arXiv subjects

Abhisek Midya

Publications and source records attributed to Abhisek Midya.

3 recordsLinked to original sources

arXiv2026

Measure Many Quantum Finite Automata on Infinite Words

We define a quantum computational model over infinite words, called Measure-Many Quantum B\"uchi Automata (MMQBA), which extends Measure-many Quantum Finite automata (MMQFA) to the infinite word setting with B\"uchi 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.

cs.FL↗

arXiv2023

Comparing Spoken Languages using Paninian System of Sounds and Finite State Machines

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.

cs.CL↗

arXiv2021

A Myhill-Nerode Theorem for Register Automata and Symbolic Trace Languages

We propose a new symbolic trace semantics for register automata (extended finite state machines) which records both the sequence of input symbols that occur during a run as well as the constraints on input parameters that are imposed by this run. Our main result is a generalization of the classical Myhill-Nerode theorem to this symbolic setting. Our generalization requires the use of three relations to capture the additional structure of register automata. Location equivalence $\equiv_l$ captures that symbolic traces end in the same location, transition equivalence $\equiv_t$ captures that they share the same final transition, and a partial equivalence relation $\equiv_r$ captures that symbolic values $v$ and $v'$ are stored in the same register after symbolic traces $w$ and $w'$, respectively. A symbolic language is defined to be regular if relations $\equiv_l$, $\equiv_t$ and $\equiv_r$ exist that satisfy certain conditions, in particular, they all have finite index. We show that the symbolic language associated to a register automaton is regular, and we construct, for each regular symbolic language, a register automaton that accepts this language. Our result provides a foundation for grey-box learning algorithms in settings where the constraints on data parameters can be extracted from code using e.g. tools for symbolic/concolic execution or tainting. We believe that moving to a grey-box setting is essential to overcome the scalability problems of state-of-the-art black-box learning algorithms.

cs.FL↗