We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z3 × Z3 Wilson lines, and a more detailed investigation shows that the homology classes of curves are H2(X, Z) = Z 3 ⊕(Z3⊕Z3). We compute the genus-0 prepotential, this is the first explicit calculation of the Gromov-Witten invariants of homology classes wi...

It was recently observed in a lattice QCD measurement that the chiral condensate in the quenched approximation shows dramatically different behavior in the three Z3-equivalent de-confined phases. We argue that this phenomenon can be understood qualitatively as an effect of Z3 twists on fermionic fields. Quarks under these Z3-twists become global anyons and hence display different thermodynamic ...

A specific new quark permits that flavor generations constitute a representation of the 3-dimensional SU(3) symmetry that characterizes the Z3 orbifold. In this context, color and local supersymmetry bind triplets and 4tuplets into composite fields of spin 3/2 and spin 2; and the symmetry E8 that characterizes (the observable sector of) 10-spacetime is interpreted as having reduced to SU(5)XSU(...

Z3 [3] is a state-of-the-art Satisfiability Modulo Theories (SMT) solver freely available from Microsoft Research. It solves the decision problem for quantifier-free formulas with respect to combinations of theories, such as arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is used in various software analysis and test-case generation projects at Microsoft Research and elsewhere....

Konrad Zuse built the machine Z3 from 1939 to 1941 in the Methfesselstraße 7 in BerlinKreuzberg with some friends and a small support by the government. With the Z3 Konrad Zuse wanted to show, that it is possible to build a reliable working machine for very complicated arithmetic calculations, which is freely programmable and is based on a binary floating point number and switching system. For ...

Satisfiability Modulo Theories, SMT, solvers are used in many applications. These applications benefit from the power of tuned and scalable theorem proving technologies for supported logics and specialized theory solvers. SMT solvers are primarily used to determine whether formulas are satisfiable. Furthermore, when formulas are satisfiable, many applications need models that assign values to f...

A standard correction for random guessing on multiple-choice examinations was implemented prospectively in an Oral and Maxillofacial Pathology course for second-year dental students. The correction was a weighted scoring formula for points awarded for correct answers, incorrect answers, and unanswered questions such that the expected gain in the multiple-choice examination score due to random g...

The Satisfiability Modulo Theories (SMT) solver Z3 can generate proofs of unsatisfiability. We present independent reconstruction of these proofs in the theorem provers Isabelle/HOL and HOL4 with particular focus on efficiency. Our highly optimized implementations outperform previous LCF-style proof checkers for SMT, often by orders of magnitude. Detailed performance data shows that LCF-style p...

The local Gauss law of quantum chromodynamics on a finite lattice is investigated. It is shown that it implies a gauge invariant, additive law giving rise to a gauge invariant Z3-valued global charge in QCD. The total charge contained in a region of the lattice is equal to the flux through its boundary of a certain Z3-valued, additive quantity. Implications for continuous QCD are discussed.