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Preprint Number 1779
1779. Wei Li, Alexey Ovchinnikov, Gleb Pogudin, and Thomas Scanlon Algorithms yield upper bounds in differential algebra E-mail: Submission date: 22 April 2020 Abstract: Consider an algorithm computing in a differential field with several
commuting derivations such that the only operations it performs with the
elements of the field are arithmetic operations, differentiation, and zero
testing. We show that, if the algorithm is guaranteed to terminate on every
input, then there is a computable upper bound for the size of the output of the
algorithm in terms of the input. We also generalize this to algorithms working
with models of good enough theories (including for example, difference fields). Mathematics Subject Classification: 12H05, 12H10, 03C10, 03C60, 03D15 Keywords and phrases: |

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