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Grammars, derivation modes and properties of indexed and type-0 languages. (English) Zbl 0636.68096
The authors introduce an extension of a context-free grammar which in addition to the usual context-free productions $$A\to \alpha$$ can contain also so-called index productions of the form Af$$\to B$$ and $$A\to Bf$$, where A and B are nonterminals and f belongs to a given set of indices. With these indices it is possible to distribute the information over context-free productions.
It is shown in the paper that the so-called V-mode of derivation yields exactly the class of indexed languages and R-mode, respectively, the class of type-0 languages. A normal-form transformation, similar to the Chomsky normal form, is carried out. Moreover, using the notion of a generalized Dyck grammar, the authors give new homomorphic characterizations for indexed languages and type-0 languages.
Reviewer: M.Linna

MSC:
 68Q45 Formal languages and automata
Full Text:
References:
 [1] Aho, A.V., Indexed grammars, J. ACM, 15, 647-671, (1968) · Zbl 0175.27801 [2] Bachmann, P., Theoretical investigations of functional grammars, Elektron. informationsverarb. kybernet., 15, 497-506, (1979) · Zbl 0436.68047 [3] Culik, K., A purely homomorphic characterization of recursively enumerable sets, J. ACM, 26, 345-350, (1979) · Zbl 0395.68076 [4] Duske, J.; Parchmann, R.; Specht, J., A homomorphic characterization of indexed languages, Elektron. informationsverarb. kybernet., 15, 187-195, (1979) · Zbl 0421.68071 [5] Duske, J.; Parchmann, P., Linear indexed languages, Theoret. comput. sci., 32, 47-60, (1984) · Zbl 0545.68067 [6] Engelfrict, J.; Rozenberg, G., Equality languages, fixed-point languages and representations of recursively enumerable languages, Proc. 19th ann. IEEE symp. on foundations of computer science, 123-126, (1978) [7] Ginsburg, S.; Greibach, S.A.; Harrison, M.A., One-way stack automata, J. ACM, 14, 389-418, (1967) · Zbl 0171.14803 [8] Ginsburg, S.; Spanier, E.H., Control set on grammars, Math. systems theory, 2, 159-177, (1968) · Zbl 0157.33604 [9] Harrison, M.A., Introduction to formal language theory, (1978), Addison-Wesley Reading, MA · Zbl 0411.68058 [10] Hayashi, T., On derivation trees of indexed grammars, Publ. res. inst. math. sci., 9, 61-92, (1973) · Zbl 0319.68043 [11] Lukaszewicz, L., On functional grammars, (), 333-344 [12] Parchmann, R.; Duske, J.; Specht, J., On deterministic indexed languages, Inform. and control, 45, 48-67, (1980) · Zbl 0438.68035 [13] Parchmann, R.; Duske, J.; Specht, J., Closure properties of deterministic indexed languages, Inform. and control, 46, 200-218, (1980) · Zbl 0453.68053 [14] Parchmann, R.; Duske, J.; Specht, J., Indexed LL(k) grammars, Acta cybernet., 7, 33-53, (1985) · Zbl 0577.68077 [15] Parchmann, R., Balanced context-free languages and indexed languages, Elektron. informationsverarb. kybernet., 20, 543-556, (1984) · Zbl 0597.68059 [16] Salomaa, A., Formal languages, (1973), Academic Press New York · Zbl 0262.68025
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