Ground Confluence Prover based on Rewriting Induction

Ground confluence of term rewriting systems guarantees that all ground terms are confluent. Recently, interests in proving confluence of term rewriting systems automatically has grown, and confluence provers have been developed. But they mainly focus on confluence and not ground confluence. In fact, little interest has been paid to developing tools for proving ground confluence automatically. We report an implementation of a ground confluence prover based on rewriting induction, which is a method originally developed for proving inductive theorems

Decreasing Diagrams and Relative Termination

In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system R is confluent if all its critical pairs are joinable and the critical pair steps are relatively terminating with respect to R. We further show how to encode the rule-labeling heuristic for decreasing diagrams as a satisfiability problem. Experimental data for both methods are presented.Comment: v3: missing references adde

Introduction and analysis of SDN and NFV security architecture (SN-SECA)

© 2015 IEEE. There have been a few literature published about the security risks expected on the implementations of SDN and NFV (SN), however, no formal Security Architecture with practical attributes was proposed until recently. The first of its kind SN-Security Architecture (SN-SECA) was presented as an IETF draft. This draft presents the architecture with specific ascription to ensure effective security evaluation and integration on the SDN/NVF designs and implementations. This paper briefly introduces the proposed architecture and employs methods to analyze and verify its underlying security attributes. A unified method to review SN-SECA through symbolic analysis previews traffic process flow behavior across an infrastructure with SDN and NFV frameworks. The result of this work highlights the fundamental but important role of each attribute and its flow, and overall viability of the proposed architecture for SDN and NFV that protractedly useful to security practitioners

A Reduction-Preserving Completion for Proving Confluence of Non-Terminating Term Rewriting Systems

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critical pairs and it also (partially) works even if the system is not terminating modulo E. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into a terminating part and a possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system

CERTIFYING CONFLUENCE PROOFS VIA RELATIVE TERMINATION AND RULE LABELING

The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule labeling in the theorem prover Isabelle. Moreover, we report on the integration of this result into the certifier CeTA, facilitating the checking of confluence certificates based on decreasing diagrams. The power of the method is illustrated by an experimental evaluation on a (standard) collection of confluence problems

Proving Confluence in the Confluence Framework with CONFident

This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically prove and disprove confluence of *Generalized Term Rewriting Systems*, where (i) only selected arguments of function symbols can be rewritten and (ii) a rather general class of conditional rules can be used. This includes, as particular cases, several variants of rewrite systems such as (context-sensitive) *term rewriting systems*, *string rewriting systems*, and (context-sensitive) *conditional term rewriting systems*. The divide-and-conquer modular strategy allows us to combine in a proof tree different techniques for proving confluence, including modular decompositions, checking joinability of (conditional) critical and variable pairs, transformations, etc., and auxiliary tasks required by them, e.g., joinability of terms, joinability of conditional pairs, etc

On the Design and Testing of Authorization Systems

Authorization deals with the specification and management of accesses principals have to resources. In the design of an authorization system, sometimes we just implement the accessenforcement without having a precise semantics for it. In this dissertation we show that, there exists a precise semantics that improves the efficiency of access-enforcement over the accessenforcement without precise semantics. We present an algorithm to produce an Access Control List (ACL), in a particular authorization system for version control syatems called gitolite, and we compare the implementation of our algorithm against the implementation that is already being used. As another design problem, we consider least-restrictive enforcement of the Chinese Wall security policy. We show that there exists a least-restrictive enforcement of the Chinese Wall Security Policy. Our approach to proving the thesis is by construction; we present an enforcement that is least-restrictive. We also prove that such an enforcement mechanism cannot be subjectindependent. We also propose a methodology that tests the implementation of an authorization system to check whether it has properties of interest. The properties may be considered to be held in the design of an authorization system, but they are not held in the implementation. We show that there exist authorization systems that do not have the properties of interest