We construct the genus two (or two loop) partition function for meromorphic bosonic conformal field theories. We use a sewing procedure involving two genus one tori by exploiting an explicit relationship between the genus two period matrix and pinching modular parameters. We obtain expressions for the partition function for the chiral bosonic string, even rank lattice theories and self-dual mer...

Effective model theory is an area of logic that analyzes the effective content of the typical notions and results of model theory and universal algebra. Typical notions in model theory and universal algebra are languages and structures, theories and models, models and their submodels, automorphisms and isomorphisms, embeddings and elementary embeddings. In this paper languages, structures, and ...

Satisfiability-checking of formulas in the theory of linear rational arithmetic (LRA) has broad applications including program verification and synthesis. Satisfiability Modulo Theories (SMT) solvers are effective at checking satisfiability of the ground fragment of LRA, but applying them to quantified formulas requires a costly quantifier elimination step. This article presents a novel decisio...

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of a...

SMT solvers have recently been extended with techniques for finding models in presence of universally quantified formulas in some restricted fragments. This paper introduces a translation which reduces axioms specifying a large class of recursive functions, including well-founded (terminating) functions, to universally quantified formulas for which these techniques are applicable. An empirical ...

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model checking, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, litt...

The paper describes an implementation of instantiation-based interpolation for quantified formulae in modified CSIsat tool. The tool supports interpolation for formulae with linear real arithmetic, uninterpreted functions and quantifiers. We propose in this paper using external SMT-solver CVC3 for quantified expressions instantiation, then we describe how we modified CSIsat and CVC3 tools in or...

The Inst-Gen-Eq method is an instantiation-based calculus which is complete for first-order clause logic modulo equality. Its distinctive feature is that it combines first-order reasoning with efficient ground satisfiability checking which is delegated in a modular way to any state-of-the-art ground SMT solver. The first-order reasoning modulo equality employs a superposition-style calculus whi...

Efficient handling of quantifiers is crucial for solving software verification problems. E-matching algorithms are used in satisfiability modulo theories solvers that handle quantified formulas through instantiation. Two novel, efficient algorithms for solving the E-matching problem are presented and compared to a well-known algorithm described in the literature.

This paper aims to do two things. Firstly, it discusses how the VAMPIRE automatic theorem prover both succeeds and fails at pretending to be an SMT solver. We discuss how Vampire reasons with problems containing both quantification and theories, the limitations this places on what it can do, and the advantages this provides over the standard SMT approach. Secondly, it focuses on the problem of ...