A quasiperiod of a finite or infinite string/word is a word whose occurrences cover every part of the string. A word or an infinite string is referred to as quasiperiodic if it has a quasiperiod. It is obvious that a quasiperiodic infinite string cannot have every word as a subword (factor). Therefore, the question arises how large the set of subwords of a quasiperiodic infinite string can be \cite{DBLP:journals/eatcs/Marcus04}. Here we show that on the one hand the maximal subword complexity of quasiperiodic infinite strings and on the other hand the size of the sets of maximally complex quasiperiodic infinite strings both are intimately related to the smallest Pisot number $t_{P}$ (also known as \emph{plastic constant}). We provide an exact estimate on the maximal subword complexity for quasiperiodic infinite words.

We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective characterizations of ftw-NFAs and a tight worst-case state size bound for determinizing an ftw-NFA $A$ as a function of the tree width and the number of states of $A$. We also introduce a lower bound technique for ftw-NFAs.

We investigate context-free languages with respect to the measures Prod and Symb of descriptional complexity, which give the minimal number of productions and the minimal total number of symbols in productions, respectively, necessary to generate the language by context-free grammars. In particular, we consider the behaviour of these measures with respect to operations. For a measure $K\in \{\Prod,\Symb\}$, given natural numbers $c_1,c_2,\dots ,c_n$ and an $n$-ary operation $\tau$ on languages, we discuss the set $g_{\tau,K}(c_1,c_2,\dots ,c_n)$ which is the range of $K(\tau(L_1,L_2,\dots , L_n))$ where, for $1\leq i\leq n$, $L_i$ is a context-free language with $K(L_i)=c_i$. The operations under discussion are union and Kleene closure.

We describe an algorithm that identifies all the repeating substrings (tandem, overlapping, and split) in a given string x = X[1..n]. Given the suffix arrays of x and of the reversed string x, the algorithm requires Θ(n) time for its execution and represents its output in Θ(n) space, either as a reduced suffix array (called an NE array) or as a reduced suffix tree (called an NE tree). The output substrings u are nonextendible (NE); that is, any extension of some occurrence of u in x, either to the left or to the right, yields a string (λu or uλ) that is unequal to the same extension of some other occurrence of u. Thus the number of substrings output is the minimum required to identify all the repeating substrings in x. The output can be used in a straightforward way to identify only repeating substrings that satisfy some proximity or minimum length condition.

In this paper we propose a notion of weak bisimulation for a class of weighted automata with unobservable transitions where weights are taken from an idempotent semiring. In particular the (max/+),...

In 1912, the Norwegian mathematician Axel Thue was the first to describe an overlapfree binary infinite word. This word was generated by a morphism which is called, since the works of Morse, the Th...