Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier-free BAPA (QFBAPA). In contrast to many other NP-complete problems (such as quantifier-free first-order logic or linear arithmetic), the appl...

Satisfiability modulo theories (SMT) solvers that support quantifier instantiations via matching triggers can be programmed to give practical support for user-defined theories. Care must be taken to avoid so-called matching loops, which may prevent termination of the solver. By design, such avoidance limits the extent to which the SMT solver is able to apply the definitions of user-defined func...

The progression of theories suggested for our world, from egoto geoto helio-centric models to universe and multiverse theories and beyond, shows one tendency: The size of the described worlds increases, with humans being expelled from their center to ever more remote and random locations. If pushed too far, a potential theory of everything (ToE) is actually more a theory of nothing (ToN). Indee...

The problem of deciding the satisfiability of a quantifier-free formula with respect to a background theory, also known as Satisfiability Modulo Theories (SMT), is gaining increasing relevance in verification: representation capabilities beyond propositional logic allow for a natural modeling of real-world problems (e.g., pipeline and RTL circuits verification, proof obligations in soft-

We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a system of set constraints, which is then solved to compute a set of sufficient ground terms for each variable. Universally quantified variables with a finit...

We present a new method that combines the efficiency of testing with the reasoning power of satisfiability modulo theory (SMT) solvers for the verification of multithreaded programs under a user specified test vector. Our method performs dynamic executions to obtain both underand over-approximations of the program, represented as quantifier-free first order logic formulas. The formulas are then...

According to more recent AdS/CFT interpretation \cite{Karch:2015rpa}, in which varying cosmological constant $\Lambda$ the bulk corresponds curvature radius governing space on field theory resides, we study criticality of thermodynamic curvatures for thermal boundary conformal theories (CFT) that are dual $d$-dimensional charged anti-de Sitter (AdS) black holes, embedded $D$-dimensional M-theor...