Related papers: Simple Linear Loops: Algebraic Invariants and Appl…

We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities).…

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…

A fundamental computational task in probabilistic programming is to infer a program's output (posterior) distribution from a given initial (prior) distribution. This problem is challenging, especially for expressive languages that feature…

One of the main challenges in the analysis of probabilistic programs is to compute invariant properties that summarise loop behaviours. Automation of invariant generation is still at its infancy and most of the times targets only expected…

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…

Program verification is vital for ensuring software reliability, especially in the context of increasingly complex systems. Loop invariants, remaining true before and after each iteration of loops, are crucial for this verification process.…

Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a "loop invariant". Beyond their role in…

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…

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…

We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…

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…

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…

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…

We present the Polar framework for fully automating the analysis of classical and probabilistic loops using algebraic reasoning. The central theme in Polar comes with handling algebraic recurrences that precisely capture the loop semantics.…

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…

In this paper, we present a novel approach to synthesize invariant clusters for polynomial programs. An invariant cluster is a set of program invariants that share a common structure, which could, for example, be used to save the needs for…

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.…

We describe the LoopInvGen tool for generating loop invariants that can provably guarantee correctness of a program with respect to a given specification. LoopInvGen is an efficient implementation of the inference technique originally…

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…

Verifiers that can prove programs correct against their full functional specification require, for programs with loops, additional annotations in the form of loop invariants---propeties that hold for every iteration of a loop. We show that…