1465:
1346:
1120:
1312:
1228:
1207:
1200:
1338:
1331:
1324:
1303:
1296:
1289:
1277:
1270:
1261:
1254:
1242:
1235:
1219:
1193:
1186:
1135:
3033:
found any BNF syntax can be converted to the above one in 1961. But he withdrew this term, "since doubtless many people have independently used this simple fact in their own work, and the point is only incidental to the main considerations of Floyd's note." While Floyd's note cites
Chomsky's
156:. The presentation here follows Hopcroft, Ullman (1979), but is adapted to use the transformation names from Lange, Leiß (2009). Each of the following transformations establishes one of the properties required for Chomsky normal form.
2840:
2890:
4116:
1377:
When choosing the order in which the above transformations are to be applied, it has to be considered that some transformations may destroy the result achieved by other ones. For example,
337:
If several terminal symbols occur on the right-hand side, simultaneously replace each of them by its associated nonterminal symbol. This does not change the grammar's produced language.
2925:
3007:
2981:
2955:
2609:
2638:
3797:
4266:
3693:
3027:
2766:
2746:
2722:
2702:
2682:
2662:
2135:
Since there are no ε-rules, step "DEL" does not change the grammar. After step "UNIT", the following grammar is obtained, which is in
Chomsky normal form:
3920:
152:
To convert a grammar to
Chomsky normal form, a sequence of simple transformations is applied in a certain order; this is described in most textbooks on
3774:
4381:
4076:
3079:
1464:
2794:
3440:
514:
To eliminate all rules of this form, first determine the set of all nonterminals that derive ε. Hopcroft and Ullman (1979) call such nonterminals
3357:
3753:
2847:
3789:
3722:
3655:
3628:
3585:
3402:
3336:
3307:
3990:
4096:
3981:
3842:
3804:
4361:
4302:
3930:
3370:
605:
omitted. By deleting in this grammar each ε-rule, unless its left-hand side is the start symbol, the transformed grammar is obtained.
3960:
3677:
3466:
3261:
3231:
4197:
4351:
4284:
3852:
122:
4391:
4126:
4010:
141:
140:
Every grammar in
Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an
3901:
3517:
1499:, describes a simplified version of the set of all syntactical valid arithmetic expressions in programming languages like
47:
4371:
4331:
4177:
3882:
4451:
3746:
3042:
Besides its theoretical significance, CNF conversion is used in some algorithms as a preprocessing step, e.g., the
4473:
3892:
3712:
3162:→ ε, it could not be "inlined", since it had no "call sites". Therefore it could not be deleted in the next step.
1400:| to 2, depending on the transformation algorithm used. The blow-up in grammar size depends on the order between
4086:
1500:
1472:
242:
being not the only symbol on the right-hand side, introduce, for every such terminal, a new nonterminal symbol
2897:
144:
one which is in
Chomsky normal form and has a size no larger than the square of the original grammar's size.
4293:
3910:
1082:
unless this is a unit rule which has already been (or is being) removed. The skipping of nonterminal symbol
20:
3376:
2788:
implied a BNF "syntax in which all definitions have such a form may be said to be in 'Floyd Normal Form'",
4066:
4478:
4311:
4157:
4033:
3940:
3862:
3739:
3425:
3059:
2986:
2960:
2934:
2781:
2584:
2616:
4257:
4106:
4023:
4000:
3832:
3100:
3069:
1468:
31:
4056:
4046:
4227:
4167:
3950:
3687:
3558:
3074:
1516:
94:
4207:
3872:
3781:
3718:
3673:
3651:
3624:
3581:
3462:
3398:
3366:
3332:
3303:
3267:
3257:
3047:
4275:
4038:
4015:
3548:
3507:
3200:
1388:
Moreover, the worst-case bloat in grammar size depends on the transformation order. Using |
4411:
4341:
3030:
2785:
2725:
481:
are new nonterminal symbols. Again, this does not change the grammar's produced language.
153:
102:
27:
3608:
3220:
193:
is the previous start symbol. This does not change the grammar's produced language, and
4187:
3641:
3617:
3325:
3012:
2751:
2731:
2707:
2687:
2667:
2647:
2571:
1524:
3512:
3204:
846:
at the call site". In the next step, they can hence be deleted, yielding the grammar:
4467:
4432:
4419:
4232:
4217:
4147:
3645:
3459:
Foundations of
Computing: An Accessible Introduction to Automata and Formal Languages
3297:
3250:
3064:
3043:
2768:
may be the start symbol. Only those context-free grammars which do not generate the
3562:
3762:
2769:
110:
43:
3397:. Leitfäden und Mongraphien der Informatik (in German). Stuttgart: B. G. Teubner.
3426:"To CNF or not to CNF? An Efficient Yet Presentable Version of the CYK Algorithm"
3353:
3492:
922:
This grammar produces the same language as the original example grammar, viz. {
3409:
Section 6.2 "Die
Chomsky-Normalform für kontextfreie Grammatiken", p. 149–152
2835:{\displaystyle \langle A\rangle ::=\,\langle B\rangle \mid \langle C\rangle }
3271:
3553:
3536:
1687:
is added to the grammar. After step "TERM", the grammar looks like this:
843:
2885:{\displaystyle \langle A\rangle ::=\,\langle B\rangle \langle C\rangle }
1416:
can incur a quadratic blow-up in the size of the grammar. The orderings
3670:
Foundations of
Computing: An Accessible Introduction to Formal Language
1504:
1520:
3256:(2nd ed.). Boston: Thomson Course Technology. Definition 2.8.
3636:(Pages 237–240 of section 6.6: simplified forms and normal forms.)
3191:
Chomsky, Noam (1959). "On
Certain Formal Properties of Grammars".
1463:
3395:
Theoretische
Informatik - Eine algorithmenorientierte Einführung
3359:
Automata, Computability, and Complexity: Theory and Applications
1673:
1515:
are considered terminal symbols here for simplicity, since in a
3735:
3731:
3663:(Pages 98–101 of section 2.1: context-free grammars. Page 156.)
3323:
Hopcroft, John E.; Motwani, Rajeev; Ullman, Jeffrey D. (2006).
3050:
for context-free grammars, and its variant probabilistic CKY.
3493:"Note on mathematical induction in phrase structure grammars"
341:
BIN: Eliminate right-hand sides with more than 2 nonterminals
3327:
Introduction to Automata Theory, Languages, and Computation
125:, and the third production rule can only appear if ε is in
3299:
Introduction to Automata Theory, Languages and Computation
1519:
their internal structure is usually not considered by the
691:
is. Hence the following intermediate grammar is obtained:
1090:
being a member of the unit closure of nonterminal symbol
608:
For example, in the following grammar, with start symbol
3619:
Introduction to Languages and the Theory of Computation
570:
Obtain an intermediate grammar by replacing each rule
160:
START: Eliminate the start symbol from right-hand sides
3291:
3289:
3287:
3285:
3283:
3281:
3228:
CS536-S21 Intro to Programming Languages and Compilers
1013:
are nonterminal symbols. To remove it, for each rule
3302:. Reading, Massachusetts: Addison-Wesley Publishing.
