Research

Post-Gradaute Work
  • DBCOMSOC: Databases meet Computationa Social Choice Theory
    Advisor: Professor P. Kolaitis
    I am researching on Computational Social Choice Theory (COMSOC) and databases. For more information, please see here. I will update this once there is more news.
  • Learnability of First-Order Definable Sets With an Application to Artificial Neural Networks
    Advisor: Professor A. Dawar
    I was working on definability and learning in sparse structures. It is at the very core of the confluence of artificial intelligence and finite model theory.

    Abstract: Learning over sparse background structures, of at most poly-logarithmic degree, has been recently shown to be in poly-logarithmic time for First-Order Logic (FOL) definable concepts. The primary aim of this proposal is to investigate if the claim holds for counting extensions of FOL and Modal Logic. I will also explore learnability of FOL definable concepts over the field of the Real Numbers as a background structure. Extensions of FOL with some basic counting and aggregation are expressible in infinitary counting logics. These logics are a central component of relational database management systems like SQL. This research, thus arches between database management and machine learning.

    Research Proposal
Undergraduate Work
  • Philosophy

    Advisors: Dr. A. Antonelli, Dr. E. Landry

    In their classical papers, Alan Turing (1936) and Alonzo Church (1936) independently proved the unsolvability of the Entscheidungsproblem. Each forwarded their own thesis, from which, in 1967 Kleene coined the Church-Turing Thesis (CTT). It is one of the most fundamental hypotheses as far as computation is concerned. More often than not, the CTT is misinterpreted as making a statement concerning the powers of the human mind, or a modern computer. These “variants” are not, as many claim, equivalent to the original thesis. In fact, most of them make claims that are stronger than the actual one and make overt assumptions rendering these “variants” uninteresting. We reject such claims and argue that neither Turing nor Church intended to characterize their hypothesis as such. Both of the theses are restricted to physical machines and are a consequence of the postulates formulated by Gandy in 1980. Further, we argue that it is of much philosophical interest to consider the standing of the CTT as a physical statement than one claiming the limitations of the human mind.

    Here is the link to a paper I wrote whilst working on this project.

  • Computer Science

    Advisors: Dr. D. Doty
    Title: Confluence of Computation Complexities: CRNs and Circuits
    I am studying the theory of Chemical Reaction Networks under Dr. Doty since January 2016. Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution.
    CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with future advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood.
    CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semi-linear predicates (a multi-dimensional generalization of “eventually periodic” sets).