On the order of an automorphism of a smooth hypersurface

In this paper we give an effective criterion as to when a positive integer q is the order of an automorphism of a smooth hypersurface of dimension n and degree d, for every d>2, n>1, (n,d)\neq (2,4), and \gcd(q,d)=\gcd(q,d-1)=1. This allows us to give a complete criterion in the case where q=p is a prime number. In particular, we show the following result: If X is a smooth hypersurface of dimension n and degree d admitting an automorphism of prime order p then p(d-1)^n then X is isomorphic to the Klein hypersurface, n=2 or n+2 is prime, and p=\Phi_{n+2}(1-d) where \Phi_{n+2} is the (n+2)-th cyclotomic polynomial. Finally, we provide some applications to intermediate jacobians of Klein hypersurfaces

Proving the Equivalence of Microstep and Macrostep Semantics

Abstract. Recently, an embedding of the synchronous programming language Quartz (an Esterel variant) in the theorem prover HOL has been presented. This embedding is based on control flow predicates that refer to macrosteps of the pro-grams. The original semantics of synchronous languages like Esterel is however normally given at the more detailed microstep level. This paper describes how a variant of the Esterel microstep semantics has been defined in HOL and how its equivalence to the control flow predicate semantics has been proved. Beneath proving the equivalence of the micro- and macrostep semantics, the work pre-sented here is also an important extension of the existing embedding: While rea-soning at the microstep level is not necessary for code generation, it is sometimes advantageous for understanding programs, as some effects like schizophrenia or causality problems become only visible at the microstep level.

A theorem proving framework for the formal verification of Web Services Composition

We present a rigorous framework for the composition of Web Services within a higher order logic theorem prover. Our approach is based on the proofs-as-processes paradigm that enables inference rules of Classical Linear Logic (CLL) to be translated into pi-calculus processes. In this setting, composition is achieved by representing available web services as CLL sentences, proving the requested composite service as a conjecture, and then extracting the constructed pi-calculus term from the proof. Our framework, implemented in HOL Light, not only uses an expressive logic that allows us to incorporate multiple Web Services properties in the composition process, but also provides guarantees of soundness and correctness for the composition.Comment: In Proceedings WWV 2011, arXiv:1108.208

PROSPER: An Investigation into Software Architecture for Embedded Proof Engines

PROSPER is a recently-completed ESPRIT Framework IV research project that investigated software architectures for component-based, embedded formal verification tools. The aim of the project was to make mechanized formal analysis more accessible in practice by providing a framework for integrating formal proof tools inside other software applications. This paper is an extended abstract of an invited presentation on PROSPER given at FroCoS 2002. It describes the vision of the PROSPER project and provides a summary of the technical approach taken and some of the lessons learned

A Mechanized Theory of the pi-calculus in HOL

: The ß-calculus is a process algebra for modelling concurrent systems in which the pattern of communication between processes may change over time. This paper describes the results of preliminary work on a definitional formal theory of the ß-calculus in higher order logic using the HOL theorem prover. The ultimate goal of this work is to provide practical mechanized support for reasoning with the ß-calculus about applications. Introduction The ß-calculus [17, 18] is a process algebra proposed by Milner, Parrow and Walker for modelling concurrent systems in which the pattern of interconnection between processes may change over time. This paper describes work on a mechanized formal theory of the ß-calculus in higher order logic using the HOL theorem prover [8]. The main aim of this work is to construct a practical and sound theorem-proving tool to support reasoning about applications using the ß-calculus, as well as metatheoretic reasoning about the ß-calculus itself. Four general prin..