# Decision procedures for arithmetic with powers

## Supervisor

## Suitable for

## Abstract

The project will look at implication and satisfaction problems involving formulas that involve additive arithmetic, inequalities, and some form of exponentiations with a constant base. For example, systems of inequalities with constant multiples of variables and constant multiple of expressions like 2^x. We will also look at first order logic built up from these inequalities. In the absence of exponentiatial terms like 2^x, the theory is known as Presburger Arithmetic, and has been heavily investigated in both theory and practice. In the presence of expenontial terms to a fixed base, it is known to be decidable, from work of Semenov in the late 70's and 80's. Recent work has shown fragments where the complexity is not too terrible, and in the process some new algorithms have been proposed.The goal of the project is to implement decision procedures for expressions of this form. A theoretically-oriented student can also work on complexity analysis. A pre-requisite for the project is good background in logic - Logic and Proof and preferably one of CAFV or KRR.