Related papers: Bounded Quantifier Instantiation for Checking Indu…
Transcorrelated methods provide an efficient way of partially transferring the description of electronic correlations from the ground state wavefunction directly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys. Rev. B,…
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilibrium points, traveling waves, periodic orbits and invariant…
Most software verification tools can be classified into one of a number of established families, each of which has their own focus and strengths. For example, concrete counterexample generation in model checking, invariant inference in…
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…
We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
In this paper we use pre existing language support for type modifiers and object capabilities to enable a system for sound runtime verification of invariants. Our system guarantees that class invariants hold for all objects involved in…
The task of choosing a preconditioner $\boldsymbol{M}$ to use when solving a linear system $\boldsymbol{Ax}=\boldsymbol{b}$ with iterative methods is difficult. For instance, even if one has access to a collection…
We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by…
The paper investigates from a proof-theoretic perspective various non-contractive logical systems circumventing logical and semantic paradoxes. Until recently, such systems only displayed additive quantifiers (Gri\v{s}in, Cantini). Systems…
Mechanistic interpretability often identifies circuits inside Transformer models, but explanations of those circuits are usually validated through examples, ablations, and manual reasoning. This leaves a gap between finding a plausible…
Regular model checking is a technique for the verification of infinite-state systems whose configurations can be represented as finite words over a suitable alphabet. The form we are studying applies to systems whose set of initial…
We introduce MathConstraint, a hard, adaptive benchmark for evaluating the combinatorial reasoning capabilities of LLMs. We combine constraint satisfaction problems with rigorous solver-based verification and design an adaptive generator to…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable their deployment in safety-critical applications. This paper…
We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided…
Proof by induction plays a critical role in formal verification and mathematics at large. However, its automation remains as one of the long-standing challenges in Computer Science. To address this problem, we developed sem_ind. Given…
In Bounded Model Checking both the system model and the checked property are translated into a Boolean formula to be analyzed by a SAT-solver. We introduce a new encoding technique which is particularly optimized for managing quantitative…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…