The Productive use of Failure to Generate Witnesses from Divergent Proof Attempts for Coinduction

Coinduction is a proof rule. It is the dual of induction. It allows reasoning about non--well--founded structures such as lazy lists or streams and is of particular use for reasoning about equivalences. A central difficulty in the automation of coinductive proof is the choice of a relation (called a bisimulation). We present an automation of coinductive theorem proving. This automation is based on the idea of proof planning. Proof planning constructs the higher level steps in a proof, using knowledge of the general structure of a family of proofs and exploiting this knowledge to control the proof search. Part of proof planning involves the use of failure information to modify the plan by the use of a proof critic which exploits the information gained from the failed proof attempt. Our approach to the problem was to develop a strategy that makes an initial simple guess at a bisimulation and then uses generalisation techniques, motivated by a critic, to refine this guess, so that a larger class of coinductive problems can be automatically verified. The implementation of this strategy has focused on the use of coinduction to prove the equivalence of programs in a small lazy functional language which is similar to Haskell. We have developed a proof plan for coinduction and a critic associated with this proof plan. These have been implemented in CoClam, an extended version of Clam with encouraging results. The planner has been successfully tested on a number of theorems.

'Immune System Approaches to Intrusion Detection - A Review'

Abstract. The use of artificial immune systems in intrusion detection is an appealing concept for two reasons. Firstly, the human immune system provides the human body with a high level of protection from invading pathogens, in a robust, self-organised and distributed manner. Secondly, current techniques used in computer security are not able to cope with the dynamic and increasingly complex nature of computer systems and their security. It is hoped that biologically inspired approaches in this area, including the use of immune-based systems will be able to meet this challenge. Here we collate the algorithms used, the development of the systems and the outcome of their implementation. It provides an introduction and review of the key developments within this field, in addition to making suggestions for future research.

Immune System Approaches to Intrusion Detection - A Review

The use of artificial immune systems in intrusion detection is an appealing concept for two reasons. Firstly, the human immune system provides the human body with a high level of protection from invading pathogens, in a robust, self-organised and distributed manner. Secondly, current techniques used in computer security are not able to cope with the dynamic and increasingly complex nature of computer systems and their security. It is hoped that biologically inspired approaches in this area, including the use of immune-based systems will be able to meet this challenge. Here we review the algorithms used, the development of the systems and the outcome of their implementation. We provide an introduction and analysis of the key developments within this field, in addition to making suggestions for future research.

'Immune System Approaches to Intrusion Detection - A Review'

Abstract. The use of artificial immune systems in intrusion detection is an appealing concept for two reasons. Firstly, the human immune system provides the human body with a high level of protection from invading pathogens, in a robust, self-organised and distributed manner. Secondly, current techniques used in computer security are not able to cope with the dynamic and increasingly complex nature of computer systems and their security. It is hoped that biologically inspired approaches in this area, including the use of immune-based systems will be able to meet this challenge. Here we collate the algorithms used, the development of the systems and the outcome of their implementation. It provides an introduction and review of the key developments within this field, in addition to making suggestions for future research.

Immune System Approaches to Intrusion Detection - A Review

The use of artificial immune systems in intrusion detection is an appealing concept for two reasons. Firstly, the human immune system provides the human body with a high level of protection from invading pathogens, in a robust, self-organised and distributed manner. Secondly, current techniques used in computer security are not able to cope with the dynamic and increasingly complex nature of computer systems and their security. It is hoped that biologically inspired approaches in this area, including the use of immune-based systems will be able to meet this challenge. Here we review the algorithms used, the development of the systems and the outcome of their implementation. We provide an introduction and analysis of the key developments within this field, in addition to making suggestions for future research.