A force de bricoler et d'essayer d'améliorer des partie de logicielle que j'ai faites, je suis tombé sur Flex et Bison puis sur des référence à la théorie des langages formel.
J'ai acheté le boucain (introduction to formal languages Révéz) mais j'ai des difficultés:
-- j'imagine des choses qui ne sont pas ce qui est présenté dans le live et donc je ne comprends pas ce que je lis.
-- je fais des digressions constamment dans différent domaines y compris en réalisant un générateur de langage utilisant une grammaire générative.
Donc je n'avance pas et ce n'est pas seulement un problème de travail assidu.
Des managers qui m'ont observé depuis le début de ma carrière on constaté un certain manque d'ambition mais on pourrait parfois émettre l'hypothèse d'une ambition démesurée qui peut aisément être prise pour de l'inconséquence, ou de la folie voir de la bêtise.
Vous avez déjà été prévenue sur les risques que je prends dans ce Blog. Ils sont démesurés par rapport à mes connaissances des sujets abordés.
Donc la théorie des langages est importante car pour moi elle chapeaute les autres théories.
Pour bien comprendre la manière de penser d'un étranger il est préférable de bien connaître sa langue, pas seulement savoir parler couramment mais connaître sa structure. Au début on est incapable de reproduire les sons aussi par ce qu'on est incapable de les reconnaître, enfin....la raison est probablement plus complexe.
Il est donc possible que les obstacles rencontrés dans la recherche fondamentale en physique soit du à l'absence d'un langage adapté. L'univers étant lui même un langage que nous essayons de traduire dans un langage compréhensible par nous. Mais quel langage chercher? La théorie des langages et les problèmes connus de traduction pourraient-ils nous aider en essayant de s'orienter vers de nouvelle structures? Ces langages seront ils encore manipulés directement par des cerveaux humains ou prises en charge presque totalement à l'aide des ordinateurs? On pourrait même se demander si les nouveaux langages qui vont être utilisés avec les ordinateur quantiques ne vont pas donner naissance à de nouvelles théories mathématiques.
J'ajoute au risque de me répéter partiellement des questions sur la modélisation et les langages.
-- Quel est le support pour un langage? Pour être le moins spécifique possible on pourrait dire que c'est une masse d'information quelconque. Mais déjà mettre cette information sur un support informatique pour pouvoir l'analyser constitue une traduction et donc une perte d'information.
-- Comment modéliser, c.a.d trouver une structure (en établissant des relations reliant des informations). Une machine de Turing génère cette masse d'information à partir de règle. Mais c'est seulement théorique car on a du simplifier les règles pour pour pouvoir générer de manière pratique le langage à cause du temps démesuré que demande dans certains cas cette machine. Même pour générer un langage finis. Il faut donc trouver les moyen d'améliorer la machine de Turing. On pourrait essayer de les utiliser pour générer une masse d'information pour les comparer aux informations collectées. Là encore on se trouvera toujours confronté à des problèmes de traduction. Dans certains cas les problèmes abordés recoupent des problèmes de cryptologie et même de compression de donnée . Une machine de Turing permet d'exprimer par exemple un langage infinis en quelques règles.
Donc on a une masse d'information qui parait chaotique et dont on ne sait rien. Rechercher un modèle ressemble à du décryptage qui peut être partiel. Pour cette masse d'information on pourrait essayer de définir des caractéristiques générales compatibles avec certain type de modèles. Générer une masse de donné à partir du modèle (même partielle) et la comparer à la masse d'information dont ont cherche à percer le sens.
Il faudrait donc faire des concours demandant de trouver le modèle le plus concis possible permettant de générer une masse quelconque de donnée. En commençant humblement avec des petits volumes de données.
continuons l'exploration:
dois-je considérer tout cryptage d'une masse de donnée comme étant en fait le même langage? Le cryptage étant censé inclure tout procédé réversible de transformation d'une masse de donné sans en changer sa taille. On devrait donc aussi inclure la compression /expansion sans perte de donnée et peut-être les permutations réversibles. Mais alors si toutes les permutations sont réversibles il n'y a qu'un seul langage fondamental. Et tous les langages sont dérivés de ce langage fondamental. Un langage peut-il être infinis? A-t-il une taille? Est-il compressible? Existe-t-il une forme de compression ultime? LA compression du langage permet-elle de trouver plus facilement son modèle, sa structure? Le modèle parfait canonique du langage est-il la forme la plus compressée du langage?
