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A note on ambiguity of internal contextual grammars. (English) Zbl 1140.68030

Summary: We continue the study of ambiguity of internal contextual grammars which was investigated in L. Ilie [Stud. Funct. Struct. Linguist. 45, 29-45 (1998; Zbl 0948.68101)] and C. Martin-Vide et al. [Stud. Funct. Struct. Linguist. 45, 59–81 (1998; Zbl 0948.68102)]. We solve some open problems formulated in these papers. The main results are: (i) there are inherently 1-ambiguous languages with respect to internal contextual grammars with arbitrary choice which are 0-unambiguous with respect to finite choice, (ii) there are inherently 2-ambiguous languages with respect to internal contextual grammars with arbitrary choice which are 1-unambiguous with respect to regular choice, and (iii) there are inherently 2-ambiguous languages with respect to depth-first internal contextual grammars with arbitrary choice which are 1-unambiguous with respect to finite choice.

MSC:

68Q42 Grammars and rewriting systems
68Q45 Formal languages and automata
68T50 Natural language processing
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References:

[1] Ilie, L., On ambiguity in internal contextual languages, (Martin-Vide, C., Second Int. Conf. on Mathematical Linguistics, Tarragona, 1996 (1997), John Benjamins: John Benjamins Amsterdam), 29-45 · Zbl 0948.68101
[2] Marcus, S., Algebraic Linguistics, Analytical Models (1967), Academic Press: Academic Press New York · Zbl 0174.02402
[3] Marcus, S., Contextual Grammars, Rev. Roumaine Math. Pures Appl., 14, 1525-1534 (1969) · Zbl 0193.32401
[4] C. Martin-Vide, J. Miquel-Verges, Gh. Păun, Contextual grammars with depth-first derivation, 10th Twente Workshop on Language Technology, Algebraic Methods in Language Processing, Twente, 1995, pp. 225-233.; C. Martin-Vide, J. Miquel-Verges, Gh. Păun, Contextual grammars with depth-first derivation, 10th Twente Workshop on Language Technology, Algebraic Methods in Language Processing, Twente, 1995, pp. 225-233.
[5] Martin-Vide, C.; Miguel-Verges, J.; Păun, Gh.; Salomaa, A., Attempting to define the ambiguity in internal contextual languages, (Martin-Vide, C., Second Int. Conf. on Mathematical Linguistics, Tarragona, 1996 (1997), John Benjamins: John Benjamins Amsterdam), 59-81 · Zbl 0948.68102
[6] Păun, Gh., Contextual Grammars (1982), The Publishing House of the Romanian Academy of Sciences: The Publishing House of the Romanian Academy of Sciences Bucuresti
[7] Păun, Gh., Marcus Contextual Grammars (1997), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht
[8] Păun, Gh.; Nguyen, X. M., On the inner contextual grammars, Rev. Roumaine Math. Pures Appl., 25, 641-651 (1980) · Zbl 0452.68080
[9] Salomaa, A., Formal Languages (1973), Academic Press: Academic Press New York · Zbl 0262.68025
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