Random Grammars
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Random Grammars Vadim Malyshev. N ˚ 3187 Juin 1997 ` THEME 1. ISSN 0249-6399. apport de recherche.
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(356) G Ta+sG S98;TeGM6#v8-AW( ? (G 8P?q? G r!vT!Q E + EH( G O G G `bT ? °GS GG;E Qa` GT!8P?7+67AE 6B?7G+-, ` v T6BO8;G S-+ G Ta+( Ta+-+-Q!E 6 E + ,+-N 68&<=` , S `bS-+;( 4 ?7E + ? `b6 G Ta+G S :aN Qv S Ta67G `bQ!+ N S9( 8;N :aTaS@?7` T T? +-67+ +@O +-67+-T?H8P?7`bL\+-6F8;TaQ+{<C?7+-TaQ.`?|AW? 8;Ta6HN 8P?7` Ta6q? 8;NbN :aTaS@?7` T!6q` T? + +-:a`G LM8;Nb(+-TaS-+G S-N 8;676- E 'v( ` E 6`b6 G | vLCE ` G :a6HNA>`bT? E 8;S@?H8P|!Nb+8;TaQKxR+6 ( 8;NbNk:a67+, G;E +eS G Ta6B? E :aS@?7`bL\+ 8PO!O 8;S ( +-6? ( r!TaQ ( + + +-TaS-+ 8;,.+-6-( G v A? `bT= ? 8P?? +-67+ Qa` 0S-:aNb?7`b+-6 89L\+ 6 ,+ :aTaQ!8;,+-T?H8;N T!8P?7: E + |!:=?S G ,.O!Nb+@?7+-NA Q!( ` t( + E +-E T? vEHG , GT G Ta+{<=`b6B?7+-TaS-G + GMv O G G `bT?76` T G T G TaS G ,.,eG :=?H8P?7`L\+> gM+ G ,.+@ ? E A #w+-6BO*+-S-` 8;NbNA `bGMT v `bg + Qa`b,.+-T!67` T!8;Nk67`?7:!8P?7` T!6z Ta+S98;TaT ?r=<8O `bT ?1`bT 6BOt8;S-+ `bTaQa+@O*+-TaQ!+-T?7NA ? ( +O8;v6B?-E G E +-N 8P?7+-Q5? G 8N G S98;N G |!67+ E L\+ E | AO!:=?B?7`bTag ( `b,8P?6 G ,.+O G `bT ? 2 + + + a T S + O b ` T s ? 9 S ; 8 > T * | + GMv ? ( +`bTa`?7`8;Nu6B? E `bTag]8;T!Q Qa+@r!T!`bTag56 G ,.+ E :aNb+-6 GMv ( `b6 I :a,O!`bT!g` T?7`b,.+; '( +-T xs+.S98;T (. ( O+. . JLK 9 N JNM.
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(360) N ( / E GMv ? ( +`bTaE `b?7` 8;N 67G ? E `bTag8;TaQ8;6767 `bgMT.T:a,|*+ E B? G `?- ( '( +-TG 8;NbN E +-G ,8;` TaE `bTag E +-N +-,.+-T?76egM+@?e? +-` T(:a,|*+ 6W8;G :=? ,8PG ?7` S98;NbNAM T!+( S98;G T `b,E 8;gME `bTa+.? 8P?e8K( N S98;N |!67+ G L\+ 6H`?7(6+-8P&T ?R/ 67`?7+ `b6FB:=' O*T Q!T 8P?7?7`b+-N!Q? x`b6F`? 67( A6 ,G |,.+N!6H`b6:=|!T 6B?7?s`?7:a:aO?7`QG 8P*T ?7+-/ Q.? + G|!? (67+ + L\G +|!67+ 6BE ?HL\89+AE*6I 8P:a?s,? O!6+ °6#:!8;67,.`bTa+gO 6 G `b,T ?-+ JG 8 E G L` 8;T 'E ( :aN + q? GWG Ta+ E GM v ? EH( G +6BAC,E | G N E 6 GMv G G;G E ? ( GG Ta+ GMv G `?76Ta( +-`bg E ( | G( : E G$6 / E / E 8P?s? ( + , ( ,.E +-T?