Related papers: Certified DQBF Solving by Definition Extraction
Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…
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…
Feature models are commonly used to specify the valid configurations of a product line. In industry, feature models are often complex due to a large number of features and constraints. Thus, a multitude of automated analyses have been…
Boolean Satisfiability (SAT) solving underpins a wide range of applications in Electronic Design Automation (EDA), particularly formal verification. However, this paper observes that the mainstream clause reduction heuristic in modern SAT…
Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to…
Algebraic Normal Form (ANF) and Conjunctive Normal Form (CNF) are commonly used to encode problems in Boolean algebra. ANFs are typically solved via Gr"obner basis algorithms, often using more memory than is feasible; while CNFs are solved…
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
A linear pseudo-Boolean constraint (LPB) is an expression of the form $a_1 \cdot \ell_1 + \dots + a_m \cdot \ell_m \geq d$, where each $\ell_i$ is a literal (it assumes the value 1 or 0 depending on whether a propositional variable $x_i$ is…
We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global…
Our recently proposed certification framework for bit-level k-induction-based model checking has been shown to be quite effective in increasing the trust of verification results even though it partially involved quantifier reasoning. In…
As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based…
In this paper, we develop a novel adaptation-based approach to constrained control design under multiple state and input constraints. Specifically, we introduce a method for synthesizing any number of time-varying candidate control barrier…
Modern high-performance SAT solvers quickly solve large satisfiability instances that occur in practice. If the instance is satisfiable, then the SAT solver can provide a witness which can be checked independently in the form of a…
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…
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…
We exploit symmetries to give short proofs for two prominent formula families of QBF proof complexity. On the one hand, we employ symmetry breakers. On the other hand, we enrich the (relatively weak) QBF resolution calculus Q-Res with the…
We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way…
We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust…
Definitions are the foundation for any scientific work, but with a significant increase in publication numbers, gathering definitions relevant to any keyword has become challenging. We therefore introduce SciDef, an LLM-based pipeline for…
Formal verification is a promising method for producing reliable software, but the difficulty of manually writing verification proofs severely limits its utility in practice. Recent methods have automated some proof synthesis by guiding a…