Related papers: Loop invariants: analysis, classification, and exa…

This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…

A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…

We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…

To remain useful for their users, software systems need to continuously enhance and extend their functionality. Nevertheless, in many object-oriented applications, features are not represented explicitly. The lack of modularization is known…

Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…

A large number of current machine learning methods rely upon deep neural networks. Yet, viewing neural networks as nonlinear dynamical systems, it becomes quickly apparent that mathematically rigorously establishing certain patterns…

Code metrics are easy to define, but not so easy to justify. It is hard to prove that a metric is valid, i.e., that measured numerical values imply anything on the vaguely defined, yet crucial software properties such as complexity and…

Software changes frequently. To efficiently deal with such frequent changes, software verification tools must be incremental. Most of today's approaches for incremental verification consider one specific verification approach. One exception…

Context: Refactoring is the art of modifying the design of a system without altering its behavior. The idea is to reorganize variables, classes and methods to facilitate their future adaptations and comprehension. As the concept of behavior…

We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a…

Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…

Refactoring is one of the most important activities in software engineering which is used to improve the quality of a software system. With the advancement of deep learning techniques, researchers are attempting to apply deep learning…

The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…

Value independence is enormously beneficial for reasoning about software systems at scale. These benefits carry over into the world of formal verification. Reasoning about programs algebraically is a simple affair in a proof assistant,…

Termination analysis of linear loops plays a key r\^{o}le in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination…

Detecting design pattern instances in unfamiliar codebases remains a challenging yet essential task for improving software quality and maintainability. Traditional static analysis tools often struggle with the complexity, variability, and…

We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. We show the subword complexity and the growth function create machine invariant classes. So the…

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…

In the verification of loop programs, disjunctive invariants are essential to capture complex loop dynamics such as phase and mode changes. In this work, we develop a novel approach for the automated generation of affine disjunctive…

We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to…