University of Birmingham > Talks@bham > Theoretical computer science seminar > On the complexity of linear arithmetic theories over the integers

On the complexity of linear arithmetic theories over the integers

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If you have a question about this talk, please contact Rajesh Chitnis.

Given a system of linear Diophantine equations, how difficult is it to determine whether it has a solution? What changes if equations are replaced with inequalities? If some of the variables are quantified universally? These and similar questions relate to the computational complexity of deciding the truth value of statements in various logics. This includes in particular Presburger arithmetic, the first-order logic over the integers with addition and order.

In this talk, I will survey constructions and ideas that underlie known answers to these questions, from classical results to recent developments, and open problems. This will include the geometry of integer linear programming, how it interacts with quantifiers, and ultimately periodic sets of integer points in several dimensions (semi-linear sets). We will also discuss “sources of hardness”, such as representations of big numbers with small logical formulae.

This talk is part of the Theoretical computer science seminar series.

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