in reply to Algorithm inspiration required.

This is my take on solving this (if I understand the spec right that is) using a finite state automaton to look for a specific arbitrary-length sequence of characters from a stream. It does not need to store any data at all except the string to look for and an array of bits of same length.

As an example the input stream is a seemingly infinite sequence of random numbers between 0 and 9.The sequence to detect is '0,1,2,3,4,5'.

For a seed of '123' this is encountered on the 151436th rand() call!

./detector.pl

#!/usr/bin/env perl #### # detects a sequence of ascii characters # unicode can be accommodated with minimal effort. # The heart of the detector is a a chain of states # who know how to read a symbol from the stream, # check if same as required, trigger a response if it is # propagate the symbol to the next state. # there are as many states as the length of the sequence # to detect # # Date: 18/06/2018 # Author: bliako # re : https://perlmonks.org/?node_id=1216847 #### use strict; use warnings; use constant DEBUG => 0; srand 123; my @to_detect = split(//, '012345'); ## # nothing to change below ## my $N = scalar(@to_detect); my @buffer_detect = (0) x $N; my $ref_buffer_detect = \@buffer_detect; my ($i); my $state = undef; my $next_state = undef; my $previous_state = undef; for($i=0;$i<$N;$i++){ $next_state = $state; $state = { # specify a state with its own data hash and a few sub +s for its operation 'init' => sub { # called first upon creation and resets the st +ate etc. my ($self, $params) = @_; if( DEBUG ){ print "init() : initialising $sel +f...\n"; } $self->{'data'} = { 'self' => $self, 'buffer-bit' => \$buffer_detect[$i], 'char-to-detect' => $to_detect[$i], 'next-state' => $next_state, 'previous-state' => $previous_state, 'current-symbol' => undef }; }, 'enter' => sub { # called when a new symbol from the stream is +available # calling enter() on the first state, will tri +gger a ripple # of enter()s through all the states my ($self, $newsymbol) = @_; if( DEBUG ){ print "enter() : self=$self, news +ymbol=$newsymbol\n"; } if( defined($self->{'data'}->{'current-symbol' +}) ){ $self->{'propagate'}->($self); } $self->{'data'}->{'current-symbol'} = $newsymb +ol; $self->{'check'}->($self); }, 'check' => sub { # check if current symbol is what we are looki +ng for at this particular state my ($self) = @_; my $d = $self->{'data'}; if( DEBUG ){ print "check() : checking if '".$ +d->{'current-symbol'}."' is the same as '".$d->{'char-to-detect'}."' +... "; } if( $d->{'current-symbol'} eq $d->{'char-to-detect'} ){ if( DEBUG ){ print "yes\n"; } ${$d->{'buffer-bit'}} = 1 } else { if( DEBUG ){ print "no\n"; } ${$d->{'buffer-bit'}} = 0 } }, 'propagate' => sub { # propagate our current symbol to the next sta +te my ($self) = @_; if( DEBUG ){ print "propagate() : self=$self\n +"; } my $d = $self->{'data'}; my $n = $d->{'next-state'}; if( defined($n) ){ if( DEBUG ){ print "propagate() : next + state exists : $n and its self is ".$n->{'data'}->{'self'}." and my +symbol is ".$d->{'current-symbol'}."\n"; } $n->{'enter'}->( $n->{'data'}->{'self'}, $d->{'current-symbol'} ); } }, }; print "i=$i, state created $state\n"; # initialise created state $state->{'init'}->($state); $previous_state = $state; }; my $FSM = $state; my $ch; for(0..50000000){ # our stream is a random ascii char generator # my $symbol = chr(32+int(rand(125-32))); # or random numbers my $symbol = int(rand(10)); # all we need to do is to enter() the symbol in the first stat +e # it will be ripple through all states $FSM->{'enter'}->($FSM, $symbol); # at the end, check the buffer for 1's $ch = 100.0 * check_buffer($ref_buffer_detect, $N); print "$0 : $_ : symbol '$symbol', buffer: ".join('', @buffer_ +detect)." : $ch %\n"; if( $ch == 100 ){ print "$0 : sequence detected, stopping here +.\n"; last } } # takes a reference to a buffer of 1 and 0's and counts the proportion + of 1s # over length. For efficiency supply ref to buffer and length # returns num(1) / total_length # sub check_buffer { my $buf = $_[0]; # the detection buffer as array ref my $l = $_[1]; # length of buffer (so that we don't find it he +re) my $i = 0; foreach(@$buf){ $i++ if $_ == 1; } return $i / $l; } 1;

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Re^2: Algorithm inspiration required.
by BrowserUk (Patriarch) on Jun 18, 2018 at 21:11 UTC

    Sorry, but I think you may have misunderstood the problem. Or perhaps I am misunderstanding your code.

    What you appear to be doing is searching the stream for a known 5-value sequence, using a FSM that uses 24,664 bytes of memory to represent those 5 characters and an extra 1056 bytes of memory for every extra byte; and takes (on my machine) 202 seconds to locate those 5 bytes 4,312,277 bytes into the stream.

    The actual problem is that the sequence I am looking for is in the stream, and can be huge; as in greater than memory. eg 100GB.

    For the 'simple' version of the problem, the sequence to find starts at the beginning of the stream, but extends to a size greater than memory, and once complete, will repeat immediately, (and obviously extend as far again). The problem is how to retain enough information about a huge, and ever growing sequence to recognise when you have seen it twice.

    It is only once you have see it twice that it is possible to know how long the sought after sequence is.

    The more complex version can have additional just existing between occurrences of the repetition(s) and you don't know whether the first characters you see constitute a part of the repetition, or junk. (But that's for another day :) ).


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      I COMPLETELY misunderstood what you wanted to do, my take is for a finite and known pattern to detect. sorry