Parsing is quite possibly not required. Assuming that the variables can be assumed to contain a true value why not just leverage perl. 

$str =~ s/\*/&&/g;
$str =~ s/\+/||/g;
# $str =~ s/'/!/g;
$str =~ s/(\w+)'/!$1/g;
$str =~ s/\(([^\)]+)\)'/!($1)/g;
$str =~ s/\w+/1/g;
my $truth = eval $str;

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If the a/b/A/B vars have associated values all that is required is to substitute them in. Perl does the parsing and calculates the truth.

Update

Modified to deal with ' postfix syntax

In reply to Re^2: Generate a truth table from input string by tachyon-II
in thread Generate a truth table from input string by Anonymous Monk

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