3015:
2989:
2963:
2937:
2900:
2850:
2797:
2754:
2734:
2710:
2690:
2670:
2650:
2619:
2587:
1885:
After step "BIN", the following grammar is obtained:
1396:, the size blow-up in the worst case may range from |
1381:
will re-introduce a unit rule if it is applied after
1056:
is a string of nonterminals and terminals, add rule
133:), the language produced by the context-free grammar
3580:(2nd ed.). Pearson Prentice Hall. p. 465.
4443:
4403:
4322:
4246:
4138:
3972:
3823:
3814:
3699:(pages 171-183 of section 7.1: Chomsky Normal Form)
3611:— uses the order TERM, BIN, START, DEL, UNIT.
3082:— its proof relies on the Chomsky normal form
4362:Distorted Morality – America's War on Terror?
3616:
3324:
3249:
3021:
3001:
2975:
2949:
2919:
2884:
2834:
2760:
2740:
2716:
2696:
2676:
2656:
2632:
2603:
2567:Another way to define the Chomsky normal form is:
4332:Manufacturing Consent: Noam Chomsky and the Media
3419:
3417:
3415:
3221:"Page 7, Lecture 9: Bottom-up Parsing Algorithms"
3034:original 1959 article, Knuth's letter does not.
2578:if all of its production rules are of the form:
1385:. The table shows which orderings are admitted.
204:TERM: Eliminate rules with nonsolitary terminals
3714:Automata and Languages: Theory and Applications
3961:New Horizons in the Study of Language and Mind
3296:Hopcroft, John E.; Ullman, Jeffrey D. (1979).
2772:can be transformed into Chomsky reduced form.
200:will not occur on any rule's right-hand side.
3747:
1392:| to denote the size of the original grammar
105:(a symbol that represents a constant value),
8:
4267:Chomsky's Universal Grammar: An Introduction
3668:Charles D. Allison (2021) (20 August 2021).
3605:Converting CFGs to CNF (Chomsky Normal Form)
3365:(1st ed.). Prentice-Hall. p. 169.
3111:For example, Hopcroft, Ullman (1979) merged
2996:
2990:
2970:
2964:
2944:
2938:
2907:
2901:
2879:
2873:
2870:
2864:
2857:
2851:
2829:
2823:
2817:
2811:
2804:
2798:
1456:lead to the least (i.e. quadratic) blow-up.
1086:in the resulting grammar is possible due to
4352:Power and Terror: Noam Chomsky in Our Times
3692:: CS1 maint: numeric names: authors list (
3576:Jurafsky, Daniel; Martin, James H. (2008).
148:Converting a grammar to Chomsky normal form
3921:The Logical Structure of Linguistic Theory
3820:
3754:
3740:
3732:
3705:Introduction to the Theory of Computation,
3128:indicating a kept and omitted nonterminal
1101:
4382:Peace, Propaganda & the Promised Land
3717:. Springer Science & Business Media.
3647:Introduction to the Theory of Computation
3552:
3537:"Backus Normal Form vs. Backus Naur Form"
3511:
3252:Introduction to the theory of computation
3014:
2988:
2962:
2936:
2913:
2899:
2863:
2849:
2810:
2796:
2753:
2733:
2709:
2689:
2669:
2649:
2626:
2618:
2594:
2586:
1495:The following grammar, with start symbol
16:Notation for context-free formal grammars
4077:The Prosperous Few and the Restless Many
3171:i.e. written length, measured in symbols
3080:Pumping lemma for context-free languages
1412:is done first, but is linear otherwise.
842:In this grammar, all ε-rules have been "
3183:
3092:
2920:{\displaystyle \langle A\rangle ::=\,a}
109:is the start symbol, and ε denotes the
3685:
3790:Colorless green ideas sleep furiously
2780:In a letter where he proposed a term
7:
3991:American Power and the New Mandarins
3711:Alexander Meduna (6 December 2012).
3099:that is, one that produces the same
4372:Noam Chomsky: Rebel Without a Pause
4097:Objectivity and Liberal Scholarship
3982:The Responsibility of Intellectuals
3843:Current Issues in Linguistic Theory
3461:. Fresh Sources, Inc. p. 176.
3230:. University of Wisconsin-Madison.
990:A unit rule is a rule of the form
596:by all versions with some nullable
4303:The Cambridge Companion to Chomsky
3931:Lectures on Government and Binding
3535:Knuth, Donald E. (December 1964).
3424:Lange, Martin; Leiß, Hans (2009).
1676:conversion algorithm, just a rule
1523:. The terminal symbol "^" denoted
14:
3002:{\displaystyle \langle C\rangle }
2976:{\displaystyle \langle B\rangle }
2950:{\displaystyle \langle A\rangle }
2604:{\displaystyle A\rightarrow \,BC}
489:An ε-rule is a rule of the form
3523:from the original on 2021-03-05.
3446:from the original on 2011-07-19.
3331:(3rd ed.). Addison-Wesley.
3237:from the original on 2021-07-19.
2633:{\displaystyle A\rightarrow \,a}
1344:
1336:
1329:
1322:
1310:
1301:
1294:
1287:
1275:
1268:
1259:
1252:
1240:
1233:
1226:
1217:
1205:
1198:
1191:
1184:
1133:
1118:
4285:Noam Chomsky: A Life of Dissent
4198:9-11: Was There An Alternative?
3853:Aspects of the Theory of Syntax
2728:. When using this definition,
1487:) and its Chomsky normal form (
518:, and compute them as follows:
4127:Requiem for the American Dream
4011:Counter-Revolutionary Violence
3578:Speech and Language Processing
3029:is a terminal symbol, because
2623:
2591:
2517:introduced in step "TERM" are
511:, the grammar's start symbol.
377:with more than 2 nonterminals
1:
4392:Is the Man Who Is Tall Happy?
3902:Conditions on Transformations
3513:10.1016/S0019-9958(61)80052-1
3356:(2007). "11.8 Normal Forms".
3205:10.1016/S0019-9958(59)90362-6
3119:into a single transformation.
3009:are nonterminal symbols, and
2704:are nonterminal symbols, and
2538:introduced in step "BIN" are
1408:. It may be exponential when
680:, is nullable, while neither
164:Introduce a new start symbol
3883:The Sound Pattern of English
3457:Allison, Charles D. (2022).
1483:" wrt. the example grammar (
1337:
1330:
1323:
1302:
1295:
1288:
1276:
1269:
1260:
1253:
1241:
1234:
1218:
1192:
1185:
4495:
3155:If the grammar had a rule
1311:
1227:
1206:
1199:
1105:of transformation results
986:UNIT: Eliminate unit rules
18:
3893:Remarks on Nominalization
3769:
3541:Communications of the ACM
3491:Floyd, Robert W. (1961).
2493:
2477:
2461:
2445:
2120:
2104:
2088:
2072:
1358:
1109:
553:exists, and every single
4427:Valeria Wasserman (wife)
4087:World Orders Old and New
3248:Sipser, Michael (2006).
1371:had been called before.
1362:preserves the result of
1098:Order of transformations
208:To eliminate each rule
19:Not to be confused with
4452:Chomsky–Foucault debate
4294:The Anti-Chomsky Reader
3911:Reflections on Language
3500:Information and Control
3193:Information and Control
1672:In step "START" of the
982:}, but has no ε-rules.
238:with a terminal symbol
21:conjunctive normal form
4067:Letters from Lexington
3951:The Minimalist Program
3672:. Fresh Sources, Inc.
