Related papers: Fair and Adventurous Enumeration of Quantifier Ins…

Quantified formulas pose a significant challenge for Satisfiability Modulo Theories (SMT) solvers due to their inherent undecidability. Existing instantiation techniques, such as e-matching, syntax-guided, model-based, conflict-based, and…

Many decision procedures for SMT problems rely more or less implicitly on an instantiation of the axioms of the theories under consideration, and differ by making use of the additional properties of each theory, in order to increase…

This paper presents a framework to derive instantiation-based decision procedures for satisfiability of quantified formulas in first-order theories, including its correctness, implementation, and evaluation. Using this framework we derive…

In this work we considerably improve the state-of-the-art SMT solving on first-order quantified problems by efficient machine learning guidance of quantifier selection. Quantifiers represent a significant challenge for SMT and are…

We present a novel approach for solving quantified bit-vector formulas in Satisfiability Modulo Theories (SMT) based on computing symbolic inverses of bit-vector operators. We derive conditions that precisely characterize when bit-vector…

This work investigates the relation between model-based quantifier instantiation (MBQI) and enumerative instantiation (EI) in Satisfiability Modulo Theories (SMT). MBQI operates at the semantic level and guarantees to find a counterexample…

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…

SMT-based program analysis and verification often involve reasoning about program features that have been specified using quantifiers; incorporating quantifiers into SMT-based reasoning is, however, known to be challenging. If quantifier…

In this work, we prove over 3000 previously ATP-unproved Mizar/MPTP problems by using several ATP and AI methods, raising the number of ATP-solved Mizar problems from 75\% to above 80\%. First, we start to experiment with the cvc5 SMT…

We present a generic tree-interpolation algorithm in the SMT context with quantifiers. The algorithm takes a proof of unsatisfiability using resolution and quantifier instantiation and computes interpolants (which may contain quantifiers).…

We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

We investigate the domain of satisfiable formulas in satisfiability modulo theories (SMT), in particular, automatic generation of a multitude of satisfying assignments to such formulas. Despite the long and successful history of SMT in…

The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…

We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

We consider the problem of checking whether a proposed invariant $\varphi$ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can…

This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…

Package-to-group recommender systems recommend a set of unified items to a group of people. Different from conventional settings, it is not easy to measure the utility of group recommendations because it involves more than one user. In…

In this paper, we address the problem of enumerating all models of a Boolean formula in conjunctive normal form (CNF). We propose an extension of CDCL-based SAT solvers to deal with this fundamental problem. Then, we provide an experimental…

Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…

There is increasing attention to evaluating the fairness of search system ranking decisions. These metrics often consider the membership of items to particular groups, often identified using protected attributes such as gender or ethnicity.…