Formalization of Incremental Simplex Algorithm by Stepwise Refinement

نویسندگان

  • Mirko Spasic
  • Filip Maric
چکیده

We present an Isabelle/HOL formalization and total correctness proof for incremental version of Simplex algorithm which is used in most state-of-the-art SMT solvers. Formalization relies on stepwise program and data refinement, starting from a simple specification, going trough a number of fine refinement steps, and ending up in a fully executable functional implementation. Symmetries present in the algorithm are handled with special care.

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

Formalizing the Edmonds-Karp Algorithm

We present a formalization of the Ford-Fulkerson method for computing the maximum flow in a network. Our formal proof closely follows a standard textbook proof, and is accessible even without being an expert in Isabelle/HOL — the interactive theorem prover used for the formalization. We then use stepwise refinement to obtain the Edmonds-Karp algorithm, and formally prove a bound on its complexi...

متن کامل

A Formal Basis for Aspect-Oriented Specification with Superposition

We present a formalization of how specifications are constructed using superposition and composition in the Ocsid specification language. The formalization covers stepwise refinement using superposition and composition of independent refinements. Independent views of a refinement hierarchy (subclassing and operation refinement) are reconciled in composition in a formally well founded way. The f...

متن کامل

Formalizing Push-Relabel Algorithms

We present a formalization of push-relabel algorithms for computing the maximum flow in a network. We start with Goldberg’s et al. generic push-relabel algorithm, for which we show correctness and the time complexity bound of O(V E). We then derive the relabel-tofront and FIFO implementation. Using stepwise refinement techniques, we derive an efficient verified implementation. Our formal proof ...

متن کامل

Refinement and Formalization of Semi-Formal Use Case Descriptions

Behavioral models of computer systems are required for their synthesis, for verification and validation. The system behavior is usually described in requirements specifications. However, most specifications are provided in natural language or in a semi-formal way. Incompleteness and ambiguity inhibit their successful exploitation by tools. In this paper an approach for stepwise refinement and f...

متن کامل

Grain Refinement Efficiency of Multi-Axial Incremental Forging and Shearing: A Crystal Plasticity Analysis

Severe plastic deformation is a technical method to produce functional material with special properties such as high strength and specific physical properties. Selection of an efficient severe plastic deformation for grain refinement is a challenging field of study and using a modeling technique to predict the refinement efficiency has gained a lot of attentions. A comparative study was carried...

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 2012