Related papers: Linear Loop Synthesis for Quadratic Invariants

Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…

Decidability and synthesis of inductive invariants ranging in a given domain play an important role in many software and hardware verification systems. We consider here inductive invariants belonging to an abstract domain $A$ as defined in…

We present a robust synthesis algorithm for uncertain linear time-varying (LTV) systems on finite horizons. The uncertain system is described as an interconnection of a known LTV system and a perturbation. The input-output behavior of the…

Linear optics (LO) prohibits certain transformations. In this paper, we study the conditions for a computation to be possible in LO. We find that there are finitely many polynomials such that each of these polynomials evaluates to the same…

Applications like program synthesis sometimes require proving that a property holds for all of the infinitely many programs described by a grammar - i.e., an inductively defined set of programs. Current verification frameworks…

We explain the exact meaning of a statement we made in a previous paper on invariants, namely that a complex-valued function of the data of the functional equation of an $L$-function is an invariant if and only if it is stable under the…

Arrays are commonly used in a variety of software to store and process data in loops. Automatically proving safety properties of such programs that manipulate arrays is challenging. We present a novel verification technique, called…

The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which…

We study Wilson loops as a necessary tool for unambiguous identification of non-Abelian synthetic gauge fields, with attention to certain crucial but often overlooked features, such as the requirement of at least three distinct loops. We…

A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…

The task of implementing a supervisory controller is non-trivial, even though different theories exist that allow automatic synthesis of these controllers in the form of automata. One of the reasons for this discord is due to the…

Program synthesis is the task of automatically generating expressions that satisfy a given specification. Program synthesis techniques have been used to automate the generation of loop invariants in code, synthesize function summaries, and…

We introduce KodCode, a synthetic dataset that addresses the persistent challenge of acquiring high-quality, verifiable training data across diverse difficulties and domains for training Large Language Models for coding. Existing…

We present an approach for implementing a formally certified loop-invariant code motion optimization by composing an unrolling pass and a formally certified yet efficient global subexpression elimination.This approach is lightweight: each…

Program invariants are important for defect detection, program verification, and program repair. However, existing techniques have limited support for important classes of invariants such as disjunctions, which express the semantics of…

Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…

Many correct-by-construction control synthesis methods suffer from the curse of dimensionality. Motivated by this challenge, we seek to reduce a correct-by-construction control synthesis problem to subproblems of more modest dimension. As a…

A representation invariant is a property that holds of all values of abstract type produced by a module. Representation invariants play important roles in software engineering and program verification. In this paper, we develop a…

We present the notion of asymptotically non-terminating initial variable values for linear loop programs. Those values are directly associated to initial variable values for which the corresponding program does not terminate. Our…

In the past few years, Large Language Models (LLMs) have exploded in usefulness and popularity for code generation tasks. However, LLMs still struggle with accuracy and are unsuitable for high-risk applications without additional oversight…