Related papers: Linear Loop Synthesis for Quadratic Invariants
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…
We propose a "formula slicing" method for finding inductive invariants. It is based on the observation that many loops in the program affect only a small part of the memory, and many invariants which were valid before a loop are still valid…
Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates…
We study the problem of synthesizing polyhedral Lyapunov functions for hybrid linear systems. Such functions are defined as convex piecewise linear functions, with a finite number of pieces. We first prove that deciding whether there exists…
We reduce synthesis for CTL* properties to synthesis for LTL. In the context of model checking this is impossible - CTL* is more expressive than LTL. Yet, in synthesis we have knowledge of the system structure and we can add new outputs.…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
A modern approach to engineering correct-by-construction systems is to synthesize them automatically from formal specifications. Oftentimes, a system can only satisfy its guarantees if certain environment assumptions hold, which motivates…
Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations…
Automating the decision of whether a code change requires manual review is vital for maintaining software quality in modern development workflows. However, the emergence of new programming languages and frameworks creates a critical…
Large language models (LLMs) have demonstrated significant potential in automating hardware synthesis, yet substantial barriers remain for industrial-scale, datapath-centric designs due to ambiguous specifications and a lack of formal…
The calculation of one loop integrals at finite temperature requires the evaluation of certain series, which converge very slowly or can even be divergent. Here we review a new method, recently devised by the author, for obtaining…
A general expression for a relative invariant of a linear ordinary differential equations is given in terms of the fundamental semi-invariant and an absolute invariant. This result is used to established a number of properties of relative…
This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear…
Early stages of system development involve outlining desired features such as functionality, availability, or usability. Specifications are derived from these features that concretize vague ideas presented in natural languages. The…
Great advances in program analysis would be enabled if it were possible to derive the function of a program from inputs to outputs (or from initial states to final states, depending on how we model program semantics). Efforts to do so have…
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.…
Identification of non-functional requirements is important for successful development and deployment of the software product. The acceptance of the software product by the customer depends on the non-functional requirements which are…
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…
This work introduces a controller synthesis method via system level synthesis for nonlinear systems characterized by polynomial dynamics. The resulting framework yields finite impulse response, time-invariant, closed-loop transfer functions…
A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by…