Related papers: SMT-Solving Induction Proofs of Inequalities
The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many…
The development of embedded systems requires formal analysis of models such as those described with MATLAB/Simulink. However, the increasing complexity of industrial models makes analysis difficult. This paper proposes a model checking…
Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first order theories. In this paper, we focus on Satisfiablity Modulo Integer Arithmetic, which is…
The need to solve non-linear arithmetic constraints presents a major obstacle to the automatic verification of smart contracts. In this case study we focus on the two overapproximation techniques used by the industry verification tool…
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…
The datasets and benchmarks commonly used to train and evaluate the mathematical capabilities of AI-based mathematical copilots (primarily large language models) exhibit several shortcomings and misdirections. These range from a restricted…
Solving nonlinear SMT problems over real numbers has wide applications in robotics and AI. While significant progress is made in solving quantifier-free SMT formulas in the domain, quantified formulas have been much less investigated. We…
We present new methods for solving the Satisfiability Modulo Theories problem over the theory of Quantifier-Free Non-linear Integer Arithmetic, SMT(QF-NIA), which consists in deciding the satisfiability of ground formulas with integer…
We present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model…
We present VMT-LIB, a language for the representation of verification problems of linear-time temporal properties on infinite-state symbolic transition systems. VMT-LIB is an extension of the standard SMT-LIB language for SMT solvers,…
Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions -- failing to capture the nature of mathematics…
Decision procedures for SMT problems based on the theory of bit-vectors are a fundamental component in state-of-the-art software and hardware verifiers. While very efficient in general, certain SMT instances are still challenging for…
Incremental SAT and QBF solving potentially yields improvements when sequences of related formulas are solved. An incremental application is usually tailored towards some specific solver and decomposes a problem into incremental solver…
String constraint solving, and the underlying theory of word equations, are highly interesting research topics both for practitioners and theoreticians working in the wide area of satisfiability modulo theories. As string constraint solving…
#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…
Mathematical reasoning is a hallmark of human intelligence, and whether large language models (LLMs) can meaningfully perform it remains a central question in artificial intelligence and cognitive science. As LLMs are increasingly…
We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work…
In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL style calculus, using a composition of symbolical and…
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…
Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal…