I'm looking at some exercices that reguards FSAs and my teacher is giving and odd solution for the language
I would have solved that language with a Not-Deterministic TM cause you have to remember n for a, b and c.
This is the given solution
Is this solution incorrect?
The example above does work and therefore is correct.
It is clear that for n = 1 the FSA posted above does work.
Now let's condiser the case n > 1, we have to have the same amount of a, b and c between every possible string composed of {a,b,c}. This string can be seen as the same string with n = 1 and the other n - 1 repetitions can be put in the {a,b,c}* group of strings, hence this FSA can accept that language correctly.
Related
I have 4 non negative real variable that are A, B, C and X. Based on the current problem that I have, I notice that the variable X must belong to the interval of [B,C] and the relation will be a bunch of if-else conditions like this:
If A < B:
x = B
elseif A > C:
x = C
elseif B<=A<=C:
x = A
As you can see, it quite difficult to reformulate as a Mixed Integer Programming problem with corresponding decision variable (d1, d2 and d3). I have try reading some instructions regarding if-then formulation using big M method at this site:
https://www.math.cuhk.edu.hk/course_builder/1415/math3220/L2%20(without%20solution).pdf but it seem that this problem is more challenging than their tutorial.
Could you kindly provide me with a formulation for this situation ?
Thank you very much !
I was teaching a friend about programming and I had a hard time convincing them that a = b and b = a are two very different things.
I eventually found the correct words to describe it (right associative) which got me thinking.
Are there any programming languages which are left associative? I have never seen a language where:
a = b results in b being set to the value of a.
You misunderstood associativity. An operator op is associative if (a op b) op c is equivalent to a op (b op c). For operators that are not associative it thus becomes relevant whether a op b op c stands for the former or the latter. Thus we distinguish between left-associative operators, where it's (a op b) op c, and right-associative operators, where it's a op (b op c).
Most operators in most languages are left-associative. Take for example -: a - b - c is equivalent to (a - b) - c in most languages, not a - (b - c).
The assignment operator is an exception from that as (a = b) = c is generally not legal (as you can't assign to the result of an assignment). Thus in most languages a = b = c is equivalent to a = (b = c). A notable exception is Python where a = b = c does not associate at all and is simply illegal.
None of this has anything to do with the difference between a = b and b = a. Since this involves only a single use of the = operator, associativity does not factor into this at all. Rather the relevant property is commutativity: An operator op is commutative if a op b is equivalent to b op a. I'm not aware of any language where assignment is commutative, nor do I have an idea of how it could be.
Concepts like left-commutativity or right-commutativity do not exist. There is, to the best of my knowledge, no term for the question "Does a = b assign b to a or vice-versa?" - that's just part of the semantics of the assignment operator.
I don't believe so. Though you can always overload the assignment operator and cause complete confusion inside your c++.
R has both <- and -> assignment operators defined.
> b <- 42
> b -> a
> a
[1] 42
If we talk about Operator associativity we should actually consider two types of associativity: side_associative (e.g. = ) or non-associative (e.g. == ) as it doesn't make any difference for a machine if it get's the line from left to right or from right to left.
There are no such programming languages that are originally left associative but some of them allow it via operator overloading and some (e.g. R) will allow both: -> and <-.
I believe no-one will like it in Europe but it might be found lovely in the Middle East. I can imagine that there are IDEs that switch right-side with left-side but at the end compilers are written in an European way.
Suppose we have N (in this example N = 3) events that can happen depending on some variables. Each of them can generate certain profit or loses (event1 = 300, event2 = -100, event3 = 200), they are constrained by rules when they happen.
event 1 happens only when x > 5,
event 2 happens only when x = 2 and y = 3
event 3 happens only when x is odd.
The problem is to know the maximum profit.
Assume x, y are integer numbers >= 0
In the real problem there are many events and many dimensions.
(the solution should not be specific)
My question is:
Is this linear programming problem? If yes please provide solution to the example problem using this approach. If no please suggest some algorithms to optimize such problem.
This can be formulated as a mixed integer linear program. This is a linear program where some of the variables are constrained to be integer. Contrary to linear programs, solving the general integer program is NP-hard. However, there are many commercial or open source solvers that can solve efficiently large-scale problems. For up to 300 variables and constraints, you can use excel's solver.
Here is a way to formulate the above constraints:
If you go down this route, you might find this document useful.
the last constraint in an interesting one. I am assuming that x has to be integer, but if x can be either integer or continuous I will edit the answer accordingly.
I hope this helps!
Edit: L and U above should be interpreted as L1 and U1.
Edit 2: z2 needs to changed to (1-z2) on the 3rd and 4th constraint.
A specific answer:
seems more like a mathematical calculation than a programming problem, can't you just run a loop for x= 1->1000 to see what results occur?
for the example:
as x = 2 or 3 = -200 then x > 2 or 3, and if x < 5 doesn't get the 300, so all that is really happening is x > 5 and x = odd = maximum results.
x = 7 = 300 + 200 . = maximum profit for x
A general answer:
I don't see how to answer the question without seeing what the events are and how the events effect X ? Weather it's a linear or functional (mathematical) answer seems rather beside the point of finding the desired solution.
I'm developing a rudimentary word finder app with sql and ruby where I have an array of letters to find available words. It's easier to make the query by narrowing down what alphabetic letters aren't in the array. For ex.
alphabet= %w{a b c d e f g h i j k l m n o p q r s t u v w x y z}
available_letters = %w{p k z l p m t l n g g r u a r t n d z w a l m n e}
I can then subtract from alphabet, letters to exclude from my search and end up with an sql query like the one below.
select * from words
where word not like '%b%' and word not like '%c%' and word not like '%f%'.....
This gives me all the available words with a combination of all available letters. It does not narrow them down by the number of times that letter occurs. So if I only have one "E", I would like the query to narrow down words that only contain one e. I'm not sure if this can be done with an sql query or whether I will need to use a procedure. Anyone know a good way of solving this?
You will probably want to look into faster ways of implementing this, but to answer your question, you can exclude words with more than one "e" with not like '%e%e%'.
I'm not sure how to express this problem, so my apologies if it's already been addressed.
I have business rules summarized as a table of outputs given two inputs. For each of five possible value on one axis, and each of five values on another axis, there is a single output. There are ten distinct possibilities in these 25 cells, so it's not the case that each input pair has a unique output.
I have encoded these rules in TSQL with nested CASE statements, but it's hard to debug and modify. In C# I might use an array literal. I'm wondering if there's an academic topic which relates to converting logical rules to matrices and vice versa.
As an example, one could translate this trivial matrix:
A B C
-- -- -- --
X 1 1 0
Y 0 1 0
...into rules like so:
if B OR (A and X) then 1 else 0
...or, in verbose SQL:
CASE WHEN FieldABC = 'B' THEN 1
WHEN FieldABX = 'A' AND FieldXY = 'X' THEN 1
ELSE 0
I'm looking for a good approach for larger matrices, especially one I can use in SQL (MS SQL 2K8, if it matters). Any suggestions? Is there a term for this type of translation, with which I should search?
Sounds like a lookup into a 5x5 grid of data. The inputs on axis and the output in each cell:
Y=1 Y=2 Y=3 Y=4 Y=5
x=1 A A D B A
x=2 B A A B B
x=3 C B B B B
x=4 C C C D D
x=5 C C C C C
You can store this in a table of x,y,outvalue triplets and then just do a look up on that table.
SELECT OUTVALUE FROM BUSINESS_RULES WHERE X = #X and Y = #Y;