Formal Languages and Automata Theory
We show that the number of all maximal $\alpha$-gapped repeats and palindromes of a word of length $n$ is at most $3(\pi^2/6 + 5/2) \alpha n$ and $7 (\pi^2 / 6 + 1/2) \alpha n - 5 n - 1$, respectively.
A sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last $n$ symbols. If the algorithm is randomized, then at each time instant it produces an incorrect…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
We consider the problem of approximate reduction of non-deterministic automata that appear in hardware-accelerated network intrusion detection systems (NIDSes). We define an error distance of a reduced automaton from the original one as the…
A vector addition system (VAS) with an initial and a final marking and transition labels induces a language. In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision…
This paper describes a construction of supermartingales realized as automatic functions. A capital of supermartingales is represented using automatic capital groups~(ACG). Properties of these automatic supermartingales are then studied.…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
We investigate the polynomial closure operation (C -> Pol(C)) defined on classes of regular languages. We present an interesting and useful connection relating the separation problem for the class C and the membership problem for it…
We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…
A deterministic finite automaton (DFA) separates two strings $w$ and $x$ if it accepts $w$ and rejects $x$. The minimum number of states required for a DFA to separate $w$ and $x$ is denoted by $sep(w,x)$. The present paper shows that the…
Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on…
Most modern libraries for regular expression matching allow back-references (i.e., repetition operators) that substantially increase expressive power, but also lead to intractability. In order to find a better balance between expressiveness…
We present a method for predicting the large-scale evolution of a tag system from its production rules. A tag system's evolution is first divided into stages called `epochs' in which the tag system evolves monotonously. The distribution of…
We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists a word contained in their…
We exhaustively explore the reprogrammability capabilities and the intrinsic universality of the Cartesian product $P \times C$ of the space $P$ of all possible computer programs of increasing size and the space $C$ of all possible…
We introduce a new type of nonuniform two--way automaton that can use a different transition function for each tape square. We also enhance this model by allowing to shuffle the given input at the beginning of the computation. Then we…
In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be…
A mimic computing oriented automaton can directly portray the behaviors of a mimic computing system. In this paper, we investigate the following theoretical problems on this type of automata: operational semantics and computational ability.…
We revisit the long-neglected problem of sequential circuit constructions from regular expressions. The class of languages that are recognized by sequential circuits is equivalent to the class of regular languages. This fact is shown in [5]…
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.