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

Well Structured Transition Systems with History

We propose a formal model of concurrent systems in which the history of a computation is explicitly represented as a collection of events that provide a view of a sequence of configurations. In our model events generated by transitions become part of the system configurations leading to operational semantics with historical data. This model allows us to formalize what is usually done in symbolic verification algorithms. Indeed, search algorithms often use meta-information, e.g., names of fired transitions, selected processes, etc., to reconstruct (error) traces from symbolic state exploration. The other interesting point of the proposed model is related to a possible new application of the theory of well-structured transition systems (wsts). In our setting wsts theory can be applied to formally extend the class of properties that can be verified using coverability to take into consideration (ordered and unordered) historical data. This can be done by using different types of representation of collections of events and by combining them with wsts by using closure properties of well-quasi orderings.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Subword balance, position indices and power sums

AbstractIn this paper, we investigate various ways of characterizing words, mainly over a binary alphabet, using information about the positions of occurrences of letters in words. We introduce two new measures associated with words, the position index and sum of position indices. We establish some characterizations, connections with Parikh matrices, and connections with power sums. One particular emphasis concerns the effect of morphisms and iterated morphisms on words