Presburger Arithmetic with algebraic scalar multiplications

We consider Presburger arithmetic (PA) extended by scalar multiplication by an algebraic irrational number $\alpha$, and call this extension $\alpha$-Presburger arithmetic ($\alpha$-PA). We show that the complexity of deciding sentences in $\alpha$-PA is substantially harder than in PA. Indeed, when...

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Bibliographic Details

Published in:	Logical Methods in Computer Science
Main Authors:	Philipp Hieronymi, Danny Nguyen, Igor Pak
Format:	Article
Language:	English
Published:	Logical Methods in Computer Science e.V. 2021-07-01
Subjects:	mathematics - logic computer science - computational complexity computer science - logic in computer science mathematics - combinatorics
Online Access:	https://lmcs.episciences.org/5916/pdf