MBNs (Monotonic Boolean Networks)
}We can allow for BN nodes to be phased as negative or positive
}Definition[Increasing/Decreasing Node]
}BN node f is increasing (decreasing) in positive (negative) variable xi à
xi: 0→1 (1→0), f cannot change 1→0 (0 →1)
}Definition[Unate Function]
}BN function f unate in xi, iff f is increasing or decreasing in xi
}Definition[Positive/Negative Nodes]
}Node ni with local function fi is +ve (-ve)
}xi is +ve (-ve) and fi is increasing in xi,OR
xi is -ve (+ve) and fi is decreasing in xi.
}Definition [Monotonic Node]
}A node is monotonic if it is either +ve or –ve.
}Definition [Monotonic Boolean Network]
}A BN is MBN if all its nodes are monotonic
}MBN is hazard-free under monotonic input transitions
20/4/2014
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CE-653 - Indicating Logic