3481:Hopcroft et al. (2006)
3393:Wegener, Ingo (1993).
3209:Here: Sect.6, p.152ff.
3023:
3003:
2977:
2951:
2921:
2886:
2836:
2762:
2742:
2718:
2698:
2678:
2658:
2634:
2605:
2558:Alternative definition
1492:
485:DEL: Eliminate ε-rules
4312:The Kingdom of Speech
4158:Middle East Illusions
4034:Manufacturing Consent
3941:Knowledge of Language
3863:Cartesian Linguistics
3554:10.1145/355588.365140
3433:Informatica Didactica
3024:
3004:
2978:
2952:
2922:
2887:
2837:
2763:
2743:
2719:
2699:
2679:
2659:
2635:
2606:
1473:arithmetic expression
1467:
4107:Hegemony or Survival
4024:The Fateful Triangle
4001:For Reasons of State
3833:Syntactic Structures
3615:John Martin (2003).
3607:, October 17, 2007.
3343:Section 7.1.5, p.272
3070:Greibach normal form
3013:
2987:
2961:
2935:
2898:
2848:
2795:
2752:
2732:
2708:
2688:
2668:
2648:
2617:
2585:
2576:Chomsky reduced form
2563:Chomsky reduced form
1469:Abstract syntax tree
42:(first described by
32:context-free grammar
4057:Deterring Democracy
4047:Necessary Illusions
3805:Political positions
1106:
1103:Mutual preservation
345:Replace each rule
271:Change every rule
95:nonterminal symbols
40:Chomsky normal form
38:, is said to be in
4168:Imperial Ambitions
3650:. PWS Publishing.
3075:Kuroda normal form
3019:
2999:
2973:
2947:
2917:
2882:
2832:
2758:
2738:
2714:
2694:
2674:
2654:
2630:
2601:
1517:compiler front end
1493:
1102:
562:is nullable, then
251:, and a new rule
171:, and a new rule
4461:
4460:
4242:
4241:
4208:Making the Future
3873:Language and Mind
3782:Chomsky hierarchy
3724:978-1-4471-0501-5
3703:Sipser, Michael.
3657:978-0-534-94728-6
3630:978-0-07-232200-2
3587:978-0-13-187321-6
3404:978-3-519-02123-0
3338:978-0-321-45536-9
3309:978-0-201-02988-8
3219:D'Antoni, Loris.
3048:bottom-up parsing
3022:{\displaystyle a}
2776:Floyd normal form
2761:{\displaystyle C}
2741:{\displaystyle B}
2717:{\displaystyle a}
2697:{\displaystyle C}
2677:{\displaystyle B}
2657:{\displaystyle A}
2504:
2503:
2131:
2130:
1881:
1880:
1668:
1667:
1375:
1374:
676:, and hence also
566:is nullable, too.
526:→ ε exists, then
113:. Also, neither
50:are of the form:
4486:
4474:Formal languages
4454:
4436:
4428:
4423:
4415:
4396:
4386:
4376:
4366:
4356:
4346:
4336:
4315:
4306:
4297:
4288:
4279:
4276:Decoding Chomsky
4270:
4261:
4235:
4222:
4212:
4202:
4192:
4182:
4172:
4162:
4152:
4131:
4121:
4111:
4101:
4091:
4081:
4071:
4061:
4051:
4041:
4039:Edward S. Herman
4028:
4018:
4016:Edward S. Herman
4005:
3995:
3985:
3965:
3955:
3945:
3935:
3925:
3915:
3905:
3896:
3887:
3877:
3867:
3857:
3847:
3837:
3821:
3807:
3800:
3798:Honorary degrees
3793:
3784:
3777:
3756:
3749:
3742:
3733:
3728:
3697:
3691:
3683:
3661:
3634:
3622:
3603:Cole, Richard.
3592:
3591:
3573:
3567:
3566:
3556:
3532:
3526:
3524:
3522:
3515:
3497:
3488:
3482:
3479:
3473:
3472:
3454:
3448:
3447:
3445:
3430:
3421:
3410:
3408:
3390:
3384:
3383:
3381:
3375:. Archived from
3364:
3350:
3344:
3342:
3330:
3320:
3314:
3313:
3293:
3276:
3275:
3255:
3245:
3239:
3238:
3236:
3225:
3216:
3210:
3208:
3188:
3172:
3169:
3163:
3153:
3147:
3144:
3136:
3126:
3120:
3109:
3103:
3097:
3060:Backus–Naur form
3028:
3026:
3025:
3020:
3008:
3006:
3005:
3000:
2982:
2980:
2979:
2974:
2956:
2954:
2953:
2948:
2926:
2924:
2923:
2918:
2891:
2889:
2888:
2883:
2841:
2839:
2838:
2833:
2782:Backus–Naur form
2767:
2765:
2764:
2759:
2747:
2745:
2744:
2739:
2723:
2721:
2720:
2715:
2703:
2701:
2700:
2695:
2683:
2681:
2680:
2675:
2663:
2661:
2660:
2655:
2639:
2637:
2636:
2631:
2610:
2608:
2607:
2602:
2140:
2139:
1890:
1889:
1692:
1691:
1532:
1531:
1351:
1348:
1347:
1340:
1339:
1333:
1332:
1326:
1325:
1314:
1313:
1305:
1304:
1298:
1297:
1291:
1290:
1279:
1278:
1272:
1271:
1263:
1262:
1256:
1255:
1244:
1243:
1237:
1236:
1230:
1229:
1221:
1220:
1209:
1208:
1202:
1201:
1195:
1194:
1188:
1187:
1141:) the result of
1140:
1137:
1136:
1131:
1125:
1122:
1121:
1116:
1115:always preserves
1107:
889: |
872: |
813:
804:
800: |
798:
792:
784:
779:
773:
770:
762:
749: |
747:
741:
733:
729:
721:
715:
709:
705:
672:the nonterminal
48:production rules
46:) if all of its
4494:
4493:
4489:
4488:
4487:
4485:
4484:
4483:
4464:
4463:
4462:
4457:
4450:
4439:
4431:
4426:
4422:(deceased wife)
4418:
4412:William Chomsky
4410:
4399:
4389:
4379:
4369:
4359:
4349:
4342:Last Party 2000
4339:
4329:
4318:
4309:
4300:
4291:
4282:
4273:
4264:
4255:
4248:
4238:
4225:
4215:
4205:
4195:
4185:
4175:
4165:
4155:
4145:
4134:
4124:
4114:
4104:
4094:
4084:
4074:
4064:
4054:
4044:
4031:
4021:
4008:
3998:
3988:
3979:
3968:
3958:
3948:
3938:
3928:
3918:
3908:
3899:
3890:
3880:
3870:
3860:
3850:
3840:
3830:
3816:
3810:
3803:
3796:
3787:
3780:
3773:
3765:
3760:
3725:
3710:
3684:
3680:
3667:
3658:
3640:
3631:
3623:. McGraw Hill.
3614:
3600:
3598:Further reading
3595:
3588:
3575:
3574:
3570:
3547:(12): 735–736.
