Related papers: On subshifts with low maximal pattern complexity
Nowadays, frequent pattern mining (FPM) on large graphs receives increasing attention, since it is crucial to a variety of applications, e.g., social analysis. Informally, the FPM problem is defined as finding all the patterns in a large…
Sequence pattern avoidance is a central topic in combinatorics. A sequence $s$ contains a sequence $u$ if some subsequence of $s$ can be changed into $u$ by a one-to-one renaming of its letters. If $s$ does not contain $u$, then $s$ avoids…
We develop a structural approach to simultaneous embeddability in temporal sequences of graphs, inspired by graph minor theory. Our main result is a classification theorem for 2-connected temporal sequences: we identify five obstruction…
An infinite word x is said to be quasiperiodic if there exists a finite word q such that x is covered by occurrences of q (such a q is called a quasiperiod of x). Using the notion of derivation, we show that this definition is not…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of constructor terms in the left-hand side; the computational intuition is that rules cannot build new data…
As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several…
In this work, we treat subshifts, defined in terms of an alphabet $A$ and (usually infinite) forbidden list $F$, where the number of $n$-letter words in $F$ has "slow growth rate" in $n$. We show that such subshifts are well-behaved in…
A sample of n generic points in the xy-plane defines a permutation that relates their ranks along the two axes. Every subset of k points similarly defines a pattern, which occurs in that permutation. The number of occurrences of small…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
The notion of almost periodicity nontrivially generalizes the notion of periodicity. Strongly almost periodic sequences (=uniformly recurrent infinite words) first appeared in the field of symbolic dynamics, but then turned out to be…
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees…
We introduce the notion of minimal inversion sequences for a pattern $\rho$, which form the smallest set of inversion sequences whose avoidance is equivalent to the avoidance of $\rho$ for inversion sequences. We give a characterization of…
We introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences. This tool allows us to provide a structural description of permutations which avoid a specified pattern, a result that…
We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal \beta-dependent…
A fundamental question in interpretability research is to what extent neural networks, particularly language models, implement reusable functions through subnetworks that can be composed to perform more complex tasks. Recent advances in…
Borel and Reutenauer (2006) showed, \emph{inter alia}, that a word $w$ of length $n>1$ is conjugate to a Christoffel word if and only if for $k=0,1, \dots , n-1$, $w$ has $k+1$ distinct circular factors of length $k$. Sturmian words are the…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
Complementary symmetric Rote sequences are binary sequences which have factor complexity $\mathcal{C}(n) = 2n$ for all integers $n \geq 1$ and whose languages are closed under the exchange of letters. These sequences are intimately linked…
We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We show that the language of v is eventually dendric and we…
A sequence $S=s_{1}s_{2}..._{n}$ is \emph{nonrepetitive} if no two adjacent blocks of $S$ are identical. In 1906 Thue proved that there exist arbitrarily long nonrepetitive sequences over 3-element set of symbols. We study a generalization…