Abhisek Midya

Shreekanth M Prabhu, Abhisek Midya

The study of spoken languages comprises phonology, morphology, and grammar. The languages can be classified as root languages, inflectional languages, and stem languages. In addition, languages continually change over time and space by picking isoglosses, as speakers move from region to/through region. All these factors lead to the formation of vocabulary, which has commonality/similarity across languages as well as distinct and subtle differences among them. Comparison of vocabularies across languages and detailed analysis has led to the hypothesis of language families. In particular, in the view of Western linguists, Vedic Sanskrit is a daughter language, part of the Indo-Iranian branch of the Indo-European Language family, and Dravidian Languages belong to an entirely different family. These and such conclusions are reexamined in this paper. Based on our study and analysis, we propose an Ecosystem Model for Linguistic Development with Sanskrit at the core, in place of the widely accepted family tree model. To that end, we leverage the Paninian system of sounds to construct a phonetic map. Then we represent words across languages as state transitions on the phonetic map and construct corresponding Morphological Finite Automata (MFA) that accept groups of words. Regardless of whether the contribution of this paper is significant or minor, it is an important step in challenging policy-driven research that has plagued this field.

Abhisek Midya, A Baskar

We define a quantum computational model over infinite words, called Measure-Many Quantum Büchi Automata (MMQBA), which extends Measure-many Quantum Finite automata (MMQFA) to the infinite word setting with Büchi acceptance condition. In MMQBA, the quantum state evolves through unitary transformations followed by repeated projective measurements. An infinite word is accearaq2ppted with respect to a cutpoint p is in (0, 1] if (i) the run visits accepting states infinitely often, (ii) the limiting cumulative acceptance probability is at least p, and (iii) the limiting cumulative rejection lprobability is strictly less than p. We formalize the semantics of MMQBA, establish a language-theoretic characterization showing that MMQBA languages are precisely of the form lim(L(M, p)) for MMQFA M , and develop a decomposition of the non-halting subspace. We prove that MMQBA is closed under union but not under intersection or complementation. On the algorithmic side, we show that the emptiness problem is semi-decidable, while universality, inclusion, equivalence, and membership remain undecidable.