3534:
3533:
3529:
3520:
3495:
3490:
3489:
3485:
3480:
3476:
3469:
3456:
3455:
3451:
3443:
3428:
3423:
3422:
3413:
3405:
3392:
3391:
3387:
3379:
3373:
3362:
3352:
3351:
3347:
3339:
3322:
3321:
3317:
3310:
3295:
3294:
3279:
3264:
3247:
3246:
3242:
3234:
3223:
3218:
3217:
3213:
3190:
3189:
3185:
3181:
3176:
3175:
3170:
3166:
3161:
3154:
3150:
3140:
3134:
3127:
3123:
3110:
3106:
3098:
3094:
3089:
3056:
3040:
3031:Robert W. Floyd
3011:
3010:
2985:
2984:
2959:
2958:
2933:
2932:
2896:
2895:
2846:
2845:
2793:
2792:
2786:Donald E. Knuth
2778:
2750:
2749:
2730:
2729:
2726:terminal symbol
2706:
2705:
2686:
2685:
2666:
2665:
2646:
2645:
2615:
2614:
2583:
2582:
2565:
2560:
2537:
2516:
2148:
1898:
1700:
1682:
1462:
1366:
1349:
1345:
1159:
1154:
1138:
1134:
1129:
1127:
1123:
1119:
1114:
1110:Transformation
1104:
1100:
1078:
1069:
1055:
1046:
1035:
1026:
988:
855:
809:
802:
794:
788:
780:
777:
771:
766:
760:
743:
737:
731:
725:
717:
713:
707:
703:
700:
690:
624:
614:
604:
592:
583:
561:
552:
543:
510:
487:
480:
467:
459:
449:
434:
428:
421:
412:
406:
392:
383:
373:
364:
358:
343:
332:
323:
314:
297:
284:
262:
250:
234:
221:
206:
199:
180:
170:
162:
154:automata theory
150:
103:terminal symbol
28:formal language
24:
17:
12:
11:
5:
4492:
4490:
4482:
4481:
4476:
4466:
4465:
4459:
4458:
4456:
4455:
4447:
4445:
4441:
4440:
4438:
4437:
4429:
4424:
4416:
4407:
4405:
4401:
4400:
4398:
4397:
4387:
4377:
4367:
4357:
4347:
4337:
4326:
4324:
4320:
4319:
4317:
4316:
4307:
4298:
4289:
4280:
4271:
4262:
4252:
4250:
4244:
4243:
4240:
4239:
4237:
4236:
4223:
4213:
4203:
4193:
4188:Gaza in Crisis
4183:
4173:
4163:
4153:
4142:
4140:
4136:
4135:
4133:
4132:
4122:
4112:
4102:
4092:
4082:
4072:
4062:
4052:
4042:
4029:
4019:
4006:
3996:
3986:
3976:
3974:
3970:
3969:
3967:
3966:
3956:
3946:
3936:
3926:
3916:
3906:
3897:
3888:
3878:
3868:
3858:
3848:
3838:
3827:
3825:
3818:
3812:
3811:
3809:
3808:
3801:
3794:
3785:
3778:
3770:
3767:
3766:
3761:
3759:
3758:
3751:
3744:
3736:
3730:
3729:
3723:
3708:
3701:
3678:
3665:
3656:
3642:Michael Sipser
3638:
3629:
3612:
3599:
3596:
3594:
3593:
3586:
3568:
3527:
3506:(4): 353–358.
3483:
3474:
3467:
3449:
3411:
3403:
3385:
3382:on 2023-01-17.
3372:978-0132288064
3371:
3345:
3337:
3315:
3308:
3277:
3262:
3240:
3211:
3199:(2): 137–167.
3182:
3180:
3177:
3174:
3173:
3164:
3159:
3148:
3146:, respectively
3121:
3104:
3091:
3090:
3088:
3085:
3084:
3083:
3077:
3072:
3067:
3062:
3055:
3052:
3039:
3036:
3018:
2998:
2995:
2992:
2972:
2969:
2966:
2946:
2943:
2940:
2929:
2928:
2916:
2912:
2909:
2906:
2903:
2893:
2881:
2878:
2875:
2872:
2869:
2866:
2862:
2859:
2856:
2853:
2843:
2831:
2828:
2825:
2822:
2819:
2816:
2813:
2809:
2806:
2803:
2800:
2777:
2774:
2757:
2737:
2713:
2693:
2673:
2653:
2642:
2641:
2629:
2625:
2622:
2612:
2600:
2597:
2593:
2590:
2572:formal grammar
2564:
2561:
2559:
2556:
2533:
2512:
2506:
2505:
2502:
2501:
2492:
2486:
2485:
2476:
2470:
2469:
2460:
2454:
2453:
2444:
2438:
2437:
2434:
2428:
2427:
2424:
2418:
2417:
2414:
2408:
2407:
2404:
2401:
2395:
2394:
2391:
2388:
2382:
2381:
2372:
2366:
2360:
2354:
2353:
2344:
2335:
2329:
2323:
2317:
2316:
2307:
2298:
2289:
2283:
2277:
2271:
2270:
2261:
2252:
2243:
2234:
2225:
2219:
2213:
2207:
2206:
2197:
2188:
2179:
2170:
2161:
2155:
2149:
2146:
2133:
2132:
2129:
2128:
2119:
2113:
2112:
2103:
2097:
2096:
2087:
2081:
2080:
2071:
2065:
2064:
2061:
2055:
2054:
2051:
2045:
2044:
2041:
2035:
2034:
2031:
2028:
2022:
2021:
2018:
2015:
2009:
2008:
1999:
1993:
1987:
1981:
1980:
1971:
1965:
1959:
1958:
1949:
1943:
1937:
1936:
1927:
1918:
1912:
1906:
1905:
1899:
1896:
1883:
1882:
1879:
1878:
1875:
1869:
1868:
1865:
1859:
1858:
1855:
1849:
1848:
1845:
1842:
1836:
1835:
1832:
1829:
1823:
1822:
1810:
1804:
1798:
1792:
1791:
1779:
1773:
1767:
1766:
1754:
1748:
1742:
1741:
1732:
1720:
1714:
1708:
1707:
1701:
1698:
1680:
1670:
1669:
1666:
1665:
1662:
1659:
1653:
1652:
1649:
1646:
1640:
1639:
1632:
1626:
1620:
1614:
1613:
1603:
1597:
1591:
1590:
1578:
1572:
1566:
1565:
1556:
1544:
1538:
1525:exponentiation
1461:
1458:
1373:
1372:
1356:
1355:
1353:
1341:
1334:
1327:
1320:
1316:
1315:
1308:
1306:
1299:
1292:
1285:
1281:
1280:
1273:
1266:
1264:
1257:
1250:
1246:
1245:
1238:
1231:
1224:
1222:
1215:
1211:
1210:
1203:
1196:
1189:
1182:
1180:
1176:
1175:
1172:
1169:
1166:
1163:
1160:
1155:
1150:
1147:
1146:
1099:
1096:
1080:
1079:
1074:
1067:
1051:
1044:
1038:
1037:
1031:
1024:
1003:
1002:
987:
984:
920:
919:
910:
897:
876:
853:
840:
839:
829:
816:
753:
698:
688:
670:
669:
659:
646:
633:
622:
612:
600:
594:
593:
588:
581:
568:
567:
557:
548:
541:
531:
508:
498:
497:
486:
483:
476:
470:
