Computer-Assisted Simulation Proofs
نویسندگان
چکیده
This paper presents a scalable approach to reasoning formally about distributed algorithms. It uses results about I/O automata to extract a set of proof obligations for showing that the behaviors of one algorithm are among those of another, and it uses the Larch tools for speci cation and deduction to discharge these obligations in a natural and easy-to-read fashion. The approach is demonstrated by proving the behavior equivalence of two high-level speci cations for a communication protocol.
منابع مشابه
Computer-Assisted Instruction (CAI), Virtual Patients (VP), and Human Patient Simulation (HPS) in Medical Education Based on Gagne’s Educational Design Pattern
Background and objectives: Educational technology is widely used in all parts of medical education. The use and application of common educational technologies and adoption of educational design patterns in medical sciences education can greatly help in medical simulations, training, and improving of clinical skills of nurses and medical students. The aim of this research was to study computer-a...
متن کاملOn Computer-assisted Proving the Existence of Periodic and Bounded Orbits
We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provid...
متن کاملInheritable Properties and Computer Assisted Proofs in Dynamics
1 0 Introduction. Computer assisted proofs are becoming an important factor of present day mathematics. Since there exist short theorems having arbitrarily long proofs (a consequence of GG odel's incompletness theorems, see 4, 6, 23]) and the power of computers is growing exponentially, this shoudbe expected. The general scheme for constructing computer assisted proofs is actually very simple a...
متن کاملNumerical and Algebraic Algorithms and Computer - assisted Proofs — Dagstuhl Seminar
The common goal of self-validating methods and computer algebra methods is to solve mathematical problems with complete rigor and with the aid of computers. The seminar focused on several aspects of such methods for computer-assisted proofs.
متن کاملOur seminars on computer-assisted proofs are intended to assemble a diverse group of scientists working on differing aspects of computer-assisted proofs and verification
A major representative of computer-assisted proofs are so-called verification methods. These are algorithms verifying the correctness of the assumptions of mathematical theorems with rigor. These methods use solely floating-point arithmetic estimating all numerical errors. Therefore these methods are particularly fast. Besides the conference, a 163-page review article on verification methods by...
متن کاملP P 2 Mathematical Proofs: an Evolution in Eight Stages
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special attention. Finally, in a highly speculative part, we will anticipate the evolution of proofs under the assumption that the quantum computer will materialize. We ...
متن کامل