Related papers: Incomplete SMT Techniques for Solving Non-Linear F…
Satisfiability modulo theories (SMT) is a core tool in formal verification. While the SMT-LIB specification language can be used to interact with theorem proving software, a high-level interface allows for faster and easier specifications…
In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories…
The problem of checking satisfiability of linear real arithmetic (LRA) and non-linear real arithmetic (NRA) formulas has broad applications, in particular, they are at the heart of logic-related applications such as logic for artificial…
Artificial Intelligence problems, ranging form planning/scheduling up to game control, include an essential crucial step: describing a model which accurately defines the problem's required data, requirements, allowed transitions and…
We study Satisfiability Modulo Theories (SMT) enriched with the so-called Ramsey quantifiers, which assert the existence of cliques (complete graphs) in the graph induced by some formulas. The extended framework is known to have…
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…
In the last decade we have witnessed an impressive progress in the expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving techniques. This has brought previously-intractable problems at the reach of state-of-the-art…
Quantified formulas with Uninterpreted Functions (UFs) over non-linear real arithmetic pose fundamental challenges for Satisfiability Modulo Theories (SMT) solving. Traditional quantifier instantiation methods struggle because they lack…
We introduce the notion of "\delta-complete decision procedures" for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of…
Satisfiability Modulo Linear Integer Arithmetic, SMT(LIA) for short, is pivotal across various critical domains. Previous research has primarily focused on SMT solving techniques. However, in practical applications such as software and…
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…
Many SMT solvers implement efficient SAT-based procedures for solving fixed-size bit-vector formulas. These approaches, however, cannot be used directly to reason about bit-vectors of symbolic bit-width. To address this shortcoming, we…
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…
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…
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…
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…
We apply Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers in the context of finding chiral heterotic string models with positive cosmological constant from $\mathbb{Z}_2\times \mathbb{Z}_2$ orbifolds. The power…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…
We study SMT problems over the reals containing ordinary differential equations. They are important for formal verification of realistic hybrid systems and embedded software. We develop delta-complete algorithms for SMT formulas that are…