Applications of scheduling theory to formal language theory

Applications of subordination theory to starlike functions

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

1 Formal Language Theory

This chapter provides a gentle introduction to formal language theory, aimed at readers with little background in formal systems. The motivation is natural language processing (NLP), and the presentation is geared towards NLP applications, with linguistically motivated examples, but without compromising mathematical rigor. The text covers elementary formal language theory, including: regular la...

Digraph Complexity Measures and Applications in Formal Language Theory

We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this connection, and obtain several new algorithmic insights regarding both cycle rank and star height. Among other results, we show that computing the cycle rank is NP-...

The Formal Language Theory Column

Formal languages can be described by several means. A basic question is how succinctly can a descriptional system represent a formal language in comparison with other descriptional systems? What is the maximal size trade-off when changing from one system to another, and can it be achieved? Here, we select some recent trends in the descriptional complexity of formal languages and discuss the pro...

Optical Elastography: From Theory to Clinical Applications