Showing papers by "Grzegorz Rozenberg published in 1978"
30 Oct 1978
225 citations
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04 Sep 1978
TL;DR: A new language generating mechanism is defined that is derived from a generalization of the two-level substitution mechanism and involves several (incomplete) grammars which communicate with each other by introducing variables for which they have no productions themselves.
Abstract: A new language generating mechanism is defined. It is derived from a generalization of the two-level substitution mechanism and involves several (incomplete) grammars which communicate with each other by introducing variables for which they have no productions themselves. When the grammars are context-free, this yields an alternative definition for the context-free programmed grammars. When the grammars are EOL (parallel) a class is found lying (strictly ?) between ETOL and CFP.
76 citations
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TL;DR: An alternative (and simpler than the one presented in [1]) proof that the D0L (sequence) equivalence problem is decidable is provided.
75 citations
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30 Oct 1978TL;DR: These systems and their languages and sequences are illustrated in particular by applying them to the development of epidermal cell layers in which hexagonal arrays of cells are generated from previoushexagonal arrays.
Abstract: In this paper we extend parallel string generating systems (string L-systems) to parallel map generating systems(BPMOL-systems). The main distinguishing feature of of these constructs is that they generate map patterns by rewriting the graph of the map directly, and not its dual graph. These systems and their languages and sequences are illustrated in particular by applying them to the development of epidermal cell layers in which hexagonal arrays of cells are generated from previous hexagonal arrays.
69 citations
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TL;DR: The notion of a simplification of a homomorphism is introduced and investigated, and its usefulness is demonstrated in providing rather short proofs of the following results.
Abstract: The notion of a simplification of a homomorphism is introduced and investigated. Its usefulness is demonstrated in providing rather short proofs of the following results: (i) Given an arbitrary homomorphism h and arbitrary words x, y it is decidable whether or not there exists an integer n such that h n ( x ) = h n ( y ). (ii) Given an arbitrary homomorphism h and arbitrary words x, y it is decidable whether or not there exists integers n and r such that h n ( x ) = h r ( y ). (iii) Given an arbitrary DOL system G and an arbitrary integer d it is decidable whether or not G is locally catenative of depth not larger thand d . (iv) The equivalence problem for elementary polynomially bounded DOL systems is decidable.
38 citations
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TL;DR: The classical concept of finite index is investigated within the framework of ETOL systems, and the results suggest that the value of an index is determined by the total number of elements in the system.
Abstract: The classical concept of finite index is investigated within the framework of ETOL systems.
36 citations
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TL;DR: It is proved that this restriction in all these cases yields the same family of languages: the family of finite index ETOL languages (Rozenberg and Vermeir, 1978), which provides another link between the "sequential" and the "parallel" formal language theories.
Abstract: In earlier papers (Rozenberg and Yermeir, 1977, 1978) the effect of the finite index restriction on ETOL systems was quite throoughly investigated. One can give two main reasons for the interest in ETOL systems of finite index: --biological; there are numerous examples of a biological development with a limited number of "active" cells, --mathematical; the finite index restriction is a classical restriction considered in formal language theory (see, e.g., Salomaa, 1973), and it is certainly worthwhile to investigate its effect on language-generating devices parallel in nature. This paper continues the research by Rozenberg and Vermeir (1975a, 1977) First of all, we investigate the effect of the finite index restriction on the classic.a[ extensions of a context-free grammar, namely, on context-free programmed grammars, ordered grammars, and matrix grammars. We prove that this restriction in all these cases yields the same family of languages: the family of finite index ETOL languages (Rozenberg and Vermeir, 1978). In this way we not only demonstrate the importance of the family of ETOL languages of finite index but we also provide another link between the "sequential" and the "parallel" formal language theories. In this way numerous results from Rozenberg and Vermeir (1978) are carried over to "sequential" families of context-free pro- 284
24 citations
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TL;DR: This paper is concerned with letter-rewriting systems in which context-free rewriting productions are equipped with context conditions and situations where the context conditions of several productions are satisfied by a given occurrence of A.
18 citations
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16 Oct 1978
TL;DR: This paper is an attempt towards a systematic investigation of equality languages and fixed point languages of homomorphisms and dgsm mappings (i.e. mappings defined by deterministic generalized sequential machines with accepting states).
