Polyinvar is a tool to infer valid polynomial relations at program points in the control flow graph of Java Code. This analysis is achieved by an incremental fixpoint iteration over a set of polynomial modules, representing the weakest precondition for a generic relation of degree n at a given program point.

Interpretation of Algebraic Polynomial Systems (Extended Abstract) Patrick Cousot 1 and Radhia Cousot 2 1 LIENS, ~cole Normale Sup4neure, 45 rue d'Ulm, 75230 Paris cedex 05, France [email protected] http://www.dmi.ens.fr/-cousot 2 LIX, CNRS & Ecole Polytechnique, 91140 Palaiseau cedex, France [email protected] http://lix.polytechnique.fr/-rcousot Abstract. We define a hierarchy of co...

This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended to infinite di...

We propose a type system to analyze the time consumed by multi-threaded imperative programs with a shared global memory, which delineates a class of safe multi-threaded programs. We demonstrate that a safe multi-threaded program runs in polynomial time if (i) it is strongly terminating wrt a non-deterministic scheduling policy or (ii) it terminates wrt a deterministic and quiet scheduling polic...

Given an undirected edge-weighted network in which one edge capacity is allowed to vary, we propose in this paper a polynomial algorithm that needs only two 2-cuttrees computations to provide the all pairs maximum 2-route flow values. Moreover, we provide an extension to the case where k edge capacities may vary, and show that 2k 2-cut-trees computations are necessary in order to determine the ...

We present a model of computation with ordinary differential equations (ODEs) which converge to attractors that are interpreted as the output of a computation. We introduce a measure of complexity for exponentially convergent ODEs, enabling an algorithmic analysis of continuous time flows and their comparison with discrete algorithms. We define polynomial and logarithmic continuous time complex...

We propose a general algorithm to enumerate all solutions of a zero-dimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady cavity flow problem in two dimensions. The key technique on which our algorithm is based is to solve polynomial optimization problems via sparse semidefinit...

Constant propagation aims at identifying expressions that always yield a unique constant value at run-time. It is well-known that constant propagation is undecidable for programs working on integers even if guards are ignored as in non-deterministic flow graphs. We show that polynomial constants are decidable in non-deterministic flow graphs. In polynomial constant propagation, assignment state...

let $d$ be a digraph with skew-adjacency matrix $s(d)$. then the skew energyof $d$ is defined to be the sum of the norms of all eigenvalues of $s(d)$. denote by$mathcal{o}_n$ the class of digraphs on order $n$ with no even cycles, and by$mathcal{o}_{n,m}$ the class of digraphs in $mathcal{o}_n$ with $m$ arcs.in this paper, we first give the minimal skew energy digraphs in$mathcal{o}_n$ and $mat...