Related papers: Inductive Satisfiability Certification for Univers…
Ensuring large language model (LLM) reliability requires distinguishing objective unsolvability (inherent contradictions) from subjective capability limitations (tasks exceeding model competence). Current LLMs often conflate these…
This paper shows effectiveness of X3SAT in proving P = NP. This is due to the fact that it is easy to check unsatisfiability of a particular truth assignment. A truth assignment leads to some reductions of clauses by means of "exactly-1…
Machine reading comprehension with unanswerable questions aims to abstain from answering when no answer can be inferred. In addition to extract answers, previous works usually predict an additional "no-answer" probability to detect…
We present symQV, a symbolic execution framework for writing and verifying quantum computations in the quantum circuit model. symQV can automatically verify that a quantum program complies with a first-order specification. We formally…
Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
In this paper we bring together the areas of combinatorics and propositional satisfiability. Many combinatorial theorems establish, often constructively, the existence of positive integer functions, without actually providing their closed…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
Symbolic execution uses various algorithms (matching, (anti)unification), whose executions are parameters for proof object generation. This paper proposes a generic method for generating proof objects for such parameters. We present in…
Symbolic Execution is a formal method that can be used to verify the behavior of computer programs and detect software vulnerabilities. Compared to other testing methods such as fuzzing, Symbolic Execution has the advantage of providing…
We study Satisfiability Modulo Theories (SMT) enriched with the so-called Ramsey quantifiers, which assert the existence of cliques (complete graphs) in the graph induced by some formulas. The extended framework is known to have…
The Why3 IDE and verification system facilitates the use of a wide range of Satisfiability Modulo Theories (SMT) solvers through a driver-based architecture. We present Where4: a portfolio-based approach to discharge Why3 proof obligations.…
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…
Most of the work on interpretable machine learning has focused on designing either inherently interpretable models, which typically trade-off accuracy for interpretability, or post-hoc explanation systems, which lack guarantees about their…
In deductive verification and software model checking, dealing with certain specification language constructs can be problematic when the back-end solver is not sufficiently powerful or lacks the required theories. One way to deal with this…
We consider a typical integration of induction in saturation-based theorem provers and investigate the effects of Skolem symbols occurring in the induction formulas. In a practically relevant setting we establish a Skolem-free…
This paper proposes a new approach to obtain uniformly valid inference for linear functionals or scalar subvectors of a partially identified parameter defined by linear moment inequalities. The procedure amounts to bootstrapping the value…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
The theory of uninterpreted functions is a key modeling tool for systems with unknown or abstracted components. Some domains such as systems biology impose further restrictions regarding monotonicity on these components, requiring specific…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…