Mais si il existe une forme de base du langage que l'on peut obtenir à partir de la compression ou de la permutation ou même du cryptage simple alors la manière de compresser ou de permuter ou de crypter doit être inclus dans ce qui définit le langage c'est à dire dans la masse de donnée que l'on analyse pour que ce langage soit vraiment définit par elle.
Je trouve aussi intéressant de voir les ponts possibles entre compression ,permutation et cryptage.
Puis je obtenir tous les cryptages possibles en permutant et vie versa? Puis-je obtenir une meilleur compression en cryptant ou en permutant?
Anjelica? C'est encore toi?
Mais je suis obligé d'arrêter, il faut quitter le mode recherche pour revenir en mode apprentissage: limiter les rêveries, fixer des horaires, quantifier le nombre de pages lues.
Pour moi la recherche nécessite une part d'incompétence: vous êtes obligé à un moment donné d'utiliser des domaines de connaissance qui vous sont étrangers . C'est pour cette raison qu'il faut des équipes pluridisciplinaires.
Je suis une grosse équipe de gens très incompétents à moi tout seul.... plus Google.
Ici une tentative de développement d'un générateur de langage (tout type Chomsky 0-3)
Cela n'est pas complètement testé donc à vos risques et périls!
Cela n'est pas complètement testé donc à vos risques et périls!
A python pgm: langage generator from grammar rules
The test suite for this programm
It works with grammars that generates words with infinit length.
It just cut the derivation when the length is higher than a chosen limit.
But it is not always possible to predict the length of the finnl word when rules would shrink a word like aPb-->ac .
That kind of rules gives normally a warning messages and we might not see all words having a length below the chosen limit in the final result.
The test suite for this programm
It works with grammars that generates words with infinit length.
It just cut the derivation when the length is higher than a chosen limit.
But it is not always possible to predict the length of the finnl word when rules would shrink a word like aPb-->ac .
That kind of rules gives normally a warning messages and we might not see all words having a length below the chosen limit in the final result.
Before publishing it I received comments that the pgm wasn't working. They can say it officially now!
This pgm might be usefull to generate special kind of permutation like in the exemple given at the end of the source: generating L={P|Na(P)=Nb(P} Vn={S,A,B} Vt={a,b}. I am still searching a way to make a test suit and generating an equivalent language with itertools.
A lot of interesting problems arise simply by trying to resolve practical problems like building a subset of the language and limiting the length of the words.
Some vague idees:
-- Structure of a language: we could compare language just by comparing the general form of the tree we explore during the derivation (abstraction of the alphabet itself).
-- how to add shrinking rules that will collapse parts of the language.
-- how to find a generative grammar from a preexisting language
-- how to optimize a generative grammar (by having less rules or more efficient rules during the derivation).
-- is it possible to have a canonical form for a generative grammar.
The general idee would be to find new langages that could by their structure expand the possibilties of existing langages.
After having tested some generative grammar with my program I had to make some modifications.
One of them was to let the program run even if I encounter situations where there are still non terminal characters but no rule can apply.
This is the case of this grammar
F=[("S","a"), ("S","CD"), ("C","ACB"), ("C","AB"), ("AB","aBA"), ("Aa","aA"), ("Ba","aB"), ("AD","Da"), ("BD","Ea"), ("BE","Ea"), ("E","a")]
This grammar generates (if I made no mistakes) a lot of non-derivable words. A lot more than the word in L: I had to wait hours before seeing the first words appearing.
A way to recognize this kind of grammar would appear be more useful to me than the Chomsky types. But I am a programmer not a linguist.
There is also perhaps a way to determine some rules that have no chance to reappear during derivation. Again a way to classify the grammar and the language.
How to transform this grammar to a more efficient one? When is it possible?
They are so many possibilities, but computers could help.
I just heard (hallucinations or electronic harassment): "He is half serious".
