Python代写 | cpts350 Symbolic graph project

本次Python代写是用BDD模块完成闭包、有限集等运算

cpts350 Symbolic graph project

0. Make yourself be familiar with Python and pyEDA package (see the email that I sent earlier this
week and read the example code in the documentation of the package).
1. Look at your class notes on how a graph is represented in a Boolean formula and then a Boolean
formula is represented in BDD, and on how the transitive closure is computed, in particular, looking
at the example of computing the transitive closure of R ◦ R.
2. Let G be a graph over 32 nodes (namely, node 0, · · ·, node 31). For all 0 ≤ i, j ≤ 31, there is
an edge from node i to node j iff (i + 3)%32 = j%32 or (i + 8)%32 = j%32. (% is the modular
operator in C; e.g., 35% 32=3.) A node i is even if i is an even number. A node i is prime if i
is a prime number. In particular, we define [even] as the set {0, 2, 4, 6, · · · , 30} and [prime] as the
set {3, 5, 7, 11, 13, 17, 19, 23, 29, 31}. We use R to denote the set of all edges in G.
3. (graded on correctness and clarity. If you use explicit graph search such as DFS, you receive
0.) (coding in Python) Every finite set can be coded as a BDD. Please write a Python program
to decide whether the following is true:
(StatementA) for each node u in [prime], there is a node v in [even] such that u can reach v
in even number of steps.
You code shall implement the following steps.
step3.1. Obtain BDDs RR, EV EN, P RIME for the finite sets R, [even], [prime] , respectively.
Pay attention to the use of BDD variables in your BDDs.
step3.2. Compute BDD RR2 for the set R ◦ R, from BDD RR. Herein, RR2 encodes the set
of node pairs such that one can reach the other in two steps.
step3.3. Compute the transitive closure RR2star of RR2. Herein, RR2star encodes the set of
all node pairs such that one can reach the other in even number of steps.
step3.4. Compute the BDD P E, from BDDs P RIME, EV EN, and RR2star, that is to encode
the set of all node pairs (u, v) such that u is prime and v is even and u can reach v in even number
of steps.
step3.5. Here comes the most difficult part. You need formulate StatementA in terms of BDD
operations on the BDD P E. There are two quantifiers in StatementA: one is ”for each”, and the
other is ”there is”. First, from what you have learned from math216 (discrete math), ”for each”
can be expressed through ”there is”. Second, ”there is” can be implemented using existential
quantifier elimination method BDD.smoothing(). As a result, the entire StatementA is a BDD
without free variables and hence it is either true or false. Return the truth vlue.
Many students find methods BDD.compose() and BDD.smoothing() are quite useful in the package.
4. (This part takes 3 pts that will be added to your existing midterm score) Code with BDD is
extremely hard to test. Here is a way to test the key part (step3.4) of your code.
(a). I pick a prime number, say, u = 5. By manually going through the definitions in 2 above,
can you tell me an even v in StatementA? Please show me the steps. Using the v that you identified,
you test your step3.4 using the u and the v; i.e., you verify (by writing test code) that the (u, v)
does satisfy your P E in step3.4.
(b). I pick a prime number, say, u = 5. I also pick an arbitrary even number, say, v = 8. Can
you write a test code to check whether the (u, v) does satisfy your P E in step3.4. ? You can try
many such pairs of (u, v) with u being a prime and v being an even and tell me your conclusion.
5. You need turn-in working code, screen-shot of code execution results. Make sure that you put
comments along with your code so it is readable. Your TAs will probably run your code!


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