Finite Euler hierarchies of field theory Lagrangians leading to universal equations of motion for new types of string and membrane theories and for classical topological field theories are constructed. The analysis uses two main ingredients. On the one hand, there exists a generic finite Euler hierarchy for one field leading to a universal equation which generalises the Plebanski equation of se...

In this paper we present a new approach for solving quantified formulas in Satisfiability Modulo Theories (SMT), with a particular focus on the theory of fixed-size bit-vectors. We combine counterexampleguided quantifier instantiation with a syntax-guided synthesis approach, which allows us to synthesize both Skolem functions and terms for quantifier instantiations. Our approach employs two gro...

This report describes several approaches for handling synthesis conjectures within an Satisfiability Modulo Theories (SMT) solver. We describe approaches that primarily focus on determining the unsatisfiability of the negated form of synthesis conjectures using new techniques for quantifier instantiation. 1 Synthesis in an SMT solver A synthesis conjecture states there exists a function f for w...

Design patterns specify generic relations among abstract design elements. In the domain of physical devices, design patterns, called generic teleological mechanisms (or GTMs), specify generic functional relations and abstract causal structure of a class of devices. We describe a functional theory of acquisition, access, and use of GTMs, but focus on their use in analogical design. In this theor...

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e. obtaining a small subset of the input constrain...

In this paper we explain the design and preliminary implementation of a solver for the positive satisfiability problem of concepts in a fuzzy description logic over the infinite-valued product logic. The same solver also works for 1-satisfiability in quasi-witnessed models. The solver works by first performing a direct reduction of the problem to a satisfiability problem of a quantifier free bo...