On Optimization Modulo Theories, MaxSMT and Sorting Networks

Optimization Modulo Theories (OMT) is an extension of SMT which allows for finding models that optimize given objectives. (Partial weighted) MaxSMT --or equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of state-of-the-art MAXSAT solvers, but they are specific-purpose and not always applicable; OMT-based approaches are general-purpose, but they suffer from intrinsic inefficiencies on MaxSMT/OMT+PB problems. We identify a major source of such inefficiencies, and we address it by enhancing OMT by means of bidirectional sorting networks. We implemented this idea on top of the OptiMathSAT OMT solver. We run an extensive empirical evaluation on a variety of problems, comparing MaxSAT-based and OMT-based techniques, with and without sorting networks, implemented on top of OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and provide interesting insights about the different approaches.Comment: 17 pages, submitted at Tacas 1

Unification of Constant-roll Inflation and Dark Energy with Logarithmic R2R^2-corrected and Exponential F(R)F(R) Gravity

In this paper we investigate how to describe in a unified way a constant-roll inflationary era with a dark energy era, by using the theoretical framework of $F(R)$ gravity. To this end, we introduce some classes of appropriately chosen $F(R)$ gravity models, and we examine in detail how the unification of early and late-time acceleration eras can be achieved. We study in detail the inflationary era, and as we demonstrate it is possible to achieve a viable inflationary era, for which the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio can be compatible with the latest observational data. In addition, the graceful exit issue is briefly discussed for a class of models. Finally, we discuss the dark energy oscillations issue, and we investigate which model from one of the classes we introduced, can produce oscillations with the smallest amplitude.Comment: Nuclear Physics B accepte

Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration

A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential $F(R)$-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck results. At low energy, late-time accelerated expansion takes place. As exponential gravity, for dark energy, must be stabilized during the matter and radiation eras, we introduce a curing term in order to avoid nonphysical singularities in the effective equation of state parameter. The results of our analysis are confirmed by accurate numerical simulations, which show that our model does fit the most recent cosmological data for dark energy very precisely.Comment: 20 pages, to appear in NP