Related papers: Monoid automata for displacement context-free lang…
Valence automata are a generalization of various models of automata with storage. Here, each edge carries, in addition to an input word, an element of a monoid. A computation is considered valid if multiplying the monoid elements on the…
Context-free languages are widely used to describe the syntax of programming languages and natural languages. Usually, we describe a context-free language mathematically with the help of context-free grammar (for generation) or pushdown…
We present an underapproximation for context-free languages by filtering out runs of the underlying pushdown automaton depending on how the stack height evolves over time. In particular, we assign to each run a number quantifying the…
The aim of the paper is to build a connection between two approaches towards categorical language theory: the coalgebraic and algebraic language theory for monads. For a pair of monads modelling the branching and the linear type we defined…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…
Indexed languages are a generalization of context-free languages and form a proper subset of context-sensitive languages. We propose to generalize to indexed languages several well known characterizations of context-free languages: namely,…
The work investigates the problem of whether a context-free language is a subset of a group language. A.~V. Anisimov has shown that the problem of determining the unambiguity of finite automata is a special case of this problem. Then the…
A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction:…
The famous theorem by Chomsky and Sch\"utzenberger (CST) says that every context-free language $L$ over an alphabet $\Sigma$ is representable as $h(D \cap R)$, where $D$ is a Dyck language over a set $\Omega$ of brackets, $R$ is a local…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids.…
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…
Stochastic automata over monoids as input sets are studied. The well-definedness of these automata requires an extension postulate that replaces the inherent universal property of free monoids. As a generalization of Turakainen's result, it…
We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent one-way and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for…
We present a family of neural-network--inspired models for computing continuous word representations, specifically designed to exploit both monolingual and multilingual text. This framework allows us to perform unsupervised training of…
We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove…
We prove that the class of finitely presented inverse monoids whose Sch\"utzenberger graphs are quasi-isometric to trees has a uniformly solvable word problem, furthermore, the languages of their Sch\"utzenberger automata are context-free.…
We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain "operad of spliced words". This motivates a more general notion of CFG over any category $C$, defined as a finite…
In this study, we propose a method that distils representations of word meaning in context from a pre-trained masked language model in both monolingual and crosslingual settings. Word representations are the basis for context-aware lexical…