truth table and formula generator from Ruby block

The truthtable library generates a truth table from a logical formula written in Ruby. The truth table can be converted to a logical formula.

Author

Tanaka Akira <akr@fsij.org>

Feature

• generate a truth table from a given block which contains logical formula written in Ruby.
• generate a formula from the table:
  • minimal one (obtained by Quine-McCluskey algorithm)
  • disjunctive normal form
  • conjunctive normal form

Usage

• require

   require 'truthtable'
  

• puts, p and pp shows truth table

   puts TruthTable.new {|v| v[0] & v[1] }
   #=>
   v[0] v[1] |
   ----------+--
    f    f   | f
    f    t   | f
    t    f   | f
    t    t   | t
  
   p TruthTable.new {|v| v[0] & v[1] }
   #=> #<TruthTable: !v[0]&!v[1]=>false !v[0]&v[1]=>false v[0]&!v[1]=>false v[0]&v[1]=>true>
  
   require 'pp'
   pp TruthTable.new {|v| v[0] & v[1] }
   #=>
   #<TruthTable:
    !v[0]&!v[1]=>false
    !v[0]& v[1]=>false
     v[0]&!v[1]=>false
     v[0]& v[1]=>true>
  

• formula generation

   p TruthTable.new {|v| v[0] }.formula         #=>"v[0]"
   p TruthTable.new {|v| !v[0] }.formula        #=> "!v[0]"
   p TruthTable.new {|v| true ^ v[0] }.formula  #=> "!v[0]"
   p TruthTable.new {|v| v[0] & v[1] }.formula  #=> "v[0]&v[1]"
   p TruthTable.new {|v| v[0] | v[1] }.formula  #=> "v[0] | v[1]"
   p TruthTable.new {|v| v[0] ^ v[1] }.formula  #=> "!v[0]&v[1] | v[0]&!v[1]"
   p TruthTable.new {|v| v[0] == v[1] }.formula #=> "!v[0]&!v[1] | v[0]&v[1]"
  

• shortcuts, && and ||, are also usable but converted to & and |

   p TruthTable.new {|v| v[0] && v[1] }.formula #=> "v[0]&v[1]"
   p TruthTable.new {|v| v[0] || v[1] }.formula #=> "v[0] | v[1]"
  

• actually any expression (without side effect)

   p TruthTable.new {|v| v[0] ? !v[1] : v[1] }.formula #=> "!v[0]&v[1] | v[0]&!v[1]"
  

• any number of inputs

   p TruthTable.new {|v| [v[0], v[1], v[2], v[3]].grep(true).length <= 3 }.formula
   #=> "!v[0] | !v[1] | !v[2] | !v[3]"