469:
463:
454:
444:
439:
436:
432:
426:
419:
414:
410:
404:
388:
381:
375:
374:
369:
362:
356:
342:
339:
335:
334:
328:
319:
312:
299:
298:
293:
282:
269:
268:
258:
246:
236:
235:
230:
219:
205:
202:
197:
187:
186:
178:
168:
161:
158:
149:
146:
79:
78:
72:
62:
15:
13:
10:
9:
6:
4:
3:
2:
4491:
4480:
4477:
4475:
4472:
4471:
4469:
4453:
4449:
4448:
4446:
4442:
4434:
4433:Aviva Chomsky
4430:
4425:
4421:
4420:Carol Chomsky
4417:
4413:
4409:
4408:
4406:
4402:
4394:
4393:
4388:
4384:
4383:
4378:
4374:
4373:
4368:
4364:
4363:
4358:
4354:
4353:
4348:
4344:
4343:
4338:
4334:
4333:
4328:
4327:
4325:
4321:
4314:
4313:
4308:
4305:
4304:
4299:
4296:
4295:
4290:
4287:
4286:
4281:
4278:
4277:
4272:
4269:
4268:
4263:
4260:
4259:
4254:
4253:
4251:
4245:
4234:
4231:(2015), with
4230:
4229:
4224:
4220:
4219:
4214:
4210:
4209:
4204:
4200:
4199:
4194:
4190:
4189:
4184:
4180:
4179:
4178:Interventions
4174:
4170:
4169:
4164:
4160:
4159:
4154:
4150:
4149:
4148:Class Warfare
4144:
4143:
4141:
4137:
4129:
4128:
4123:
4119:
4118:
4117:Failed States
4113:
4109:
4108:
4103:
4099:
4098:
4093:
4089:
4088:
4083:
4079:
4078:
4073:
4069:
4068:
4063:
4059:
4058:
4053:
4049:
4048:
4043:
4040:
4037:(1988), with
4036:
4035:
4030:
4026:
4025:
4020:
4017:
4014:(1973), with
4013:
4012:
4007:
4003:
4002:
3997:
3993:
3992:
3987:
3983:
3978:
3977:
3975:
3971:
3963:
3962:
3957:
3953:
3952:
3947:
3943:
3942:
3937:
3933:
3932:
3927:
3923:
3922:
3917:
3913:
3912:
3907:
3903:
3898:
3894:
3889:
3885:
3884:
3879:
3875:
3874:
3869:
3865:
3864:
3859:
3855:
3854:
3849:
3845:
3844:
3839:
3835:
3834:
3829:
3828:
3826:
3822:
3819:
3813:
3806:
3802:
3799:
3795:
3791:
3786:
3783:
3779:
3776:
3772:
3771:
3768:
3764:
3757:
3752:
3750:
3745:
3743:
3738:
3737:
3734:
3726:
3720:
3716:
3715:
3709:
3706:
3702:
3700:
3695:
3689:
3681:
3679:9780578944173
3675:
3671:
3666:
3664:
3659:
3653:
3649:
3648:
3643:
3639:
3637:
3632:
3626:
3621:
3620:
3613:
3610:
3606:
3602:
3601:
3597:
3589:
3583:
3579:
3572:
3569:
3564:
3560:
3555:
3550:
3546:
3542:
3538:
3531:
3528:
3519:
3514:
3509:
3505:
3501:
3494:
3487:
3484:
3478:
3475:
3470:
3468:9780578944173
3464:
3460:
3453:
3450:
3442:
3438:
3434:
3427:
3420:
3418:
3416:
3412:
3406:
3400:
3396:
3389:
3386:
3378:
3374:
3368:
3361:
3360:
3355:
3349:
3346:
3340:
3334:
3329:
3328:
3319:
3316:
3311:
3305:
3301:
3300:
3292:
3290:
3288:
3286:
3284:
3282:
3278:
3273:
3269:
3265:
3263:0-534-95097-3
3259:
3254:
3253:
3244:
3241:
3233:
3229:
3222:
3215:
3212:
3206:
3202:
3198:
3194:
3187:
3184:
3178:
3168:
3165:
3158:
3152:
3149:
3145:
3143:
3137:
3131:
3125:
3122:
3118:
3114:
3108:
3105:
3102:
3096:
3093:
3086:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3065:CYK algorithm
3063:
3061:
3058:
3057:
3053:
3051:
3049:
3045:
3044:CYK algorithm
3037:
3035:
3032:
3016:
2993:
2967:
2941:
2914:
2910:
2904:
2894:
2876:
2867:
2860:
2854:
2844:
2826:
2820:
2814:
2807:
2801:
2791:
2790:
2789:
2787:
2783:
2775:
2773:
2771:
2755:
2735:
2727:
2711:
2691:
2671:
2651:
2627:
2620:
2613:
2598:
2595:
2588:
2581:
2580:
2579:
2577:
2573:
2568:
2562:
2557:
2555:
2553:
2549:
2548:PowOp_Primary
2545:
2541:
2536:
2532:
2528:
2524:
2520:
2515:
2511:
2500:
2497:
2491:
2488:
2487:
2484:
2481:
2475:
2474:PowOp_Primary
2472:
2471:
2468:
2465:
2459:
2456:
2455:
2452:
2449:
2443:
2440:
2439:
2435:
2433:
2430:
2429:
2425:
2423:
2420:
2419:
2415:
2413:
2410:
2409:
2405:
2402:
2400:
2397:
2396:
2392:
2389:
2387:
2384:
2383:
2380:
2377:
2373:
2371:
2367:
2365:
2361:
2359:
2356:
2355:
2352:
2351:PowOp_Primary
2349:
2345:
2343:
2340:
2336:
2334:
2330:
2328:
2324:
2322:
2319:
2318:
2315:
2312:
2308:
2306:
2305:PowOp_Primary
2303:
2299:
2297:
2294:
2290:
2288:
2284:
2282:
2278:
2276:
2273:
2272:
2269:
2266:
2262:
2260:
2257:
2253:
2251:
2248:
2244:
2242:
2241:PowOp_Primary
2239:
2235:
2233:
2230:
2226:
2224:
2220:
2218:
2214:
2212:
2209:
2208:
2205:
2202:
2198:
2196:
2193:
2189:
2187:
2184:
2180:
2178:
2177:PowOp_Primary
2175:
2171:
2169:
2166:
2162:
2160:
2156:
2154:
2150:
2145:
2142:
2141:
2138:
2137:
2136:
2127:
2124:
2118:
2115:
2114:
2111:
2108:
2102:
2101:PowOp_Primary
2099:
2098:
2095:
2092:
2086:
2083:
2082:
2079:
2076:
2070:
2067:
2066:
2062:
2060:
2057:
2056:
2052:
2050:
2047:
2046:
2042:
2040:
2037:
2036:
2032:
2029:
2027:
2024:
2023:
2019:
2016:
2014:
2011:
2010:
2007:
2004:
2000:
1998:
1994:
1992:
1988:
1986:
1983:
1982:
1979:
1978:PowOp_Primary
1976:
1972:
1970:
1966:
1964:
1961:
1960:
1957:
1954:
1950:
1948:
1944:
1942:
1939:
1938:
1935:
1932:
1928:
1926:
1923:
1919:
1917:
1913:
1911:
1908:
1907:
1904:
1900:
1895:
1892:
1891:
1888:
1887:
1886:
1876:
1874:
1871:
1870:
