Repetitive subwords

The central notionof thisthesisis repetitionsin words. We studyproblemsrelated to contiguous repetitions. More specifically we will consider repeating scattered subwords of non-primitive words, i.e. words which are complete repetitions of other words. We will present inequalities concerning these occurrences as well as giving apartial solutionto an openproblemposedby Salomaaet al. We will characterize languages, whichare closed under the operation ofduplication, thatis repeating any factor of a word. We alsogive newbounds onthe number of occurrencesof certain types of repetitions of words. We give a solution to an open problem posed by Calbrix and Nivat concerning regular languages consisting of non-primitive words. We alsopresentsomeresultsregarding theduplication closureoflanguages,among which a new proof to a problem of Bovet and Varricchio

Revisiting Sevilla Carpets: A New Tool for the P-Lingua Era

Sevilla Carpets have already been used to compare di erent solutions of the Subset Sum problem: either designed in the framework of P systems with active membranes (both in the case of membrane division and membrane creation), and also another one in the framework of tissue-like P systems with cell division. Recently, the degree of parallelism and other descriptive complexity details have been found to be relevant when designing parallel simulators running on GPUs. We present here a new way to use the information provided by Sevilla carpets, and a script that allows to generate them automatically from P-Lingua les.Ministerio de Economía y Competitividad TIN2012-3743

On derivation languages of a class of splicing systems

Derivation languages are language theoretical tools that describe halting derivation processes of a generating device. We consider two types of derivation languages, namely Szilard and control languages for splicing systems where iterated splicing is done in non-uniform way defined by Mitrana, Petre and Rogojin in 2010. The families of Szilard (rules and labels are mapped in a one to one manner) and control (more than one rule can share the same label) languages generated by splicing systems of this type are then compared with the family of languages in the Chomsky hierarchy. We show that context-free languages can be generated as Szilard and control languages and any non-empty context-free language is a morphic image of the Szilard language of this type of system with finite set of rules and axioms. Moreover, we show that these systems with finite set of axioms and regular set of rules are capable of generating any recursively enumerable language as a control language

On Erasing Rules in Regulated Grammars

V této práci je diskutován vliv vymazávacích pravidel na generativní sílu řízených gramatik, což je velký otevřený problém teorie řízeného přepisování. Tato práce studuje možnost odstranění vymazávacích pravidel z těchto gramatik tak, že shromažďuje aktuální výsledky na toto téma a přináší novou podmínku, nazvanou k-limitované vymazávání, která zaručuje, že jsme bez vlivu na generovaný jazyk schopni odstranit všechna vymazávací pravidla z libovolné bezkontextové gramatiky řízené regulárním jazykem splňující tuto podmínku. Tento výsledek je částečným řešením výše zmíněného problému. Mimoto je prezentován nový algoritmus k odstranění vymazávacích pravidel z bezkontextových gramatik, který nepotřebuje předurčovat tzv. epsilon-neterminály (na rozdíl od standardního algoritmu používaného v učebnicích). V závěru je zhodnocen přínos těchto výsledků pro syntaktickou analýzu.This work discusses the effect of erasing rules to the generative power of regulated grammars, which is a big open problem in the theory of regulated rewriting. It studies the possibility of removal of erasing rules from regulated grammars by aggregation of current, up-to-date results concerning this elimination and by presentation of a new condition, called k-limited erasing, under which all erasing rules can be always removed from regularly controlled context-free grammars without affecting their generative power. This result partially solves the abovementioned problem. Moreover, a new algorithm for elimination of erasing rules from context-free grammars is presented. This algorithm does not require any predetermination of so called epsilon-nonterminals (in contrast to the standard algorithm used in textbooks). In the conclusion, a significance of these results concerning syntactical analysis is discussed.