Below you find a list over my current research interests together with some selected papers.
Weak First-Order Theories (selected papers):
- Kristiansen, L. & Murwanashyaka, J.: First-Order Concatenation Theory with Bounded Quantifiers. Archive for Mathematical Logic (2020). doi: 10.1007/s00153-020-00735-6
- Kristiansen, L. & Murwanashyaka, J.: On Interpretability Between some Weak Essentially Undecidable Theories. LNCS (2020). doi: 10.1007/978-3-030-51466-2_6
You can read more about first-order theories in Wikipedia.
Computable Analysis (selected papers):
- Georgiev, I., Kristiansen, L. & Stephan, F.: Computable Irrational Numbers with Representations of Surprising Complexity. Annals of Pure and Applied Logic (2020). doi: 10.1016/j.apal.2020.102893 Preprint.
- Kristiansen, L.: On Subrecursive Representability of Irrational Numbers, Part II. Computability (2018) . doi: 10.3233/COM-170081
- Kristiansen, L.: On Subrecursive Representability of Irrational Numbers. Computability (2017). doi: 10.3233/COM-160063
You can read more about computable analysis in Wikipedia.
Subrecursive Degree Theory (selected papers):
- Kristiansen, L., Schlage-Puchta, J. & Weiermann, A: Streamlined Subrecursive Degree Theory. Annals of Pure and Applied Logic (2012). doi: 10.1016/j.apal.2011.11.004
- Kristiansen, L.: A Jump Operator on Honest Subrecursive Degrees. Archive for Mathematical Logic (1998). doi: 10.1007/s001530050086
You cannot read more about subrecursive degree theory in Wikipedia. But you can read about the Grzegorczyk hierarchy. Subrecursive degrees are in some sense a generalization of the Grzegorczyk hierarchy.
Implicit Computational Complexity and related stuff (selected papers):
- Kristiansen, L.: Reversible Computing and Implicit Computational Complexity. link: https://doi.org/10.1016/j.scico.2021.102723 Science of Computer Programming (2021)
- Kristiansen, L., Ben-Amram, A. & Jones, N. D.: Linear, Polynomial or Exponential? Complexity Inference in Polynomial Time. LNCS (2008). See here
- Kristiansen, L.: Neat function Algebraic Characterizations of LOGSPACE and LINSPACE. Computational Complexity (2005). doi: 10.1007/s00037-005-0191-0
- Kristiansen, L. & Niggl, K.-H.: On the Computational Complexity of Imperative Programming Languages. Theoretical Computer Science (2004). doi: 10.1016/j.tcs.2003.10.016
You can read more about implicit computational complexity in Wikipedia.
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