Formal methods its uses and limitations

A little about formality Objective knowledge / information Objective knowledge / information Information brought out into the open Information brought out into the open From the brain/ideas From the brain/ideas To ‘get what you want’ To ‘get what you want’ Analysis from observers Analysis from observers Possible or not? Possible or not? AI – artificial intelligence AI – artificial intelligence

Advantages and uses Unambiguous Unambiguous An expression is ‘formal’ when it has an invariant meaning An expression is ‘formal’ when it has an invariant meaning With this ‘definition’: With this ‘definition’: Ideas are stored for longer time. Ideas are stored for longer time. Science use it for theories and definitions Science use it for theories and definitions Communication Communication Context wise – person with person, or to few Context wise – person with person, or to few Independent formulation from context Independent formulation from context

more… Testability Testability Context of a test where you check the validity of an expression Context of a test where you check the validity of an expression New test for another expression will not have the same context. New test for another expression will not have the same context. With formal methods you will be able to test without the context and hence be able to verify more expression. With formal methods you will be able to test without the context and hence be able to verify more expression.

even more… Combination of the three previous reasons to use formal method gives: Combination of the three previous reasons to use formal method gives: Accumulate and improve knowledge. Accumulate and improve knowledge. Testability implies ability to select good formal descriptions over bad ones. Testability implies ability to select good formal descriptions over bad ones. Storability means that you can keep the good ones maintained. Storability means that you can keep the good ones maintained.

And all this means… Universally this means Universally this means Researchers all over the world Researchers all over the world Information gathered and collected Information gathered and collected Well tested information Well tested information Will formal methods make context related extinct? Will formal methods make context related extinct? Ideas might come from anywhere Ideas might come from anywhere Personal experiences, daily happenings, etc. Personal experiences, daily happenings, etc.

What does this mean to us as computer scientists? Correctness as a concern in software Correctness as a concern in software Security- and safety critical systems Security- and safety critical systems Nuclear plan shutdown systems Nuclear plan shutdown systems Air traffic controller systems Air traffic controller systems Space travels Space travels Sensitive information that is carried over the net Sensitive information that is carried over the net Loads of more examples Loads of more examples

Limitations Ideas to be expressed formally Ideas to be expressed formally Context cannot be eliminated Context cannot be eliminated Problems defining things Problems defining things E.g. Mathematically = 2 E.g. Mathematically = 2 Vs Drops of water = 1 larger Vs Drops of water = 1 larger

Limitations of some definitions Usefulness of definition Usefulness of definition How to define ‘that thing’? How to define ‘that thing’? It is a statue on 34rd and 4 th avenue in New York It is a statue on 34rd and 4 th avenue in New York Where is New York? Where is New York? Longitude and latitude? Longitude and latitude? Where is equator and where is the meridian? Where is equator and where is the meridian? Compared to New York? Compared to New York? Circle… Circle…

What did we just see? As shown on the two previous slides As shown on the two previous slides Some arguments that can only be shown trough experience, the insight or forms of awareness that can not be: Some arguments that can only be shown trough experience, the insight or forms of awareness that can not be: Expressed in words Expressed in words Any other explicit symbolic forms Any other explicit symbolic forms

So where am I going with all this Imagine you’re the designer of a system Imagine you’re the designer of a system It have to be flawless It have to be flawless You heard formal method gives secure systems You heard formal method gives secure systems You come up with a good specification You come up with a good specification Time to verify the system Time to verify the system Verification ended good but after some test runs you find a malfunction Verification ended good but after some test runs you find a malfunction

What went wrong? Aspects of the system Aspects of the system Is the specification good enough? Is the specification good enough? How can you prevent this? How can you prevent this? Most likely you can not prevent it Most likely you can not prevent it You can hope you will discover more aspects of the specification as you work with it You can hope you will discover more aspects of the specification as you work with it Anything can happen, one are never safe Anything can happen, one are never safe

What can we do about it We have to make specifications as good as possible, covering most of the aspects the system will endure/meet We have to make specifications as good as possible, covering most of the aspects the system will endure/meet We must know the systems normal conditions and then keep a keen eye on what might arise that is abnormal We must know the systems normal conditions and then keep a keen eye on what might arise that is abnormal Will it the system be secure? Will it the system be secure? If you/your team have done a good job it will be secure to an extend that most likely is satisfactory If you/your team have done a good job it will be secure to an extend that most likely is satisfactory