the exe. commands if you are going to run your syntax as a whole.
Later Edit, after the poster updated the question:
Your syntax would be something like this. Note the use of the range function, which is not mandatory, but might be useful for you in the future.
I am also assuming that work is a string variable, so its values need to be referenced using quotation signs.
if missing(age) ck_age=1.
if missing(work) and range(age,17,44) ck_work=1.
if missing(hours) and work="yes" ck_hours=1.
if not (missing (age)) and not(1>0) ck_age=2. /*this will never happen because of the not(1>0).
if not(missing(work)) and (not range(age,17,44)) ck_work=2. /*note that if age is missing, this ck_work won't be set here.
if not(missing(hours)) and (not(work="yes")) ck_hours=2.
EXECUTE.
String variables are case sensitive
There is no missing equivalent in strings; an empty blank string ("") is still a string. not(work="yes") is True when work is blank ("").
I am trying to find an optimal solution using the Z3 API for python. I have used set_option("verbose", 1) to print statements that Z3 generates while checking for sat. One of the statements it prints is pb.conflict statements. The statements look something like this -
pb.conflict statements.
I want to know what exactly is pb.conflict. What do these statements signify? Also, what are the two numbers that get printed along with it?
pb stands for Pseudo-boolean. A pseudo-boolean function is a function from booleans to some other domain, usually Real. A conflict happens when the choice of a variable leads to an unsatisfiable clause set, at which point the solver has to backtrack. Keeping the backtracking to a minimum is essential for efficiency, and many of the SAT engines carefully track that number. While the details are entirely solver specific (i.e., those two numbers you're asking about), in general the higher the numbers, the more conflict cases the solver met, and hence might decide to reset the state completely or take some other action. Often, there are parameters that users can set to specify when such actions are taken and exactly what those are. But again, this is entirely solver and implementation specific.
A google search on pseudo-boolean optimization will result in a bunch of scholarly articles that you might want to peruse.
If you really want to find Z3's treatment of pseudo-booleans, then your best bet is probably to look at the implementation itself: https://github.com/Z3Prover/z3/blob/master/src/smt/theory_pb.cpp
I use == and != a lot in my code and I was wondering which is quicker in objective c so that I can make my app as fast as possible.
Situation
I have a variable which is one of two things and I want the quickest method to see which one it is
Thanks in advance
You should not worry about this level of detail for performance reasons, unless you've identified a performance issue.
However, wondering to satisfy an inquiring mind is a different matter! :-) The answer is they are identical.
A comparison is usually compiled as an instruction which sets condition flags; this could be a specific comparison instruction or something like an arithmetic instruction which sets condition codes; followed by a conditional jump which tests the condition flags - and a test for "equal" is the same cost as for "not equal", just a different setting of those condition flags.
This also means that statements such as if([some method call]) ... and if(![some method call]) ... have the same cost - the "not" operator produces no extra code.
You can test yourself.
Check current milliseconds before and after operating.
I guess there's no differences..
If you really need to know,
you could make a lot of operating with loop.
then you will get the answer.
This is silly. You would have to execute millions of iterations of code using the 2 versions of if statement in order to even detect a difference in speed. This is a triviality, and not worth worrying about.
As the other poster said, == and != should take exactly the same amount of time for non-floatingpoint values. For floating point, there might be some differences, since for an equal comparison the processor has to first normalize the 2 floating point values, then compare them, and normalizing is relatively time-consuming. I don't know if testing for non-equality if slower than equality. IT's unlikely but not impossible.
Following up on a debate that I was having with a colleague. What is the community's opinion on whether or not a section of code can be adequate with respect to decision coverage (all possible decisions have evaluated to true and false) but not block coverage, and if a section of code can be adequate with respect to condition coverage (each simple condition in a compound conditions has evaluated to true and false) but not block coverage. Thanks.
Well... I guess I can't imagine how you could have forced all decisions into both the true and false conditions without having covered every block. The condition coverage doesn't seem like it guarantees decision coverage, though, unless you are saying that every single cell in the truth-table made up by all of the conditions has been hit.
Is this purely academic, or does it support a more practical argument such as "do we have enough test coverage?"