Formal Languages and Automata Theory
The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from…
Let $\alpha,\beta$ be real numbers and $b\geq2$ be an integer. Allouche and Shallit showed that the sequence $\{\lfloor\alpha n+\beta\rfloor\}_{n\geq0}$ is $b$-regular if and only if $\alpha$ is rational. In this paper, using a…
It is well known that if $G$ admits a f.g. subgroup $H$ with a weaklyaperiodic SFT (resp. an undecidable domino problem), then $G$itself has a weakly aperiodic SFT (resp. an undecidable domino problem).We prove that we can replace the…
We introduce a weight assignment logic for reasoning about quantitative languages of infinite words. This logic is an extension of the classical MSO logic and permits to describe quantitative properties of systems with multiple weight…
This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multi-valued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with…
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable.…
We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have…
An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is…
Abelian networks are systems of communicating automata satisfying a local commutativity condition. We show that a finite irreducible abelian network halts on all inputs if and only if all eigenvalues of its production matrix lie in the open…
We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak $\log\log n$ space, (ii) $\log\log n$ is a…
In this paper we prove several results on normal forms for linear displacement context-free grammars. The results themselves are rather simple and use well-known techniques, but they are extensively used in more complex constructions.…
We present two restricted versions of one-tape Turing machines. Both characterize the class of context-free languages. In the first version, proposed by Hibbard in 1967 and called limited automata, each tape cell can be rewritten only in…
We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems…
In this paper, we have introduced the deterministic variant of parallel communicating Watson-Crick automata systems. We show that similar to the non-deterministic version, the deterministic version can also recognise some non-regular…
In the book we present main concepts of probabilistic automata theory.
We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed…
There are languages A such that there is a Pushdown Automata (PDA) that recognizes A which is much smaller than any Deterministic Pushdown Automata (DPDA) that recognizes A. There are languages A such that there is a Linear Bounded Automata…
When a property needs to be checked against an unknown or very complex system, classical exploration techniques like model-checking are not applicable anymore. Sometimes a~monitor can be used, that checks a given property on the underlying…