Boolean functions

A Boolean function may be expressed two ways:


<variable>
<function-identifier> arg1 arg2 ...


where <function-identifier> is one of the following predefined function identifiers, and arg# is either a variable, a Boolean function or a reference to a Boolean function. The token <variable> is a character string and its use in an input file creates a simple Boolean function which is identified by that name, the value of which is the value of the variable named <variable>. Every Boolean function is implemented as a BDD (see Section 10.1) and may have value T, or F, or have no value, depending on its arguments: values of Boolean functions are given as follows for each <function-identifier>.

Remark: Each function takes a fixed number of arguments, hence, commas and parenthesis are considered whitespace and are ignored, however, their use is recommended to enhance the human readability of input files.

VAR


$\parbox{110mm}{ Variables may be defined as Boolean functions using ... ...$' refer to previously defined functions or manipulators instead of variables.}$

NOT


$\parbox{110mm}{ The unary Boolean function {\tt NOT} has a value eq... ...ace of {\tt NOT} (functions cannot be complemented in this way). Examples are:}$


not(x32)
-x32

AND


$\parbox{110mm}{ The binary Boolean function {\tt AND} has value {\em... ...f at least one of its arguments has value {\em F}. Examples are the following:}$


and(x3, x4)
and x3 x4

NAND


$\parbox{110mm}{ The binary Boolean function {\tt NAND} has value {\e... ...lue {\em T} if at least one of its arguments has value {\em F}. An example is:}$


nand(x3, x4)

OR


$\parbox{110mm}{ This binary Boolean function has value {\em T} if on... ...and has value {\em F} if both its arguments have value {\em F}. An example is:}$


or(and(x3, x4), x5)

NOR


$\parbox{110mm}{ This binary Boolean function has value {\em F} if at... ... T} and has value {\em T} if both arguments have value {\em F}. An example is:}$


nor(x3, ite(a, b, -c))

EQU


$\parbox{110mm}{ This binary Boolean function has value {\em T} if bo... ...mple {\tt equ} acts as a way to assign the value {\em T} to variable {\tt x4}.}$


equ(T, x4)

XOR


$\parbox{110mm}{ This binary Boolean function has value {\em T} if it... ...{\em F} if its two arguments have been assigned the same value. An example is:}$


xor(x3, x4)
This is functionally equivalent to:
equ(x3, not(x4))

IMP


$\parbox{110mm}{ This binary Boolean function has value {\em T} if e... ... its first argument has value {\em F} and second value {\em T}. An example is:}$


imp(x3, x4)

NIMP


$\parbox{110mm}{ This binary Boolean function has value {\em F} if ei... ... its first argument has value {\em F} and second value {\em T}. An example is:}$


nimp(x3, x4)

ITE


$\parbox{110mm}{ The ternary Boolean function {\tt ITE} has the value... ...first argument has value {\em F}. Examples of this function are the following:}$


ite(ite( x3, $5, -x5), x4, x7)
ite ite x3 $5 -x5 x4 x7