title: Quasi-Quantifier Elimination Algorithms and Definability Problems in Arithmetics with Divisibility
metadata.name: dc.contributor.author
metadata.value: Starchak, Mikhail R.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-11-27T18:54:38Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-11-27T18:54:38Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-11
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Mikhail R. Starchak. Quasi-Quantifier Elimination Algorithms and Definability Problems in Arithmetics with Divisibility. PhD thesis, Saint Petersburg State University, 2022.
metadata.lang: en_GB
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/47993
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This thesis is primarily going to focus on the relationship between two important tools
  applied in theoretical computer science: quantifier elimination algorithms and the theorem on
  decidability of the existential theory of the natural numbers with unit, addition and divisibility.
  The questions of definability using the relations, which can be defined in terms of addition and
  divisibility of the integers, are directly related to these problems.
  In the first chapter, we will introduce the notion of quasi-quantifier elimination (quasi-QE)
  algorithm, which is in some sense a generalization of quantifier elimination algorithm. Next, we
  construct two quasi-QE algorithms, which form a new decidability proof for the existential theory
  of the natural numbers with unit, addition and divisibility. The language of addition and divisibility
  is rather rich and difficult to study; in the second part of the thesis, a quasi-QE algorithm is also
  used to obtain results about definability in weaker structures. In the third chapter, from such
  questions of quasi-elimination we move towards some closely related definability problems.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St. Petersburg University
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Presburger arithmetic
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: divisibility
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: decidability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quantifier elimination
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: definability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Quasi-Quantifier Elimination Algorithms and Definability Problems in Arithmetics with Divisibility
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Thesis
metadata.lang: en_GB
resources.filename: starchak-CSc2022.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/47993/1/starchak-CSc2022.pdf
resources.format: Adobe PDF
resources.description: Mikhail R. Starchak. Quasi-Quantifier Elimination Algorithms and Definability Problems in Arithmetics with Divisibility. PhD thesis, Saint Petersburg State University, 2022
resources.size: 975,38 kB