Related papers: Linear Loop Synthesis for Quadratic Invariants

Automatic verification of concurrent programs faces state explosion due to the exponential possible interleavings of its sequential components coupled with large or infinite state spaces. An alternative is deductive verification, where…

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…

Program synthesis is the generation of a program from a specification. Correct synthesis is difficult, and methods that provide formal guarantees suffer from scalability issues. On the other hand, neural networks are able to generate…

Programmers frequently maintain implicit data invariants, which are relations between different data structures in a program. Traditionally, such invariants are manually enforced and checked by programmers. This ad-hoc practice is difficult…

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 present the first approach to prove non-termination of integer programs that is based on loop acceleration. If our technique cannot show non-termination of a loop, it tries to accelerate it instead in order to find paths to other…

This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…

Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially…

Loop-invariant synthesis is the basis of program verification. Due to the undecidability of the problem in general, a tool for invariant synthesis necessarily uses heuristics. Despite the common belief that the design of heuristics is vital…

Loops, seamlessly repeatable musical segments, are a cornerstone of modern music production. Contemporary artists often mix and match various sampled or pre-recorded loops based on musical criteria such as rhythm, harmony and timbral…

This paper proposes a technique to specify and verify whether a loop can be parallelised. Our approach can be used as an additional step in a parallelising compiler to verify user annotations about loop dependences. Essentially, our…

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 problem of synthesizing provably non-overflowing integer arithmetic expressions or Boolean relations among integer arithmetic expressions. First we use a numerical abstract domain to infer numerical properties among program…

Ensuring that a program operates correctly is a difficult task in large, complex systems. Enshrining invariants -- desired properties of correct execution -- in code or comments can support maintainability and help sustain correctness.…

Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…

We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants…

In formal synthesis of reactive systems an implementation of a system is automatically constructed from its formal specification. The great advantage of synthesis is that the resulting implementation is correct by construction; therefore…

This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis.…

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.…