The branch-and-bound framework has already been successfully applied in SAT-modulo-theories (SMT) solvers to check the satisfiability of linear integer arithmetic formulas. In this paper we study how it can be used in SMT solvers for non-linear integer arithmetic on top of two real-algebraic decision procedures: the virtual substitution and the cylindrical algebraic decomposition methods. We im...

Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post- quantum cryptography. Solving is also one the most difficult problems mathematics. In this paper, we propose an automated reasoning procedure for deciding satisfiability a non-linear equations fields. We introduce zero de...

BACKGROUND Increasing evidence supports somato-visceral effects of manual therapies. We have previously demonstrated that a single spinal manipulative treatment (SMT) accompanied by audible release has an inhibitory effect on the production of proinflammatory cytokines in asymptomatic subjects. The purpose of this study is to report on SMT-related changes in the production of the immunoregulato...

Spinal manipulative therapy (SMT) creates health benefits for some while for others, no benefit or even adverse events. Understanding these differential responses is important to optimize patient care and safety. Toward this, characterizing how loads created by SMT relate to those created by typical motions is fundamental. Using robotic testing, it is now possible to make these comparisons to d...

Suppose R is a union of two subsets Rl and R2 whose Steiner minimal trees SMT(R 1) and SMT(R2) are known. The decomposition question is when the Steiner minimal tree SMT(R) for R is just the union of two Steiner minimal trees on R 1 and R2 In this paper a special case studied, that R 1 =bcda, R2=defg are two non-overlapping rectangles with a common vertex d so that a,d,e lie on one line. We con...

Post-editing the output of a statistical machine translation (SMT) system to obtain high-quality translation has become an increasingly common application of SMT, which henceforth we refer to as post-editing-based SMT (PE-SMT). PE-SMT is often deployed as an incrementally retrained system that can learn knowledge from human post-editing outputs as early as possible to augment the SMT models to ...

Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some decidable first-order theory T (SMT (T )). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingly important due to its applications in many domains in different communities, in particular in f...

SMT-based Bounded Model Checking (BMC) consists of two primary tasks: (1) encoding a bounded model checking problem into a propositional formula that represents the problem, and (2) using a SMT solver to solve the formula, that is, finding a set of variable assignments that makes the formula true. Solving the formula (namely, SMT solving) involves computation-intensive processes and is thus tim...

Solvers for the Satisfiability Modulo Theories (SMT) problem are making rapid progress. However, many verification tools aren’t making use of the full power of modern SMT solvers. We believe that the verification community could be benefiting more from the work of the SMT community; at the same time, the SMT community could benefit from a more active and engaged verification user community.

SMT stands for Satisfiability Modulo Theories. An SMT solver decides the satisfiability of propositionally complex formulas in theories such as arithmetic and uninterpreted functions with equality. SMT solving has numerous applications in automated theorem proving, in hardware and software verification, and in scheduling and planning problems. This paper describes Yices, an efficient SMT solver...