Journal article

Publication year: 2021

Pages: 53-76

Journal: Fundamenta Informaticae

Volume number: 180

Issue number: 1-2

ISSN: 0169-2968

eISSN: 1875-8681

DOI Link: https://doi.org/10.3233/FI-2021-2034

Publisher: SAGE Publications

Abstract: 
Insertion systems or insertion grammars are a generative formalism in which words can only be generated by starting with some axioms and by iteratively inserting strings subject to certain contexts of a fixed maximal length. It is known that languages generated by such systems are always context sensitive and that the corresponding language classes are incomparable with the regular languages. On the other hand, it is possible to generate non-semilinear languages with systems having contexts of length two. Here, we study decidability questions for insertion systems. On the one hand, it can be seen that emptiness and universality are decidable. Moreover, the fixed membership problem is solvable in deterministic polynomial time. On the other hand, the usually studied decidability questions such as, for example, finiteness, inclusion, equivalence, regularity, inclusion in a regular language, and inclusion of a regular language turn out to be undecidable. Interestingly, the latter undecidability results can be carried over to other models which are basically able to handle the mechanism of inserting strings depending on contexts. In particular, new undecidability results are obtained for pure grammars, restarting automata, clearing restarting automata, and forgetting automata.

Harvard Citation style: Malcher, A. (2021) Decidability Questions for Insertion Systems and Related Models, Fundamenta Informaticae, 180(1-2), pp. 53-76. https://doi.org/10.3233/FI-2021-2034

APA Citation style: Malcher, A. (2021). Decidability Questions for Insertion Systems and Related Models. Fundamenta Informaticae. 180(1-2), 53-76. https://doi.org/10.3233/FI-2021-2034