1866:
1864:
1861:
1860:
1856:
1854:
1851:
1850:
1846:
1843:
1841:
1838:
1837:
1833:
1830:
1828:
1825:
1824:
1821:
1818:
1815:
1811:
1809:
1805:
1803:
1799:
1797:
1794:
1793:
1790:
1787:
1784:
1780:
1778:
1774:
1772:
1769:
1768:
1765:
1762:
1759:
1755:
1753:
1749:
1747:
1744:
1743:
1740:
1737:
1733:
1731:
1728:
1725:
1721:
1719:
1715:
1713:
1710:
1709:
1706:
1702:
1697:
1694:
1693:
1690:
1689:
1688:
1686:
1679:
1675:
1663:
1660:
1658:
1655:
1654:
1650:
1647:
1645:
1642:
1641:
1637:
1633:
1631:
1627:
1625:
1621:
1619:
1616:
1615:
1612:
1608:
1604:
1602:
1598:
1596:
1593:
1592:
1589:
1586:
1583:
1579:
1577:
1573:
1571:
1568:
1567:
1564:
1561:
1557:
1555:
1552:
1549:
1545:
1543:
1539:
1537:
1534:
1533:
1530:
1529:
1528:
1526:
1522:
1518:
1514:
1510:
1506:
1502:
1498:
1490:
1486:
1482:
1478:
1474:
1470:
1466:
1459:
1457:
1455:
1451:
1447:
1443:
1439:
1435:
1431:
1427:
1423:
1419:
1415:
1411:
1407:
1403:
1399:
1395:
1391:
1386:
1384:
1380:
1370:
1365:
1361:
1357:
1354:
1342:
1335:
1328:
1321:
1318:
1317:
1309:
1307:
1300:
1293:
1286:
1283:
1282:
1274:
1267:
1265:
1258:
1251:
1248:
1247:
1239:
1232:
1225:
1223:
1216:
1213:
1212:
1204:
1197:
1190:
1183:
1181:
1178:
1177:
1173:
1170:
1167:
1164:
1161:
1158:
1153:
1149:
1148:
1144:
1113:
1108:
1097:
1095:
1093:
1089:
1085:
1077:
1073:
1066:
1062:
1059:
1058:
1057:
1054:
1050:
1043:
1034:
1030:
1023:
1019:
1016:
1015:
1014:
1012:
1008:
1000:
996:
993:
992:
991:
985:
983:
981:
977:
973:
969:
965:
961:
957:
953:
949:
945:
941:
937:
933:
929:
925:
918:
914:
911:
909:
905:
901:
898:
896:
892:
888:
884:
880:
877:
875:
871:
867:
863:
859:
852:
849:
848:
847:
845:
837:
833:
830:
828:
824:
820:
817:
815:
812:
806:
799:
797:
791:
785:
783:
774:
769:
763:
757:
754:
752:
748:
746:
740:
734:
728:
722:
720:
710:
697:
694:
693:
692:
687:
683:
679:
675:
667:
663:
660:
658:
654:
650:
647:
645:
641:
637:
634:
632:
628:
621:
618:
617:
616:
611:
606:
603:
599:
591:
587:
580:
576:
573:
572:
571:
565:
560:
556:
551:
547:
540:
536:
532:
529:
525:
521:
520:
519:
517:
512:
507:
503:
495:
492:
491:
490:
484:
482:
479:
475:
466:
462:
457:
453:
447:
443:
440:
437:
431:
425:
418:
415:
409:
403:
399:
396:
395:
394:
391:
387:
380:
372:
368:
361:
355:
351:
348:
347:
346:
340:
338:
331:
327:
322:
318:
311:
307:
304:
303:
302:
296:
292:
288:
281:
277:
274:
273:
272:
266:
261:
257:
254:
253:
252:
249:
245:
241:
233:
229:
225:
218:
214:
211:
210:
209:
203:
201:
196:
192:
184:
177:
174:
173:
172:
167:
159:
157:
155:
147:
145:
143:
138:
136:
132:
128:
124:
120:
116:
112:
108:
104:
100:
97:, the letter
96:
92:
88:
84:
76:
73:
70:
66:
63:
60:
56:
53:
52:
51:
49:
45:
41:
37:
33:
29:
22:
4479:Noam Chomsky
4390:
4380:
4370:
4360:
4350:
4340:
4330:
4310:
4301:
4292:
4283:
4274:
4265:
4256:
4228:On Palestine
4226:
4216:
4206:
4196:
4186:
4176:
4166:
4156:
4146:
4125:
4115:
4105:
4095:
4085:
4075:
4065:
4055:
4045:
4032:
4022:
4009:
3999:
3989:
3959:
3949:
3939:
3929:
3919:
3909:
3881:
3871:
3861:
3851:
3841:
3831:
3817:bibliography
3775:Bibliography
3763:Noam Chomsky
3713:
3707:2nd edition.
3704:
3698:
3669:
3662:
3646:
3635:
3618:
3604:
3577:
3571:
3544:
3540:
3530:
3503:
3499:
3486:
3477:
3458:
3452:
3436:
3432:
3394:
3388:
3377:the original
3358:
3354:Rich, Elaine
3348:
3326:
3318:
3298:
3251:
3243:
3227:
3214:
3196:
3192:
3186:
3167:
3156:
3151:
3141:
3139:
3133:
3129:
3124:
3116:
3112:
3107:
3095:
3041:
2930:
2779:
2770:empty string
2643:
2575:
2569:
2566:
2551:
2547:
2544:MulOp_Factor
2543:
2539:
2534:
2530:
2526:
2522:
2518:
2513:
2509:
2507:
2498:
2495:
2489:
2482:
2479:
2473:
2466:
2463:
2458:MulOp_Factor
2457:
2450:
2447:
2441:
2431:
2421:
2411:
2398:
2385:
2378:
2375:
2369:
2363:
2357:
2350:
2347:
2341:
2338:
2332:
2326:
2320:
2314:MulOp_Factor
2313:
2310:
2304:
2301:
2295:
2292:
2286:
2280:
2274:
2267:
2264:
2258:
2255:
2250:MulOp_Factor
2249:
2246:
2240:
2237:
2231:
2228:
2222:
2216:
2210:
2203:
2200:
2194:
2191:
2186:MulOp_Factor
2185:
2182:
2176:
2173:
2167:
2164:
2158:
2152:
2143:
2134:
2125:
2122:
2116:
2109:
2106:
2100:
2093:
2090:
2085:MulOp_Factor
2084:
2077:
2074:
2068:
2058:
2048:
2038:
2025:
2012:
2005:
2002:
1996:
1990:
1984:
1977:
1974:
1968:
1962:
1956:MulOp_Factor
1955:
1952:
1946:
1940:
1933:
1930:
1924:
1921:
1915:
1909:
1902:
1893:
1884:
1872:
1862:
1852:
1839:
1826:
1819:
1816:
1813:
1807:
1801:
1795:
1788:
1785:
1782:
1776:
1770:
1763:
1760:
1757:
1751:
1745:
1738:
1735:
1729:
1726:
1723:
1717:
1711:
1704:
1695:
1684:
1677:
1671:
1656:
1643:
1635:
1629:
1623:
1617:
1610:
1606:
1600:
1594:
1587:
1584:
1581:
1575:
1569:
1562:
1559:
1553:
1550:
1547:
1541:
1535:
1527:in Algol60.
