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Generalized Forbidding Matrix Grammars and Their Membrane Computing Perspective

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Membrane Computing (CMC 2020)


Matrix grammars are one of the first approaches ever proposed in regulated rewriting, prescribing that rules have to be applied in a certain order. In traditional regulated rewriting, the most interesting case shows up when all rules are context-free. Typical descriptional complexity measures incorporate the number of nonterminals or the length, i.e., the number of rules per matrix. When viewing matrices as program fragments, it becomes natural to consider additional applicability conditions for such matrices. Here, we focus on forbidding sets, i.e., a matrix is applicable to a sentential form w only if none of the words in its forbidding set occurs as a subword in w. This gives rise to further natural descriptional complexity measures: How long could words in forbidding sets be? How many words could be in any forbidding set? How many matrices contain non-empty forbidding contexts? As context-free grammars with forbidding sets are known as generalized forbidding grammars, we call this variant of matrix grammars also generalized forbidding. In this paper, we attempt to answer the above four questions while studying the computational completeness of generalized forbidding matrix grammars. We also link our research to processing strings with membrane computing and discuss appropriate variations of \(\textsf {P}\) systems.

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  1. 1.

    Notice that computational completeness results have quite some history in the literature of \(\textsf {GF}\) grammars; we only refer to [7, 17,18,19,20] in some historical order. In the long version of [7] which is appearing in Discrete Applied Mathematics [8], we obtained some further improved results of the conference version [7].

  2. 2.

    For the subtle distinction between possibly allowing or disallowing the empty word for v or u, respectively, we refer to the discussions in [7].


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Without the numerous contributions of Gheorghe Păun to the theory of Formal Languages, the present paper could hardly be written, as it is based in particular on [12, 22, 23]. Also, the second author profusely thanks Gheorghe Păun for being his source of inspiration since from his Ph.D. days. Happy birthday, Gheorghe!

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Correspondence to Henning Fernau .

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Fernau, H., Kuppusamy, L., Raman, I. (2021). Generalized Forbidding Matrix Grammars and Their Membrane Computing Perspective. In: Freund, R., Ishdorj, TO., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. CMC 2020. Lecture Notes in Computer Science(), vol 12687. Springer, Cham.

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