truthtable - truth table to logical formula

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

Install

gem install 'truthtable'

Features

• generate a truth table from a given block written in Ruby.

• generate a formula from the table:

  • minimal one (obtained by Quine-McCluskey algorithm)

  • disjunctive normal form

  • conjunctive normal form

Usage

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>
  

• ‘?’ is shown for non-evaluated variable

  puts TruthTable.new {|v| v[0] && v[1] }'
  #=>
  v[0] v[1] | 
  ----------+--
   f    ?   | f
   t    f   | f
   t    t   | t
  
  puts TruthTable.new {|v| v[0] || v[1] }'
  #=>
  v[0] v[1] | 
  ----------+--
   f    f   | f
   f    t   | t
   t    ?   | t
  
  puts TruthTable.new {|v| !v[0] ? !v[1] : !v[2] }'
  #=>
  v[0] v[1] v[2] | 
  ---------------+--
   f    f    ?   | t
   f    t    ?   | f
   t    ?    f   | t
   t    ?    t   | f
  

• formula generation

  p TruthTable.new {|v| !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 not preserved

  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]"
  

Reference Manual

See rdoc/classes/TruthTable.html or www.a-k-r.org/truthtable/rdoc/TruthTable.html

Home Page

www.a-k-r.org/truthtable/