Related papers: Around Context-Free Grammars -- a Normal Form, a R…
A recent study on structural properties of regular and context-free languages has greatly promoted our basic understandings of the complex behaviors of those languages. We continue the study to examine how regular languages behave when they…
In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of $\omega$-context-free…
Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic…
Let G be a context-free grammar with a total alphabet V, and let F be a final language over an alphabet W such that W is a subset of V. A final sentential form is any sentential form of G that, after omitting symbols from V - W, it belongs…
The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids…
We propose a holographic dictionary which comes from reducing the bulk theories in an asymptotically flat spacetime to its null infinity. A general boundary theory is characterized by a fundamental field, an infinite tower of descendant…
In derivational morphology, what mechanisms govern the variation in form-meaning relations between words? The answers to this type of questions are typically based on intuition and on observations drawn from limited data, even when a wide…
In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of that sentence. To do so, we exploited the perfect structural match of grammar and…
We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most $\ell.$ The goal is to learn a cover context-free…
In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language…
Quantum computing is a relatively new field of computing, which utilises the fundamental concepts of quantum mechanics to process data. The seminal paper of Moore et al. [2000] introduced quantum grammars wherein a set of amplitudes was…
In this paper we introduce a class of noncommutative (finitely generated) monomial algebras whose Hilbert series are algebraic functions. We use the concept of graded homology and the theory of unambiguous context-free grammars for this…
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 continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
Within the tensor product $K \mathop{\otimes_{\cal R}} C_2'$ of any ${}^*$-continuous Kleene algebra $K$ with the polycyclic ${}^*$-continuous Kleene algebra $C_2'$ over two bracket pairs there is a copy of the fixed-point closure of $K$:…
Originally motivated by connections to integrable systems, two natural subalgebras of the rational Cherednik algebra have been considered in the literature. The first is the subalgebra of all degree zero elements and the second is the Dunkl…
This article contributes in that it clarifies and indeed completes an approach (initiated by Dunn and this author several years ago and again pursued by the present author over the last three years or so) to the relational semantics of…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
This paper proves a long standing conjecture in formal language theory. It shows that all regular languages are Church-Rosser congruential. The class of Church-Rosser congruential languages was introduced by McNaughton, Narendran, and Otto…
In this paper, we propose a globally normalized model for context-free grammar (CFG)-based semantic parsing. Instead of predicting a probability, our model predicts a real-valued score at each step and does not suffer from the label bias…