Thursday 25 July 2019

Solution of problems kind of P149 (ege23.doc) via 08.2016 technique "GRAPHS AND SYSTEMS OF LOGICAL EQUATIONS"

"Poor understanding of Mapping Method (08.2016) is still a half of distress" B.D.

First of all be aware that intellectual property of approach been applied completely belongs to Helen Mironchick (unpublished manuscript ). See also PDF attachment to thread on USE in Informatics Polyakov's  forum  http://egekp.unoforum.pro/?1-6-0-00000120-000-0-0-1561979337   MEA's post 229. Posting below is nothing different from exercising technique proposed by MEA in mentioned PDF attachment targeting better understanding of solution been suggested in those  thread.
We would consider a sample P149 and one more system which doesn't look as standard as P149 and requires a bit more experience in building 08.2016 diagrams.



  ((¬x1=>y1)^z1)≡((¬x2 v y2)=>z2)
  ((¬x2=>y2)^z2)≡((¬x3 v y3)=>z3)
  ((¬x3=>y3)^z3)≡((¬x4 v y4)=>z4)
  ((¬x4=>y4)^z4)≡((¬x5 v y5)=>z5)

  Convert system to equivalent

  ((x1 v y1)^z1)≡((x2=>y2)=>z2)
  ((x2 v y2)^z2)≡((x3=>y3)=>z3)
  ((x3 v y3)^z3)≡((x4=>y4)=>z4)
  ((x4 v y4)^z4)≡((x5=>y5)=>z5)


      Traditional solution ( classic version of Mapping Method as of 2013 ) might be found in my old  blog entry  http://mapping-metod.blogspot.com/2017/12/149-ege23pdf.html
  Passing Polyakov's control



Consider a bit more complicated system

  ((x1 v y1)^z1)=> ((x2=>y2)=>z2)=1

  ((x2 v y2)^z2)=> ((x3=>y3)=>z3)=1
  ((x3 v y3)^z3)=> ((x4=>y4)=>z4)=1
  ((x4 v y4)^z4)=> ((x5=>y5)=>z5)=1

Now build diagrams required to solve updated problem with implications



     Passing Polyakov's Control


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