Related papers: Invariant Generation for Multi-Path Loops with Pol…

Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…

We investigate the termination problem of a family of multi-path polynomial programs (MPPs), in which all assignments to program variables are polynomials, and test conditions of loops and conditional statements are polynomial equalities.…

Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…

We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method…

Provably correct software is one of the key challenges of our software-driven society. Program synthesis -- the task of constructing a program satisfying a given specification -- is one strategy for achieving this. The result of this task…

This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…

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…

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in…

While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The…

The discovery of inductive invariants lies at the heart of static program verification. Presently, many automatic solutions to inductive invariant generation are inflexible, only applicable to certain classes of programs, or unpredictable.…

This paper presents a new method for automatically generating numerical invariants for imperative programs. Given a program, our procedure computes a binary input/output relation on program states which over-approximates the behaviour of…

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and…

In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…

We describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize inductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large…

In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…

We show that computing the strongest polynomial invariant for single-path loops with polynomial assignments is at least as hard as the Skolem problem, a famous problem whose decidability has been open for almost a century. While the…

Automated program verification has always been an important component of building trustworthy software. While the analysis of real-world programs remains a theoretical challenge, the automation of loop invariant analysis has effectively…

Instances generation is crucial for linear programming algorithms, which is necessary either to find the optimal pivot rules by training learning method or to evaluate and verify corresponding algorithms. This study proposes a general…

A loop invariant is a property of a loop that remains true before and after each execution of the loop. The identification of loop invariants is a critical step to support automated program safety assessment. Recent advancements in Large…

Loop invariants are essential for proving the correctness of programs with loops. Developing loop invariants is challenging, and fully automatic synthesis cannot be guaranteed for arbitrary programs. Some approaches have been proposed to…