Unification of Boolean Differential Rings Is Unitary

Abstract

The theory of Boolean differential rings is a natural extension of the theory of Boolean rings, that additionaly provides an abstract notion of differential. Boolean rings are important and extensively studied concepts arising naturally in many parts of mathematics, especially logic, and computer science. One important result is that the theory of Boolean rings has the unitary unification type. We show that the unification of Boolean differential rings can be reduced to the unification of Boolean rings and that the theory of Boolean differential rings also has the unitary unification type, and we provide an algorithm that calculates a most general unifier. We also show that terms of Boolean differential rings have a flat normal form similar to the polynomial form of terms of Boolean rings and that terms of Boolean differential rings correspond to terms of Boolean rings in a way that respects both equivalences.

Cite

bdr-unification:
  type: Thesis
  title: Unification of Boolean Differential Rings Is Unitary
  author: Grubmüller, Fabian Lukas
  date: 2024-09-10
  organization: Ludwig-Maximilians-Universität München
  serial-number:
    doi: 10.5282/ubm/epub.125897
  note: Bachelor thesis

@mastersthesis{bdr-unification,
    title = {Unification of Boolean Differential Rings Is Unitary},
    author = {Grubm\"{u}ller, Fabian Lukas},
    year = {2024},
    school = {Ludwig-Maximilians-Universit\"{a}t M\"{u}nchen},
    type = {Bachelor thesis},
    doi = {10.5282/ubm/epub.125897}
}

Notes

Type: Bachelor Thesis
Supervisor: Felix Weitkämper DPhil (Oxon)
Programme: Computer Science B.Sc.
University: Ludwig-Maximilians-Universität München