Conceptually, jumping scattered context grammars coincide with their standard counterparts, but they work differently. Indeed, a jumping version can apply a rule of the form ( A 1 , A 2 , . . . , A n ) → ( x 1 , x 2 , . . . , x n ) so it simultaneously erases A 1 , A 2 , . . . , A n in the current sentential form while inserting x 1 , x 2 , . . . , x n possibly at different positions than the erased nonterminals. In fact, this paper introduces and studies scattered context grammars working under nine different jumping derivation modes, all of which give rise to the computational completeness. Indeed, the paper characterize the family of recursively enumerable languages by scattered context grammars working under any of these jumping modes. In its conclusion, the paper sketches application perspectives and formulates several open problems.

This paper gives simple tree-based conditions under which regular-controlled context-free grammars generate context-free languages of finite index, so they cannot even generate all context-free languages. It defines the notion of path-changing derivation step which corresponds to performing two consecutive rewritings of nonterminal symbols present in the different branches of the derivation tree. It proves that if there exists a certain constant that limits the number of path-changing derivation steps, then, the regular-controlled grammar generates a context-free language of finite index. At the end, we generalize achieved result and provide some open problems for future study.

In essence, simple matrix grammars can be seen as sequences of context-free grammars, referred to as their components, which work in parallel. The present paper demonstrates that two-component simple matrix grammars are as powerful as ordinary matrix grammars. Then, it places three leftmost derivation restrictions upon these grammars and demonstrates that under two of these restrictions, simple matrix grammars are computational complete — that is, they are equivalent with Turing machines. From a historical perspective, concerning simple matrix grammars, the paper also makes several remarks that correct false statements published about them in the past.

International Journal of Foundations of Computer ScienceVol. 27, No. 05, pp. 651-652 (2016) Free AccessCorrigendum: "Simple Matrix Grammars and Their Leftmost Variants [3]"is erratum ofSimple Matrix Grammars and Their Leftmost VariantsAlexander Meduna and Ondřej SoukupAlexander MedunaBrno University of Technology, Faculty of Information Technology Centre of Excellence, Božetěchova 1/2, 612 66 Brno, Czech Republic and Ondřej SoukupBrno University of Technology, Faculty of Information Technology Centre of Excellence, Božetěchova 1/2, 612 66 Brno, Czech Republichttps://doi.org/10.1142/S0129054116940018Cited by:0 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail [International Journal of Foundations of Computer Science, Vol. 27, No. 3, pp. 359–373 (2016), DOI: 10.1142/S0129054116400141] Remember to check out the Most Cited Articles! Check out these Handbooks in Computer Science FiguresReferencesRelatedDetailsRelated articlesSimple Matrix Grammars and Their Leftmost Variants7 Jun 2016International Journal of Foundations of Computer Science Recommended Vol. 27, No. 05 Metrics History PDF download

In the presented paper we discuss pure versions of pushdown automata that have no extra non-input symbols. More specifically, we study pure multi-pushdown automata, which have several pushdown lists. We restrict these automata by the total orders defined over their pushdowns or alphabets and determine the accepting power of the automata restricted in this way. Moreover, we explain the significance of the achieved results and relate them to some other results in the automata theory.