1512:
1508:
1496:
1494:
1488:
1484:
1480:
1476:
1453:
1449:
1445:
1441:
1437:
1433:
1429:
1425:
1421:
1417:
1413:
1409:
1405:
1401:
1397:
1393:
1389:
1387:
1382:
1378:
1376:
1368:
1363:
1359:
1156:
1151:
1142:
1111:
1091:
1087:
1083:
1081:
1075:
1071:
1064:
1060:
1052:
1048:
1041:
1039:
1032:
1028:
1021:
1017:
1010:
1006:
1004:
998:
994:
989:
979:
975:
971:
967:
963:
959:
955:
951:
947:
943:
939:
935:
931:
927:
923:
921:
916:
912:
907:
903:
899:
894:
890:
886:
882:
878:
873:
869:
865:
861:
857:
850:
841:
835:
831:
826:
822:
818:
810:
808:
801:
795:
789:
787:
781:
776:
767:
765:
759:
755:
750:
744:
738:
736:
726:
724:
718:
712:
702:
695:
685:
681:
677:
673:
671:
665:
661:
656:
652:
648:
643:
639:
635:
630:
626:
619:
609:
607:
601:
597:
595:
589:
585:
578:
574:
569:
563:
558:
554:
549:
545:
538:
534:
530:is nullable.
527:
523:
515:
513:
505:
501:
499:
493:
488:
477:
473:
471:
464:
460:
455:
451:
445:
441:
429:
423:
416:
407:
401:
397:
389:
385:
378:
376:
370:
366:
359:
353:
349:
344:
336:
329:
325:
320:
316:
309:
305:
300:
294:
290:
286:
279:
275:
270:
264:
259:
255:
247:
243:
239:
237:
231:
227:
223:
216:
212:
207:
194:
190:
188:
182:
175:
165:
163:
151:
139:
134:
130:
126:
123:start symbol
118:
114:
111:empty string
106:
98:
90:
86:
82:
80:
74:
68:
64:
58:
54:
44:Noam Chomsky
39:
35:
25:
4375:(2003) (TV)
4323:Filmography
4249:works about
4139:Collections
3824:Linguistics
3525:Here: p.354
3038:Application
1130:may destroy
121:may be the
71:, or
61:, or
4468:Categories
4435:(daughter)
4233:Ilan Pappé
3179:References
2552:Expr_Close
2540:AddOp_Term
2490:Expr_Close
2442:AddOp_Term
2393:| −
2379:Expr_Close
2342:Expr_Close
2296:Expr_Close
2259:AddOp_Term
2232:Expr_Close
2195:AddOp_Term
2168:Expr_Close
2117:Expr_Close
2069:AddOp_Term
2020:| −
2006:Expr_Close
1925:AddOp_Term
1834:| −
1651:| −
1367: if
533:If a rule
522:If a rule
393:by rules
142:equivalent
30:theory, a
3688:cite book
2997:⟩
2991:⟨
2971:⟩
2965:⟨
2945:⟩
2939:⟨
2908:⟩
2902:⟨
2880:⟩
2874:⟨
2871:⟩
2865:⟨
2858:⟩
2852:⟨
2830:⟩
2824:⟨
2821:∣
2818:⟩
2812:⟨
2805:⟩
2799:⟨
2624:→
2592:→
4414:(father)
4247:Academic
3984:" (1967)
3973:Politics
3904:" (1973)
3895:" (1970)
3644:(1997).
3563:47537431
3518:Archived
3441:Archived
3272:58544333
3232:Archived
3101:language
3054:See also
2370:variable
2333:variable
2287:variable
2223:variable
2159:variable
1997:variable
1808:variable
1630:variable
1513:variable
516:nullable
4444:Related
4258:Chomsky
2784:(BNF),
2483:Primary
2358:Primary
2110:Primary
1985:Primary
1969:Primary
1796:Primary
1789:Primary
1777:Primary
1618:Primary
1611:Primary
1601:Primary
1507:. Both
1505:Algol60
1471:of the
1460:Example
1040:where
844:inlined
504:is not
4404:Family
4395:(2013)
4385:(2004)
4365:(2003)
4355:(2002)
4345:(2001)
4335:(1992)
4221:(2012)
4218:Occupy
4211:(2012)
4201:(2011)
4191:(2010)
4181:(2007)
4171:(2005)
4161:(2003)
4151:(1996)
4130:(2017)
4120:(2006)
4110:(2003)
4100:(1997)
4090:(1994)
4080:(1993)
4070:(1993)
4060:(1991)
4050:(1989)
4027:(1983)
4004:(1973)
3994:(1969)
3964:(2000)
3954:(1995)
3944:(1986)
3934:(1981)
3924:(1975)
3914:(1975)
3886:(1968)
3876:(1968)
3866:(1966)
3856:(1965)
3846:(1964)
3836:(1957)
3815:Select
3721:
3676:
3654:
3627:
3584:
3561:
3465:
3401:
3369:
3335:
3306:
3270:
3260:
2931:where
2644:where
2574:is in
2550:, and
2529:. The
2525:, and
2467:Factor
2364:number
2348:Factor
2327:number
2321:Factor
2302:Factor
2281:number
2238:Factor
2217:number
2174:Factor
2153:number
2094:Factor
1991:number
1975:Factor
1963:Factor
1947:Factor
1802:number
1783:Factor
1771:Factor
1764:Factor
1752:Factor
1624:number
1607:Factor
1595:Factor
1588:Factor
1576:Factor
1521:parser
1509:number
1489:bottom
1179:START
1128:resp.
1005:where
500:where
472:where
189:where
89:, and
81:where
3609:(pdf)
3559:S2CID
3521:(PDF)
3496:(PDF)
3444:(PDF)
3429:(PDF)
3380:(PDF)
3363:(PDF)
3235:(PDF)
3224:(PDF)
3087:Notes
2724:is a
2527:Close
2519:PowOp
2499:Close
2480:PowOp
2464:MulOp
2448:AddOp
2432:Close
2412:PowOp
2399:MulOp
2386:AddOp
2265:AddOp
2201:AddOp
2126:Close
2107:PowOp
2091:MulOp
2075:AddOp
2059:Close
2039:PowOp
2026:MulOp
2013:AddOp
1931:AddOp
1873:Close
1853:PowOp
1840:MulOp
1827:AddOp
1820:Close
1786:PowOp
1761:MulOp
1736:AddOp
1727:AddOp
1674:above
1657:MulOp
1644:AddOp
1634:| (
1585:MulOp
1560:AddOp
1551:AddOp
1479:^2+4*
1438:START
1418:START
1379:START
1369:START
1319:UNIT
1214:TERM
1174:UNIT
1162:START
438:... ,
384:,...,
101:is a
3719:ISBN
3694:link
3674:ISBN
3652:ISBN
3625:ISBN
3582:ISBN
3463:ISBN
3399:ISBN
3367:ISBN
3333:ISBN
3304:ISBN
3268:OCLC
3258:ISBN
3138:and
3115:and
3113:TERM
3046:, a
2983:and
2684:and
2523:Open
2508:The
2496:Expr
2451:Term
2436:→ )
2426:→ (
2422:Open
2416:→ ^
2406:| /
2403:→ *
2390:→ +
2376:Open
2339:Open
2311:Term
2293:Open
2275:Term
2268:Term
2256:Expr
2247:Term
2229:Open
2211:Expr
2204:Term
2192:Expr
2183:Term
2165:Open
2123:Expr
2078:Term
2063:→ )
2053:→ (
2049:Open
2043:→ ^
2033:| /
2030:→ *
2017:→ +
2003:Open
1953:Term
1941:Term
1934:Term
1922:Expr
1916:Term
1910:Expr
1903:Expr
1877:→ )
1867:→ (
1863:Open
1857:→ ^
1847:| /
1844:→ *
1831:→ +
1817:Expr
1814:Open
1758:Term
1746:Term
1739:Term
1730:Term
1724:Expr
1718:Term
1712:Expr
1705:Expr
1685:Expr
1664:| /
1661:→ *
1648:→ +
1636:Expr
1582:Term
1570:Term
1563:Term
1554:Term
1548:Expr
1542:Term
1536:Expr
1511:and
1497:Expr
1454:TERM
1450:UNIT
1436:and
1434:UNIT
1422:TERM
1414:UNIT
1404:and
1383:UNIT
1360:UNIT
1284:DEL
1249:BIN
1165:TERM
1070:...
