相关论文: A profinite approach to complete bifix decodings o…
We give necessary and sufficient conditions for the group of a rational maximal bifix code $Z$ to be isomorphic with the $F$-group of $Z\cap F$, when $F$ is recurrent and $Z\cap F$ is rational. The case where $F$ is uniformly recurrent,…
We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the…
We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurrent tree sets, where the tree sets are defined by a condition…
Despite strong performance on a variety of tasks, neural sequence models trained with maximum likelihood have been shown to exhibit issues such as length bias and degenerate repetition. We study the related issue of receiving…
Inspired by a series of papers initiated in 2015 by Berth\'e et al., we introduce a new condition called suffix-connectedness. We show that the groups generated by the return sets of a uniformly recurrent suffix-connected language lie in a…
The starting point of algebraic language theory is that regular languages of finite words are exactly those recognized by finite monoids. This finiteness condition gives rise to a topological space whose points, called profinite words,…
We study the problem of deciding whether a given language is directed. A language $L$ is \emph{directed} if every pair of words in $L$ have a common (scattered) superword in $L$. Deciding directedness is a fundamental problem in connection…
A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise…
Often, when analyzing the behaviour of systems modelled as context-free languages, we wish to know if two languages overlap. To this end, we present an effective semi-decision procedure for regular separability of context-free languages,…
We study distributional learning of context-free languages under a fixed recognizable congruence $\sim_h$ given as the kernel of an explicit finite monoid homomorphism $h:\Sigma^*\to M$. For this fixed-$h$ setting, we develop a finite typed…
Many recent studies have shown that the perception of speech can be decoded from brain signals and subsequently reconstructed as continuous language. However, there is a lack of neurological basis for how the semantic information embedded…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
Consider a polynomial $F$ in $m$ variables and a finite point ensemble $S=S_1 \times ... \times S_m$. When given the leading monomial of $F$ with respect to a lexicographic ordering we derive improved information on the possible number of…
In this paper, we provide a new characterization of uniformly recurrent words with finite defect based on a relation between the palindromic and factor complexity. Furthermore, we introduce a class of morphisms P_ret closed under…
A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix-, factor-, and subword-free languages are defined similarly, where "subword" means "subsequence". A language is bifix-free if it is…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that…
We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a…
In this paper, we use reinforcement learning to find effective decoding strategies for binary linear codes. We start by reviewing several iterative decoding algorithms that involve a decision-making process at each step, including…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…