Related papers: Formula Slicing: Inductive Invariants from Precond…

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an…

Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been…

Model slicing is a useful technique for identifying a subset of a larger model that is relevant to fulfilling a given requirement. Notable applications of slicing include reducing inspection effort when checking design adequacy to meet…

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…

Factorization machine (FM) variants are widely used for large scale real-time content recommendation systems, since they offer an excellent balance between model accuracy and low computational costs for training and inference. These systems…

Concurrent Constraint Programming (CCP) is a declarative model for concurrency where agents interact by telling and asking constraints (pieces of information) in a shared store. Some previous works have developed (approximated) declarative…

Error invariants are assertions that over-approximate the reachable program states at a given position in an error trace while only capturing states that will still lead to failure if execution of the trace is continued from that position.…

Given a program, a quotient can be obtained from it by deleting zero or more statements. The field of program slicing is concerned with computing a quotient of a program which preserves part of the behaviour of the original program. All…

Constraint-solving-based program invariant synthesis takes a parametric invariant template and encodes the (inductive) invariant conditions into constraints. The problem of characterizing the set of all valid parameter assignments is…

We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…

Loop invariants play a very important role in proving correctness of programs. In this paper, we address the problem of generating invariants of polynomial loop programs. We present a new approach, for generating polynomial equation…

We propose a novel framework of program and invariant synthesis called neural network-guided synthesis. We first show that, by suitably designing and training neural networks, we can extract logical formulas over integers from the weights…

We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…

This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…

Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…

An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…

Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing.…

Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement.…

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…

Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such…