CPTS515 - Python - EDA Package - Point Iteration Algorithm - BDD - IT And Computer Science Assessment Answer

CPTS515 - Python - Point Iteration Algorithm - IT And Computer Science Assessment Answer

Assessment Task:

Question 

1. Let p be a CTL formula while [p] is the set of nodes in G that satisfy p. Pleasedesignafix-point iteration algorithm that computes [EF p](the set of nodes in G that satisfy EF p from R and [p]). Pleasedesignafix-point iteration algorithm that computes [EGp](the set of nodes in G that satisfy EGp from R and [p]).

2. Every finite set can be coded as a BDD. Please write a Python program to compute [EG(even EFprime)] (the set of nodes that satisfy the formula EG( even EF prime).), and verify your answer by checking node 5 satisfies EG(even EF prime) and node 6 doesn't satisfy EG(even EF prime). (Important: your code shall first encode R, [even], [prime] in BDDs using pyEDA and then using methods provided with the package, implement the iteration algorithms provided in 3 symbolically in BDD using methods in the package. ManystudentsfindmethodsBDD. compose()and BDD. smoothing() are quite useful in the package.)

3. To make use of the idea of BDDs, a major difficulty is which graph is chosen to model a given set of data. When the graph is too large, the symbolic exploration algorithm would not even run efficiently. However, if the graph is too small, the modelling might not be even realistic. We now think about an example problem. Consider a finite set L of DNA strands, where each strand is simply a string on alphabet {A, T, C, G} (that is, a strand is a sequence of nucleotides, each of which is chosen from four nitrogen-containing nucleobases.). One may use a deterministic finite automaton (DFA)1 M (which itself is a graph) to model the set L; i.e L L(M ). That is, each strand w in L, there is a walk-in M (from the initial state to an accepting state) such that the symbols sequentially collected on the transitions on the walk form exactly the w. Clearly, many many different M can be used to model L(e.g., M can be ridiculously simple with only one state and accepting every word on the alphabet.). Consequently, one need come up with a metric Q(M, L), which is a real number, to characterize the “precision” on using the given M to model L. When this is done, one can argue, for two given DFAs M1 and M2 which both models the given L, which model is more precise. Now, you need write a mini-paper (of 1 or 2 or more pages) in figuring out ways to define Q(M, L) and to design algorithms to compute Q(M, L).

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