This randomly generates numbers (sets) -- 82% valid, 9% with a digit missing, 9% with an extra digit -- and builds 4 indexes as it runs:

1. $knowns: is a 125MB bitmap that can hold all your 9-digit numbers, and has a bit set representing each number known (seen) good value.
2. $deletions: is a 12.5MB bitmap that can hold all 8-digit numbers, and gets a bit set to represent each of the 8-digit numbers, that are a match-with-1-deletion, for each of the known 9-digit numbers.
3. $insertions: Is a 1.25GB bitmap that can hold all 10-digit numbers, and gets a bit set to represent each of the 10-digit numbers, that are a match-with-1-insertion for each of the known 9 digit numbers.
4. $transformations: Is a 125MB bitmap that holds all the match-with-1-substitutions, for each of the known 9-digit numbers.

It requires a 64-bit perl > 5.18; consumes a fixed 3GB ram when running, and processes the numbers at a rate of 4000 per second; with a run of 10 million taking 40 minutes.

The bitmaps can be saved to disk after a run using the option -SAVE and restored at the beginning of another run using the option -LOAD. The mechanism is currently quite crude using a fixed name of "$0.bin".

It currently prints out whether a number matches a known number: exactly or with 1 deletion, insertion or substitution.

It does not currently tell you which known number(s) it matches -- storing the information required to do that would require terabytes of data -- but given the process of generating the possibilities for any given 1-digit edit is so fast, repeating the process just for those detected -- approximately 0.01% for my randoms -- prior to doing your full message text match is no hardship.

The comments are sparse, but should gives some cluebats. Yell if you want more.

#! perl -slw
use strict;
use Time::HiRes qw[ time ];
use Data::Dump qw[ pp ];

sub receive{
    my $n = join '', map 1+int( rand 9 ), 1 .. 9;
    chop $n if rand() < 0.1;
    $n .= 1+int( rand 9 ) if rand() > 0.9;
    return $n;
}

$|++;
our $SAVE //= 0;
our $LOAD //= 0;
our $SRAND //= 0; srand( $SRAND ) if $SRAND;
our $N //= 1e5;


my( $knowns, $deletions, $insertions, $transformations ) = ( chr(0)x12
+5_000_000, chr(0)x12_500_000, chr(0)x1_250_000_000, chr(0)x125_000_00
+0 );
my( $known, $new, $deletion, $insertion, $transformed ) = (0) x 5;

if( $LOAD ) {
    open BIN, '<:raw', "$0.bin" or die $!;
    { local $/ = \1_250_000_000; $insertions         = <BIN>; }
    { local $/ = \  125_000_000; $knowns             = <BIN>; }
    { local $/ = \  125_000_000; $transformations    = <BIN>; }
    { local $/ = \   12_500_000; $deletions          = <BIN>; }
    close BIN;
    $known = unpack '%32b*', $knowns;
}

my $start = time;

for ( 1 .. $N ) {
    printf STDERR "\r%10d\t", $_ unless $_ % 1000;
    my $received = receive();

    if( length( $received ) == 9 ) {
        if( vec( $knowns, $received, 1 ) ) {
            print( "$received matched a known number" );
            ++$known;
            next;
        }
        elsif( vec( $transformations, $received, 1 ) ) {
            print "$received matches a known number with a substitutio
+n.";
            ++$transformed;
            next;
        }
    } elsif( length( $received ) == 8 ) {
        if( vec( $deletions, $received, 1 ) ) {
            print "$received matches a known number with a deletion.";
            ++$deletion;
        }
        next;
    } elsif( length( $received ) == 10 ) {
        if( vec( $insertions, $received, 1 ) ) {
            print "$received matches a known number with an insertion.
+";
            ++$insertion;
        }
        next;
    }

    ++$new, vec( $knowns, $received, 1 ) = 1; ## new number

    for my $pos ( 0 .. 8 ) {
        my $copy;
        vec( $deletions, substr( $copy = $received, $pos, 1, '' ), 1  
+    ) = 1;                ## add all possible 1-digit deletions to th
+eir index

        vec( $insertions, substr( $copy = $received, $pos, 1, $_ ), 1 
+    ) = 1 for 1 .. 9;     ## add all possible 1-digit insertions to t
+heir index

        my $digit = substr( $received, $pos, 1 );
        vec( $transformations, substr( $copy = $received, $pos, 1, $_ 
+), 1  ) = 1 for 1 .. $digit-1, $digit+1 .. 9; ## all poss 1-digit sub
+stitutions
    }
    vec( $insertions, $received . $_, 1 ) = 1 for 1 .. 9;             
+                          ##  all possible insertions after last digi
+t.
}

printf STDERR "From %d received there were: %d new; %d known; %d delet
+ions; %d insertions; %d transformations.\n",
    $N, $new, $known, $deletion, $insertion, $transformed;

printf STDERR "Numbers processed at a rate of %.f/second\n", $N / ( ti
+me() - $start );

if( $SAVE ) {
    open BIN, '>:raw', "$0.bin" or die $!;
    printf BIN "%s%s%s%s", $knowns, $deletions, $insertions, $transfor
+mations;
    close BIN;
}

__END__
C:\test>\Perl22\bin\perl.exe 1172842.pl -N=1e7 -SAVE > null
  10000000      From 10000000 received there were: 8116086 new; 86155 
+known; 0 deletions; 9459 insertions; 0 transformations.
Numbers processed at a rate of 4082/second

C:\test>\Perl22\bin\perl.exe 1172842.pl -N=1e7 -SAVE -LOAD > null
  10000000      From 10000000 received there were: 7963211 new; 836492
+9 known; 0 deletions; 24187 insertions; 0 transformations.
Numbers processed at a rate of 4218/second
[download]

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.i; } { local $/ = \12_500_000; $deletions = /li

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