72 citations · 74 across the 4 of their papers we have counts for
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On representations of real numbers and the computational complexity of converting between such representations
Amir M. Ben-Amram, Lars Kristiansen, Jakob Grue Simonsen
We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-1…
First-Order Concatenation Theory with Bounded Quantifiers
Lars Kristiansen, Juvenal Murwanashyaka
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a…
Notes on Fragments of First-Order Concatenation Theory
Lars Kristiansen, Juvenal Murwanashyaka
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments…
Subrecursive Approximations of Irrational Numbers by Variable Base Sums
Ivan Georgiev, Lars Kristiansen, Frank Stephan
There are numerous ways to represent real numbers. We may use, e.g., Cauchy sequences, Dedekind cuts, numerical base-10 expansions, numerical base-2 expansions and continued fracti…