A2 Flow Table Reduction

Remember that none of the pairs of states above that

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Remember that none of the pairs of states above that failed the equivalence test can be compatible, either because they have different outputs, which is common to the definition of equivalence and compatibility, or because some link in the chain of compatibility eventually requires that a pair of states having different outputs be compatible, which is false for the same reason as stated previously. This means that we can incorporate the above information into our implication table for step 2:
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 We have the following compatibilities: 1-2, 2-4, 2-7, 3-5, 4-7, 6-8, 6-9, 6-10, 8-9, 8-10, 9-10. We can assemble the following maximally compatible sets of states: {1,2};{2,4,7};{3,5};{6,8,9,10}. All of these sets of states are “essential” to the cover, but it’s possible that we can eliminate state 2 from one of the sets that contains it. In fact, since all of the individual pairs of states are compatible by inspection, there are no possible closure violations for any compatibility class that we might choose. We can therefore investigate two choices for the reduced table, the one covering compatibility classes {1,2};{3,5};{4,7};{6,8,9,10}, and the one covering {1}; {2,4,7};{3,5};{6,8,9,10}. One or the other might be a better choice because it preserves don’t cares in the reduced flow table. Here is the reduced table based on the first choice of compatibility classes: 00 01 11 10 1,2 1 / 0 2 / 0 4 / - 3 / - 3,5 5 / 1 8 / - 6 / - 3 / 1 4,7 1 / - 2 / - 4 / 0 7 / 0 6,8,9,10 10 / 0 8 / 0 6 / 0 9 / 0 And here is the same table with new state names substituted for the old ones: 00 01 11 10 a a / 0 a / 0 c / - b / - b b / 1 d / - d / - b / 1 c a / - a / - c / 0 c / 0 d d / 0 d / 0 d / 0 d / 0 Notice how this table explicitly expresses the fact that once we get into state d , we can’t get out of it. This is
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern