Related papers: Solvable Polynomial Ideals: The Ideal Reflection f…

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…

We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…

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…

We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…

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…

Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task already for syntactically restricted classes of loops. Rather…

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number…

There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops), where questions regarding the runtime and the size…

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…

The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program…

This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…

In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an…

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…

Context. Since the eighties, the combination of program analysis techniques has been increasingly recognized as a promising approach to overcome the limitations of standalone methods. While individual techniques, based on either static or…

This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…

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…

The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others.…

The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…

We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and…