- +-TT:a,W|*+ E + E `b6O +-67S E `|*+-Q>? G;E7E ? +eG 6BAC,W| Nkx ' + G +W? + |67+ L\+ `b6 E 8;T!Q ? + +-,8;`bTa`bTag+-(Nb+-,.G +-T ?76E 8 E+ (+-+-G T :!,.I + 8P?7+-Q>GS G +-67GMO v T!Qa`bTagMNAM( G +-E 67S98PO*+Qa`b6H6H8PO*+98 8;TaS-+ ` T>S98;67G;.+ E G6 ;w!? G + |!E 67+ EL\G + 6 :aN Q :a,O>G ? Ta+G;E7E `?76G Ta+-`bvg | : G 6- G G E E J 8gM`L\+-T |!67+ L\+ T!+S98;T]Qa+@r!Ta+N S98;N£S +-N 8P?7` T :aTaS@?7` Ta69 4 N S98;N |!67+ L\+ O EHG LCG`bQaG +-6:a6 x`? ( 8 + E#G O G `bT?W8;T!Q? ( :!6x`? ( 8;T +-T :a,+ E 8P?7` G T 8P?e8;TA?7E `b,.(@+ U{ '( (+-T xR+N E 8P? 2G 1( E G 2 1 G # wk8P?( ?7`b,@+ U#G; E7E A ?`b6G S-Nb+98 v ? 8P?G ` T? + gM+-G T!+ `bS67`?7:!8P?7( ` G T ?G + 8;G TaQ , r!+-NbQ T % Qa+@r!Ta+-Q|AK? +-6H+S +-N 8P?7` T :aTaS@?7` Ta6x `bNbN T ?|+67O8;S-+ , gM+-G T!+ :a6-E ( 4 68;T +{<=8;,.O!Nb+S Ta67` Qa+ ? +S98;67+Wx`? ( 67:=|6B?7`?7:=?7` G T!6 GMv ? ( + vG;E , G G / uS G T ?7+{<C? vE +-+g E 8;,.,8 E 6x`? ( G :=??7+ E ,.`bT8;N*6BA,| G Nb 6 # ¢}+@? ( ? ( + G |!67+ E L\+ EI :a,OE 6 8;G NxR89(A6F? G ? ( + ( E `bg E ( ?6BA,G | G N GMv ? ( +6B? E `bT!g '( +-T8P? O G `bT ? Bxs+6 8;NbN*67+-+W8rTa`?7+J 8 L]S 8;`bT>x`? ? 8;Ta67`?7` T>` T?7+-Ta6H`?7`b+-6 H. H. H +. . . Q. 6M1. 3 . C1. 3 221. D+a ! . K. o. . *. . . N/ +. 1 . -+ T G G ?7+v `b?76167?HG 8P?7` G T!8 E AKQ!`b6B? E `|:=?7` G T>|A ' ( -+ T6B?H8P?7` G T!8 E AKQa` 6B? E `|!:a?7` G T MG v ? ( +S G;E7E +{z N8P?7` T :!TaS@?7` T #. 9N/. 0. . . /H . . 2H . . . $N/ . *. . N/?+. *. "H N/X+a . G T? E 8 E AK? G ? ( `b6-w? ( +Nb` ,.`?7`bTagQa`b6B? E `b|!:=?7` G T GMv / `b6`bTaQ!+@O+-T!Qa+-T? v E#G I , / e8;T!Q`b61? ( + E G M G v E G ( ( ( N `b,.`?7`bT!gWQa`b67? `|!:=?7` T ? +r!T!`?7+J 8 L]S 8;` T>x`? `bT ?7+-Ta67`b?7`b+-6 0. . . . *. N/ +. . . H. ;G E ? ( +6H8;,.++{<=8;,ONb+FS G Ta6H`bQa+ E G |!67+ E L\+ E 6 G |!67+ E L\+ E 6}O:=?k8P?kQ!`t+ E +-T?kO G ` T?76}8P?q?7`b,.+?B 1+ E G +`?R`b6s+@L`bQ!+-T?R? ( 8P?N G S98;N v :aT!S@?7` G Ta6R8P?RT!+-`bg ( | G : E ( G G Qa6 GMv Qa`+ E +-T ?sN G S98;N G |!67+ E L\+ E 6 |*+-S ,.+W,:=?7:8;NbNA`bT!Qa+@O*+-TaQa+-T ?- J. NNPO?QSRUTVXW. 1.
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