Optimization Modulo the Theories of Signed Bit-Vectors and Floating-Point Numbers

Abstract

Optimization modulo theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or Pseudo-Boolean terms. However, many SMT and OMT applications, in particular from SW and HW verification, require handling bit-precise representations of numbers, which in SMT are handled by means of the theory of bit-vectors ($${{\mathcal {B}}}{{\mathcal {V}}}$$ B V ) for the integers and that of floating-point numbers ($$\mathcal {FP}$$ FP ) for the reals respectively. Whereas an approach for OMT with (unsigned) $${{\mathcal {B}}}{{\mathcal {V}}}$$ B V objectives has been proposed by Nadel & Ryvchin, unfortunately we are not aware of any existing approach for OMT with $$\mathcal {FP}$$ FP objectives. In this paper we fill this gap, and we address for the first time $$\text {OMT}$$ OMT with $$\mathcal {FP}$$ FP objectives. We present a novel OMT approach, based on the novel concept of attractor and dynamic attractor, which extends the work of Nadel and Ryvchin to work with signed-$${{\mathcal {B}}}{{\mathcal {V}}}$$ B V objectives and, most importantly, with $$\mathcal {FP}$$ FP objectives. We have implemented some novel $$\text {OMT}$$ OMT procedures on top of OptiMathSAT and tested them on modified problems from the SMT-LIB repository. The empirical results support the validity and feasibility of our novel approach.