Making such assumptions about fondamental research is easy: I mean, every-body should be aware of concepts limitation induced by languages.
Knowing quite nothing about quantum mechanic I can't try to detect when a failure is due to langage limitation (wrong language) or wrong model using the right language.
So along with new observations we might have to find new langages (not only based on numbers). Of course we can't throw away number. But what else can we do with them? Do we need the continuity given by real numbers? Is integral calculus still the only way?
So making fondamental research is some kind of reverse engineering toward a langage we don't even know. Would people working on language and people making even simple models be useful?
After hours of trying to study the book written by Gyorgy E.Revesez (introduction to formal langage), I haven't been able to fully understand any of the proof given for the theorems. If I say "fully" it is just because I don't want to be too hard with myself. Even understanding some theorem concepts is a problem. I don't know the reasons: perhaps I am to old or I stayed to much time without training my brain or I got unwillingly some pils that weaken intellectual abilities.
They decided that I am a kind of Jean Paul Farré but I don't have his talent. I just like to amuse people and myself. It is not easy with science. Science isn't an entertainment but music is.
To illustrate the kind of difficulties I have with the introduction to formal language, I'll give this example and later an attempt to resolve the problem in a way that allow somebody like me who doesn't have the training or the gifts. Some people might find this as ridiculous as counting with your hand-fingers.
This pgm might be usefull to generate special kind of permutation like in the exemple given at the end of the source: generating L={P|Na(P)=Nb(P} Vn={S,A,B} Vt={a,b}. I am still searching a way to make a test suit and generating an equivalent language with itertools.
A lot of interesting problems arise simply by trying to resolve practical problems like building a subset of the language and limiting the length of the words.
Some vague idees:
-- Structure of a language: we could compare language just by comparing the general form of the tree we explore during the derivation (abstraction of the alphabet itself).
-- how to add shrinking rules that will collapse parts of the language.
-- how to find a generative grammar from a preexisting language
-- how to optimize a generative grammar (by having less rules or more efficient rules during the derivation).
-- is it possible to have a canonical form for a generative grammar.
The general idee would be to find new langages that could by their structure expand the possibilties of existing langages.
After having tested some generative grammar with my program I had to make some modifications.
One of them was to let the program run even if I encounter situations where there are still non terminal characters but no rule can apply.
This is the case of this grammar
F=[("S","a"), ("S","CD"), ("C","ACB"), ("C","AB"), ("AB","aBA"), ("Aa","aA"), ("Ba","aB"), ("AD","Da"), ("BD","Ea"), ("BE","Ea"), ("E","a")]
generating L={ a^n² |n in 1,2,3,....}
A way to recognize this kind of grammar would appear be more useful to me than the Chomsky types. But I am a programmer not a linguist.
There is also perhaps a way to determine some rules that have no chance to reappear during derivation. Again a way to classify the grammar and the language.
How to transform this grammar to a more efficient one? When is it possible?
They are so many possibilities, but computers could help.
I just heard (hallucinations or electronic harassment): "He is half serious".
Making such assumptions about fondamental research is easy: I mean, every-body should be aware of concepts limitation induced by languages.
Knowing quite nothing about quantum mechanic I can't try to detect when a failure is due to langage limitation (wrong language) or wrong model using the right language.
So along with new observations we might have to find new langages (not only based on numbers). Of course we can't throw away number. But what else can we do with them? Do we need the continuity given by real numbers? Is integral calculus still the only way?
So making fondamental research is some kind of reverse engineering toward a langage we don't even know. Would people working on language and people making even simple models be useful?
After hours of trying to study the book written by Gyorgy E.Revesez (introduction to formal langage), I haven't been able to fully understand any of the proof given for the theorems. If I say "fully" it is just because I don't want to be too hard with myself. Even understanding some theorem concepts is a problem. I don't know the reasons: perhaps I am to old or I stayed to much time without training my brain or I got unwillingly some pils that weaken intellectual abilities.
They decided that I am a kind of Jean Paul Farré but I don't have his talent. I just like to amuse people and myself. It is not easy with science. Science isn't an entertainment but music is.