Abstract: A considerable part of formal language'theory deals with mappings on free monoids. A way to measure the similarity of mappings a,a on the free monoid r* generated by an alphabet E is to consider the equality language of a and a denoted by Eq(a,8) and consisting of all words x in E* such that a(x) = 6(x). To measure the similarity of a mapping with the identity mapping on the same domain one considers the fixed point language of a de~oted by Fp(a) and consisting of all words x in E such that a(x) = x (if a is a relation in r* x E* then we take Fp(a) = {x £ E* : x £ a(x)}). Thus equality languages and fixed point languages are very natural from the mathematical point of view. If we consider homomorphisms of free monoids then their equality languages represent sets of instances of the Post correspondence Problem; in this sense considering equality languages of homomorphisms is a classical topic in formal language theory (and computability theory). A revival of interest in those languages was stimulated recently by research concerning some very challenging decision problems in formal language theory; it became apparent that in several cases equality languages of homomorphisms playa vital role in (positive!) solutions of some basic equivalence problems of L systems (see e.g. (2) and [4]). This paper is an attempt towards a systematic investigation of equality languages and fixed point languages of homomorphisms and dgsm mappings (i.e. mappings defined by deterministic generalized sequential machines with accepting states). Homomorphisms and dgsm mappings are certainly among the most important mappings in formal language theory and so they form a good departure point for building up a systematic theory. Related work appears in [3] and [8]. In this extended abstract we summarize" some of the results we have obtained in this direction. It is organized as follows. Section 2 provides basic language-theoretic properties of equality languages and fixed point languages of homomorphisms. In Section 3 we present some results on the equality languages and fixed point languages of dgsm mappings but we concentrate on the subclass of dgsm mappings (that we introduce) called symmetric dgsm mappings. The theorem on fixed point languages of these mappings seems to be quite central in our theory. Then Section 4 provides an illustration of the usefulness of the classes of languages we have considered to provide various
11 citations
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01 May 1978
TL;DR: A systematic treatment of the relationships between parallel rewriting systems (top-down tree transducer, ETOL system) and two-way machines (2-way gsm, tree-walking automaton, checking stack automaton) is given.
Abstract: This extended abstract is a condensed version of the results presented in two technical reports ([16] and [13]). In [16] a systematic treatment of the relationships between parallel rewriting systems (top-down tree transducer, ETOL system) and two-way machines (2-way gsm, tree-walking automaton, checking stack automaton) is given. Particular attention is paid to the effect of restricting the copying power of these devices. In [13] the results of [16] are employed to show that the iteration of nondeterministic top-down tree transducers, of nondeterministic 2-way gsm's and of control on ETOL systems each gives rise to a proper hierarchy.
11 citations
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TL;DR: This work claims that by using the notion of X -uniformity and cc -interpretation this drawback of ordinary interpretations of EOL forms can be overcome.
Abstract: Ordinary interpretations of EOL forms permit the omission of productions and the replacement of different occurrences of the same symbol in a production by different symbols. This drastically weakens the relation between the structure of an interpretation and its underlying EOL form. We claim that by using the notion of X -uniformity and cc -interpretation this drawback can be overcome.
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17 Jul 1978TL;DR: In this article, simple EOL forms (forms with a single terminal and a single nonterminal) under uniform interpretations are considered and the analysis of the generative power of such forms is presented.
Abstract: In this paper we consider simple EOL forms (forms with a single terminal and single nonterminal) under uniform interpretations We present a contribution to the analysis of generative power of simple EOL forms by establishing easily decidable necessary and sufficient conditions for simple EOL forms to generate (under uniform interpretations) CF languages only
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TL;DR: The main theorem says that in a deterministic ETOL system each derivation of a long enough word of a special kind has a rather strong combinatorial structure.
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TL;DR: It is proved that the number of axioms used determines an infinite hierarchy of length set families both in DOL and PDOL case.
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TL;DR: It is demonstrated that there exist EOL languages that are not codings of languages that is generated by propagating OL systems with finite axiom sets, which solves Problem 10 from the L Systems Problem Book '75.
01 Jan 1978
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TL;DR: A language-generating mechanism, inspired on the two-level van Wijngaarden syntax for Algol 68, is considered, called a 2 MSG, for “two-level metacontrolled substitution grammar.”
Abstract: A language-generating mechanism, inspired on the two-level van Wijngaarden syntax for Algol 68, is considered. Its language generating properties are studied and compared to those of well-known classical systems and grammars. The new mechanism is called a 2 MSG, for "two-level metacontrolled substitution grammar."
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TL;DR: A new type of rewriting system is introduced in which every string in a derivation is preceded by one (clocking) symbol which must be rewritten at every moment of time, (hence in a parallel mode).