Related papers: Interpolating Strong Induction
Bounded model checking (BMC) is a well-known and successful technique for finding bugs in software. k-induction is an approach to extend BMC-based approaches from falsification to verification. Automatically generated auxiliary invariants…
We present a proof by induction algorithm, which combines k-induction with invariants to model check embedded C software with bounded and unbounded loops. The k-induction algorithm consists of three cases: in the base case, we aim to find a…
We present a novel proof by induction algorithm, which combines k-induction with invariants to model check C programs with bounded and unbounded loops. The k-induction algorithm consists of three cases: in the base case, we aim to find a…
Variational Inference (VI) is a method that approximates a difficult-to-compute posterior density using better behaved distributional families. VI is an alternative to the already well-studied Markov chain Monte Carlo (MCMC) method of…
This technical report presents implementation of two symbolic model checking algorithms that use SAT/SMT Solvers, namely interpolation based model checking and k-induction based model checking. We also do a comparative analysis of these two…
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…
Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…
We present our implementation of DRUP-based interpolants in CaDiCaL 2.0, and evaluate performance in the bit-level model checker Avy using the Hardware Model Checking Competition benchmarks. CaDiCaL is a state-of-the-art, open-source SAT…
The magnetic inversion method is one of the non-destructive geophysical methods, which aims to estimate the subsurface susceptibility distribution from surface magnetic anomaly data. Recently, supervised deep learning methods have been…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
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…
The remarkable success of modern AI has been closely tied to scaling laws, yet the finite supply of high-quality data makes data efficiency--learning more from less--an increasingly important frontier. A model's inductive bias is a critical…
Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate…
The article "Interpolation and SAT-Based Model Checking" (McMillan, 2003) describes a formal-verification algorithm, which was originally devised to verify safety properties of finite-state transition systems. It derives interpolants from…
We introduce a class of generic spike-and-slab priors for high-dimensional linear regression with grouped variables and present a Coordinate-ascent Variational Inference (CAVI) algorithm for obtaining an optimal variational Bayes…
Purpose: To evaluate an iterative learning approach for enhanced performance of Robust Artificial-neural-networks for K-space Interpolation (RAKI), when only a limited amount of training data (auto-calibration signals, ACS) are available…
Semi-implicit variational inference (SIVI) is a powerful framework for approximating complex posterior distributions, but training with the Kullback-Leibler (KL) divergence can be challenging due to high variance and bias in…
High-quality reconstruction of MRI images from under-sampled `k-space' data, which is in the Fourier domain, is crucial for shortening MRI acquisition times and ensuring superior temporal resolution. Over recent years, a wealth of deep…
We introduce a new form of SAT-based symbolic model checking. One common idea in SAT-based symbolic model checking is to generate new clauses from states that can lead to property violations. Our previous work suggests applying induction to…