Abstract Interpretation of Algebraic Polynomial Systems

نویسندگان

  • Patrick Cousot
  • Radhia Cousot
چکیده

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 compositional formal semantics of algebraic polynomial systems over ~'-algebras by abstract interpretation. This generalizes classical formal language theoretical results and contextfree grammar flow-analysis algorithms in the same uniform framework of universal algebra and abstract interpretation. We define a hierarchy of compositional formal semantics of algebraic polynomial systems over ~'-algebras by abstract interpretation. This generalizes classical formal language theoretical results and contextfree grammar flow-analysis algorithms in the same uniform framework of universal algebra and abstract interpretation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generating Polynomial Invariants for Hybrid Systems

We present a powerful computational method for automatically generating polynomial invariants of hybrid systems with linear continuous dynamics. When restricted to linear continuous dynamical systems, our method generates a set of polynomial equations (algebraic set) that is the best such over-approximation of the reach set. This shows that the set of algebraic invariants of a linear system is ...

متن کامل

Generation of polynomial inequalities as invariants

Embedded software in critical systems rise a need for software analysis, especially for guaranteeing safety properties. In the late seventies, Cousot & Cousot introduced a general framework, called abstract interpretation, dedicated to the conception of particular analyses: static analyses. Among the program properties of interest, discovering algebraic relationships between variables allows fo...

متن کامل

Generation of Basic Semi-algebraic Invariants Using Convex Polyhedra

A technique for generating invariant polynomial inequalities of bounded degree is presented using the abstract interpretation framework. It is based on overapproximating basic semi-algebraic sets, i.e., sets defined by conjunctions of polynomial inequalities, by means of convex polyhedra. While improving on the existing methods for generating invariant polynomial equalities, since polynomial in...

متن کامل

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

متن کامل

Darboux integrability and invariant algebraic curves for planar polynomial systems

In this paper we study the normal forms of polynomial systems having a set of given generic invariant algebraic curves. PACS numbers: 02.30.Ik, 02.10.De

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997