Related papers: The Chomsky-Sch\"utzenberger Theorem for Quantitat…
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…
Motivated by the question of which completely regular semigroups have context-free word problem, we show that for certain classes of languages $\mathfrak{C}$(including context-free), every completely regular semigroup that is a union of…
We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include…
Semantic degeneracy represents a fundamental property of natural language that extends beyond simple polysemy to encompass the combinatorial explosion of potential interpretations that emerges as semantic expressions increase in complexity.…
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with…
The central role of the lexicon in Meaning-Text Theory (MTT) and other dependency-based linguistic theories cannot be replicated in linguistic theories based on context-free grammars (CFGs). We describe Tree Adjoining Grammar (TAG) as a…
The human-like reasoning capabilities exhibited by Large Language Models (LLMs) challenge the traditional neural network theory's understanding of the flexibility of fixed-parameter systems. This paper proposes the "Cognitive Activation"…
In the realm of quantum computing, circuit description languages represent a valid alternative to traditional QRAM-style languages. They indeed allow for finer control over the output circuit, without sacrificing flexibility nor modularity.…
We present a method for approximating context-free languages with one-counter automata. This approximation allows the reconstruction of parse trees of the original grammar. We identify a decidable superset of regular languages whose…
Finite-state automata are a very effective tool in natural language processing. However, in a variety of applications and especially in speech precessing, it is necessary to consider more general machines in which arcs are assigned weights…
Pumping lemmata are the main tool to prove that a certain language does not belong to a class of languages like the recognizable languages or the context-free languages. Essentially two pumping lemmata exist for the recognizable weighted…
We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and…
Ambiguities in natural language give rise to probability distributions over interpretations. The distributions are often over multiple ambiguous words at a time; a multiplicity which makes them a suitable topic for sheaf-theoretic models of…
We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory…
Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…
We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting which generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this…
The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton's method to…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
Parikh's theorem states that the Parikh image of a context-free language is semilinear or, equivalently, that every context-free language has the same Parikh image as some regular language. We present a very simple construction that, given…
The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are…