Related papers: Proofdoors and Efficiency of CDCL Solvers
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
Scalable formal verification constitutes an important challenge for the design of asynchronous circuits. Deadlock freedom is a property that is desired but hard to verify. It is an emergent property that has to be verified monolithically.…
Current pseudo-Boolean solvers implement different variants of the cutting planes proof system to infer new constraints during conflict analysis. One of these variants is generalized resolution, which allows to infer strong constraints, but…
Existing techniques for Craig interpolation for the quantifier-free fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning $(A, B)$ of the interpolation…
Cook's theorem is commonly expressed such as any polynomial time-verifiable problem can be reduced to the SAT problem. The proof of Cook's theorem consists in constructing a propositional formula A(w) to simulate a computation of TM, and…
We study the design of stochastic local search methods to prove unsatisfiability of a constraint satisfaction problem (CSP). For a binary CSP, such methods have been designed using the microstructure of the CSP. Here, we develop a method to…
Since their introduction by Atserias, Kolaitis, and Vardi in 2004, proof systems where each line is represented by an ordered binary decision diagram (OBDD) have been intensively studied as they allow to compactly represent Boolean…
The Conflict-Driven Cylindrical Algebraic Covering algorithm has proven well suited for performing theory validation checks in the satisfiability modulo theories paradigm for non-linear real arithmetic. CDCAC repurposes the theory…
If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts…
Generalized counting constraint satisfaction problems include Holant problems with planarity restrictions; polynomial-time algorithms for such problems include matchgates and matchcircuits, which are based on Pfaffians. In particular, they…
Theorem provers has been used extensively in software engineering for software testing or verification. However, software is now so large and complex that additional architecture is needed to guide theorem provers as they try to generate…
The main ideas in the CDSAT (Conflict-Driven Satisfiability) framework for SMT are summarized, leading to approaches to proof generation in CDSAT.
General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
We investigate the complexity of uniform OR circuits and AND circuits of polynomial-size and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant (0/1) gates.…
The circuit satisfaction problem CSAT(A) of an algebra A is the problem of deciding whether an equation over A (encoded by two circuits) has a solution or not. While solving systems of equations over finite algebras is either in P or…
This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair…
Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational…
We apply the foundational proof certificate (FPC) framework to the problem of designing high-level outlines of proofs. The FPC framework provides a means to formally define and check a wide range of proof evidence. A focused proof system is…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…