Related papers: Automated Generation of Non-Linear Loop Invariants…

We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…

When we consider a finite abelian group acting linearly on a polynomial ring, we can find monomial generators for the subring of invariants. By Noether's degree bound and Hilbert's finiteness theorem, we know that there are finitely many…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…

This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…

Invariant sets are a key ingredient for verifying safety and other properties of cyber-physical systems that mix discrete and continuous dynamics. We adapt the elimination-theoretic Rosenfeld-Gr\"{o}bner algorithm to systematically obtain…

Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…

We study possibilities for automated invariant generation in parametric systems. We use (a refinement of) an algorithm for symbol elimination in theory extensions to devise a method for iteratively strengthening certain classes of safety…

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…

We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…

Template abstract domains allow to express more interesting properties than classical abstract domains. However, template generation is a challenging problem when one uses template abstract domains for program analysis. In this paper, we…

We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…

In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…

Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without…

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…

We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…

We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops. Our method is built on a denotational semantics represented by probability generating…

Probabilistic programming languages (PPLs) are a popular tool for high-level modelling across many fields. They provide a range of algorithms for probabilistic inference, which analyse models by learning their parameters from a dataset or…

We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…

We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…