Related papers: Determinism in the Certification of UNSAT Proofs
Certified robustness circumvents the fragility of defences against adversarial attacks, by endowing model predictions with guarantees of class invariance for attacks up to a calculated size. While there is value in these certifications, the…
In this paper, by constructing extremely hard examples of CSP (with large domains) and SAT (with long clauses), we prove that such examples cannot be solved without exhaustive search, which is stronger than P $\neq$ NP. This constructive…
Universal quantifiers occur frequently in proof obligations produced by program verifiers, for instance, to axiomatize uninterpreted functions and to express properties of arrays. SMT-based verifiers typically reason about them via…
Proof certificates can be used to validate the correctness of algebraic derivations. However, in practice, we frequently observed that the exact same proof steps are repeated for different sets of variables, which leads to unnecessarily…
The robustness and correctness of SAT solvers are receiving more and more attention. In recent SAT competitions, a proof of unsatisfiability emitted by SAT solvers must be checked. So far, no proof checker has been efficient for every case.…
Quantifier elimination (QE) is an important problem that has numerous applications. Unfortunately, QE is computationally very hard. Earlier we introduced a generalization of QE called $\mathit{partial}$ QE (or PQE for short). PQE allows to…
We propose to use local search algorithms to produce SAT instances which are harder to solve than randomly generated k-CNF formulae. The first results, obtained with rudimentary search algorithms, show that the approach deserves further…
Uncertainty quantification is a set of techniques that measure confidence in language models. They can be used, for example, to detect hallucinations or alert users to review uncertain predictions. To be useful, these confidence scores must…
Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited…
Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce…
One of the effective model checking methods is to utilize the efficient decision procedure of SAT (or SMT) solvers. In a SAT-based model checking, a system and its property are encoded into a set of logic formulas and the safety is checked…
Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…
Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
SAT provers are powerful tools for solving real-sized logic problems, but using them requires solid programming knowledge and may be seen w.r.t.\ logic like assembly language w.r.t.\ programming. Something like a high level language was…
We build a SAT solver implementing the DPLL algorithm in the verification-enabled programming language Dafny. The resulting solver is fully verified (soundness, completeness and termination are computer checked). We benchmark our Dafny…
We introduce FRAT, a new proof format for unsatisfiable SAT problems, and its associated toolchain. Compared to DRAT, the FRAT format allows solvers to include more information in proofs to reduce the computational cost of subsequent…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
We present an executable formally verified SAT encoding of classical AI planning. We use the theorem prover Isabelle/HOL to perform the verification. We experimentally test the verified encoding and show that it can be used for reasonably…
This note considers checking satisfiability of sets of propositional clauses (SAT instances). It shows that "unipolar sets" of clauses (containing no positive or no negative clauses) provide an "early sign" of satisfiability of SAT…