Related papers: On automatic infinite permutations
The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. For any given…
Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
We find a formula for the number of permutations of $[n]$ that have exactly $s$ runs up and down. The formula is at once terminating, asymptotic, and exact.
Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs…
A concept of randomness for infinite time register machines (ITRMs), resembling Martin-L\"of-randomness, is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies…
We propose a new extension of higher-order pushdown automata, which allows to use an infinite alphabet. The new automata recognize languages of data words (instead of normal words), which beside each its letter from a finite alphabet have a…
A permutation p is realized by the shift on N symbols if there is an infinite word on an N-letter alphabet whose successive left shifts by one position are lexicographically in the same relative order as p. The set of realized permutations…
We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
An involution is a permutation that is its own inverse. Given a permutation $\sigma$ of $[n],$ let $\mathbf{N}_{n}(\sigma)$ denote the number of ways to write $\sigma$ as a product of two involutions of $[n].$ If we endow the symmetric…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…
In data languages the positions of strings and trees carry a label from a finite alphabet and a data value from an infinite alphabet. Extensions of automata and logics over finite alphabets have been defined to recognize data languages,…