1047:...
1027:...
940:abac
936:abab
932:abaa
684:nor
584:...
544:...
496:→ ε,
365:...
324:...
315:...
301:to
289:...
285:...
226:...
222:...
117:nor
93:are
77:→ ε,
3549:doi
3508:doi
3201:doi
3132:by
3117:BIN
2911:::=
2861:::=
2808:::=
2748:or
2374:|
2368:|
2346:|
2337:|
2331:|
2309:|
2300:|
2291:|
2285:|
2254:|
2245:|
2236:|
2227:|
2221:|
2190:|
2181:|
2172:|
2163:|
2157:|
2001:|
1995:|
1973:|
1951:|
1920:|
1812:|
1806:|
1781:|
1756:|
1722:|
1628:|
1605:|
1580:|
1546:|
1503:or
1485:top
1446:DEL
1442:BIN
1430:DEL
1426:BIN
1410:DEL
1406:BIN
1402:DEL
1364:DEL
1171:DEL
1168:BIN
1063:→
1020:→
968:bac
964:bab
960:baa
948:abc
944:abb
928:aba
858:AbB
838:| ε
668:| ε
627:AbB
26:In
4470::
3690:}}
3686:{{
3557:.
3543:.
3539:.
3516:.
3502:.
3498:.
3439:.
3435:.
3431:.
3414:^
3280:^
3266:.
3226:.
3195:.
2957:,
2892:or
2842:or
2664:,
2611:or
2570:A
2554:.
2546:,
2542:,
2521:,
2494:→
2478:→
2462:→
2446:→
2362:→
2325:→
2279:→
2263:|
2215:→
2199:|
2151:→
2121:→
2105:→
2089:→
2073:→
1989:→
1967:→
1945:→
1929:|
1914:→
1901:→
1800:→
1775:→
1750:→
1734:|
1716:→
1703:→
1638:)
1622:→
1609:^
1599:→
1574:→
1558:|
1540:→
1145::
1094:.
1009:,
997:→
976:bc
972:bb
956:ba
924:ab
915:→
906:|
902:→
893:|
891:AC
885:|
883:AA
881:→
868:|
866:bB
864:|
862:Ab
860:|
856:→
834:→
825:|
821:→
807:|
786:|
775:|
764:|
761:AA
758:→
735:|
723:|
711:|
701:→
664:→
655:|
651:→
644:AC
642:|
640:AA
638:→
629:|
625:→
615:,
577:→
537:→
458:-1
450:→
448:-2
422:→
400:→
352:→
308:→
278:→
263:→
215:→
181:→
137:.
85:,
67:→
59:BC
57:→
34:,
3980:"
3900:"
3891:"
3792:"
3788:"
3755:e
3748:t
3741:v
3727:.
3696:)
3682:.
3660:.
3633:.
3590:.
3565:.
3551::
3545:7
3510::
3504:4
3471:.
3437:8
3407:.
3341:.
3312:.
3274:.
3207:.
3203::
3197:2
3160:0
3157:S
3142:N
3135:N
3130:N
3017:a
2994:C
2968:B
2942:A
2927:,
2915:a
2905:A
2877:C
2868:B
2855:A
2827:C
2815:B
2802:A
2756:C
2736:B
2712:a
2692:C
2672:B
2652:A
2640:,
2628:a
2621:A
2599:C
2596:B
2589:A
2535:i
2531:A
2514:a
2510:N
2147:0
2144:S
1897:0
1894:S
1699:0
1696:S
1683:→
1681:0
1678:S
1501:C
1491:)
1481:b
1477:a
1475:"
1452:,
1448:,
1444:,
1440:,
1432:,
1428:,
1424:,
1420:,
1398:G
1394:G
1390:G
1352:)
1350:Y
1343:(
1157:X
1152:Y
1143:Y
1139:N
1132:(
1126:)
1124:Y
1117:(
1112:X
1092:A
1088:B
1084:B
1076:n
1072:X
1068:1
1065:X
1061:A
1053:n
1049:X
1045:1
1042:X
1036:,
1033:n
1029:X
1025:1
1022:X
1018:B
1011:B
1007:A
1001:,
999:B
995:A
980:c
978:,
974:,
970:,
966:,
962:,
958:,
954:,
952:b
950:,
946:,
942:,
938:,
934:,
930:,
926:,
917:a
913:A
908:c
904:b
900:C
895:C
887:A
879:B
874:C
870:b
854:0
851:S
836:a
832:A
827:c
823:b
819:C
814:C
811:A
805:C
803:A
796:A
793:ε
790:A
782:A
778:A
772:A
768:A
756:B
751:C
745:B
742:b
739:A
732:B
730:b
727:A
719:B
716:b
714:A
708:B
706:b
704:A
699:0
696:S
689:0
686:S
682:C
678:B
674:A
666:a
662:A
657:c
653:b
649:C
636:B
631:C
623:0
620:S
613:0
610:S
602:i
598:X
590:n
586:X
582:1
579:X
575:A
564:A
559:i
555:X
550:n
546:X
542:1
539:X
535:A
528:A
524:A
509:0
506:S
502:A
494:A
478:i
474:A
468:,
465:n
461:X
456:n
452:X
446:n
442:A
435:,
433:2
430:A
427:2
424:X
420:1
417:A
413:,
411:1
408:A
405:1
402:X
398:A
390:n
386:X
382:1
379:X
371:n
367:X
363:2
360:X
357:1
354:X
350:A
333:.
330:n
326:X
321:a
317:N
313:1
310:X
306:A
295:n
291:X
287:a
283:1
280:X
276:A
267:.
265:a
260:a
256:N
248:a
244:N
240:a
232:n
228:X
224:a
220:1
217:X
213:A
198:0
195:S
191:S
185:,
183:S
179:0
176:S
169:0
166:S
135:G
131:G
129:(
127:L
119:C
115:B
107:S
99:a
91:C
87:B
83:A
75:S
69:a
65:A
55:A
36:G
23:.
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