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The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…

Logic in Computer Science · Computer Science 2026-02-19 Stefan Ratschan , Anggha Nugraha , Mikoláš Janota , Marek Dančo

This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving polynomial equalities and disequalities modulo different…

Logic in Computer Science · Computer Science 2025-05-22 Elizaveta Pertseva , Alex Ozdemir , Shankara Pailoor , Alp Bassa , Sorawee Porncharoenwase , Işil Dillig , Clark Barrett

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…

Logic in Computer Science · Computer Science 2013-10-31 Sicun Gao , Soonho Kong , Edmund Clarke

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number…

Programming Languages · Computer Science 2015-05-27 Thomas Martin Gawlitza , David Monniaux

This paper provides an NP procedure that decides whether a linear-exponential system of constraints has an integer solution. Linear-exponential systems extend standard integer linear programs with exponential terms $2^x$ and remainder terms…

Logic in Computer Science · Computer Science 2024-07-10 Dmitry Chistikov , Alessio Mansutti , Mikhail R. Starchak

The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…

Mathematical Physics · Physics 2008-11-18 D H Gebremedhin , C A Weatherford , X Zhang , A Wynn , G Tanaka

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…

Logic in Computer Science · Computer Science 2020-10-26 Martin Bromberger , Thomas Sturm , Christoph Weidenbach

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…

Logic in Computer Science · Computer Science 2019-07-02 Aina Niemetz , Mathias Preiner , Andrew Reynolds , Yoni Zohar , Clark Barrett , Cesare Tinelli

This short paper proposes to learn models of satisfiability modulo theories (SMT) formulas during solving. Specifically, we focus on infinite models for problems in the logic of linear arithmetic with uninterpreted functions (UFLIA). The…

Logic in Computer Science · Computer Science 2025-03-24 Mikoláš Janota , Bartosz Piotrowski , Karel Chvalovský

Bit-vectors, which are integers in a finite number of bits, are ubiquitous in software and hardware systems. In this work, we consider the satisfiability modulo theories (SMT) of bit-vectors. Unlike normal integers, the arithmetics of…

Logic in Computer Science · Computer Science 2024-02-27 Jiaxin Song , Hongfei Fu , Charles Zhang

This paper introduces a new approach to solving a continuous-time version of the multi-agent path finding problem. The algorithm translates the problem into an extension of the classical Boolean satisfiability problem, satisfiability modulo…

Multiagent Systems · Computer Science 2023-12-18 Tomáš Kolárik , Stefan Ratschan , Pavel Surynek

We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…

Symbolic Computation · Computer Science 2021-06-17 Erika Ábrahám , James H. Davenport , Matthew England , Gereon Kremer

To check the satisfiability of (non-linear) real arithmetic formulas, modern satisfiability modulo theories (SMT) solving algorithms like NLSAT depend heavily on single cell construction, the task of generalizing a sample point to a…

Symbolic Computation · Computer Science 2025-12-17 Valentin Promies , Jasper Nalbach , Erika Ábrahám , Paul Wagner

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…

Logic in Computer Science · Computer Science 2024-12-05 Emiko Soroka , Mykel J. Kochenderfer , Sanjay Lall

Satisfiability Modulo Theories (SMT) has significant application in various domains. In this paper, we focus on quantifier-free Satisfiablity Modulo Real Arithmetic, referred to as SMT(RA), including both linear and non-linear real…

Logic in Computer Science · Computer Science 2023-08-03 Bohan Li , Shaowei Cai

Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical…

Artificial Intelligence · Computer Science 2024-01-02 Jinzhao Li , Nan Jiang , Yexiang Xue

We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…

Logic in Computer Science · Computer Science 2025-07-10 Chad E. Brown , Karel Chvalovský , Mikoláš Janota , Mirek Olšák , Stefan Ratschan

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…

Logic in Computer Science · Computer Science 2022-12-14 Matan Peled , Bat-Chen Rothenberg , Shachar Itzhaky

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…

Artificial Intelligence · Computer Science 2012-02-08 Roberto Sebastiani , Silvia Tomasi

The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of…

Logic in Computer Science · Computer Science 2015-07-01 Alberto Griggio , Thi Thieu Hoa Le , Roberto Sebastiani