To illustrate the kind of difficulties I have with the introduction to formal language, I'll give this example and later an attempt to resolve the problem in a way that allow somebody like me who doesn't have the training or the gifts. Some people might find this as ridiculous as counting with your hand-fingers.
and the proof in a form of an algorithm: I'm a programmer.
if P=a^i b1 W1 b2 W2 .... bi Wi = a^iX
then X=b1 WA b2 W2 ....biWi and we have i more b's in X than a's.
Na(X) +i = Nb(X)
the character at the beginning of X is X[0 ] =b1
if X1 = X[1,len(X)] substring of X from pos 1 to the end
we have Na(X1) + i -1 = Nb(X1)
As far as we haven't encountered all the bi's they are more b's than a' in Xn
If Xn beginns with a 'a' we are sure to find a string Wi=Xn[n,n+k)] in Xn. (with n+k=<len(X))
Suppose we start with k=1
we have Wi="a" and Nb(Wi)-Na(Wi) = -1
when we reach n+k we will have Nb(Wi)-Na(Wi) = i -1 >=0 (by incrementing or decrementing)
So we will find a k where Nb(Wi)-Na(Wi) = 0
But Wi must be followed by a 'b'
if Xn beggins with a 'b' we will consider this as a bi that counter balance the ai's at the beginning of P. When we have found all of them n the remaining string has surely Na=Nb
Now the pgm.
#!/bin/python
'''
'''
import re as RE
class TestA():
'''
Split a word P | Na(P)=Nb(P) and P=a^i b1 W1 b2 W2b .....bi Wi
we want to get w1,W2....wi in a list
and rebuild P from it to copare to the original P
'''
def __init__(self,P):
if len(P) % 2 == 0 and len(P) != 0:
self.P = P
else:
raise Exception("P must have even length and not empty")
if not self.NaEqNb(P) :
raise Exception("P must have Na = Nb ")
if P[0] == "a":
try:
match = RE.match( "(a+)(b.*)$", P )
except:
raise Exception("P doesn't match '(a+)(b.*)$' -> %s" %(P,))
self.A="a"
self.B="b"
elif P[0] == "b":
try:
match = RE.match( "(b+)(a.*)$", P )
except:
raise Exception("P doesn't match '(b+)(a.*)$' ->%s" %(P,))
self.A="b"
self.B="a"
Alist,X=match.groups()
##print Alist,X
self.wlist=[Alist]
self.X=X
self.i=len(Alist)
self.extract(X)
def NaEqNb(self,X):
Na = X.count("a")
Nb = X.count("b")
if Na == Nb :
return True
else:
return False
def extract(self,X):
n=0
ii=0
while n < len(X):
if ii == self.i :
# when we have consumed all bi's (from the ai's)
# the remaining string is either empty or Na =Nb
subX=X[n:]
if self.NaEqNb(subX) :
#print "last sub X,ii",subX,ii
self.wlist.append(subX)
return
else:
raise Exception("Error:Na(X) != Nb(X)")
# ii < i still have bi's to process
if X[n] == self.A:
for x in xrange(n+2,len(X)+1,2):
subX=X[n:x]
if self.NaEqNb(subX) :
if X[x] == self.B:
self.wlist.append(subX)
n = x
break
elif X[n] == self.B:
n += 1
ii += 1
self.wlist.append(self.B)
if n == len(X):
self.wlist.append("")
if __name__ =="__main__":
'''
'''
sample = ["aabababbab"]
##print sample
for P in sample:
p="".join(P)
t=TestA(p)
pp="".join( t.wlist)
if p != pp:
raise Exception("P != PP: %s %s" %(p,pp))
else :
pass
#print p,pp, t.wlist
print "Test ik ok for all asmple"
Fuck!
By looking at the program made from this algorithm and making several tests I could pretend that the program would never fail for any P of L in finding this expression: P=a^ibW1bW2....bWi
But could an automatic analysis of the program say it to me?
Could we have a special language that could be analysed automatically?
Or could we have something like symbolic calculus for sets and tuples and lists?
It could be the first step in asking machines to take the risks for us,
and mathematicians loosing part of the control they want to keep.
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