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Nuns on the run
Sep. 6th, 2005 09:15 pmAnyone else remember that film?
*shudders*
Anyway, I'm just about to head off to Germany for the APPSEM II summer school and workshop in Frauenchiemsee, Germany. Which is in a convent. With actual nuns. On an island. In the middle of a lake. There will, inevitably, be photographs. I'm back late on Friday 16th.
I may or may not have email or phone access there. In theory, they will have WiFi piped through ISDN, so I should hopefully still be able to (slowly) check email.
I'm giving a paper at the workshop. I haven't even started doing the slides yet. Bad me. The paper details the proof I ended up at accidentally a couple of months ago that shows that it is, surprisingly to me, impossible to build a delay-insensitive circuit that is capable of rejecting all possible glitches at its inputs. The proof falls out of the wierd maths that itself falls out of my transitional logic. Basically, ordinary 2-value Boolean logics are well behaved in terms of group theory, so they are effectively algebras that do all the expected stuff. You can kind-of think of AND as multiplication, and OR as addition, and everything kind-of works the way you'd expect. Kind-of. However, if you take time into account, as my extended logic does, you find that this only holds for steady states -- if values change their truth status over time, you end up with algebraic laws that look quite a bit different. You don't get groups. You probably get something a bit like a very degenerate group, which someone who knows more group theory than I could no doubt name. I vaguely remember thinking it was probably a semigroup, but I'm not certain about that. My supervisor thought it wasn't, although it seemed to fit with what I'd read in my group theory textbook. Anyway. Going back to what I was doing, I was trying to prove the correctness of the classic triple modular redundancy voting logic circuit that is commonly used in lots of aerospace applications. I was initially pretty sure that it would come out correct, and that it would make for a nice, clean, friendly example for my thesis. What I found, in contrary, was that the standard digital voting logic circuit (e.g. (a & b) | (a & c) | (b & c) ) is not actually correct at all, in the sense that under certain circumstances it not only passes on glitches, but can actually multiply them! I then had a go at generalising the result, and found that I could do a neat bit of induction to show that the conditions necessary for a correct circuit can not be achieved by any possible delay insensitive circuit, regardless of its size or topology. Even infinitely large circuits don't get a get-out-of-glitchiness-free card. It all falls out of algebraic properties of the transitional logic, which itself is already known to be properly predictive of the real world thanks to a nifty series of proofs from my SAS'04 paper that showed a Galois insertion to exist between the concrete and abstract worlds, and that my operators (AND, OR, NOT and a couple of different kinds of delay) are also sound and in many cases complete. (This is an abstract interpretation definition of 'sound' and 'complete', which differs a bit from the definitions used by logicians, so don't shoot me, I've not cured anything fundamental about classical logic here!)
Whoops, rambled on a bit there. I'm currently at the CL, so I'd better go and feed myself, go home and pack for leaving in the morning. (Like a plank, I booked the plane a day too early because I believed the conference web site when it said that the summer school starts on Thursday, whereas in fact it actually starts Friday, and Thursday was arrival and registration only).
In other news, my LifeDrive arrived. Very very shiny. Does a good impersonation of an iPod. I've not watched a movie on it yet, so more on that when I have tried it. Best of all, like all Palms, it is totally wonderful for calendar and to-do-list stuff, and it has already helped reduce my stress levels due to getting all my stuff organised. Maybe I'll take 'Getting Things Done' (thanks for the pointer,![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
keithlard) with me and finally finish reading the damned thing! Otherwise, I'll probably continue reading Harry Potter et le Prisonnier d'Azkaban, which is way more fun than real French homework. I should really brush up on my German a bit, under the circumstances. Maybe on the plane on the way there. We shall see if I am good and avoid just buying a crappy airport adventure novel like I usually seem to.
See you all in a couple of weeks!
*shudders*
Anyway, I'm just about to head off to Germany for the APPSEM II summer school and workshop in Frauenchiemsee, Germany. Which is in a convent. With actual nuns. On an island. In the middle of a lake. There will, inevitably, be photographs. I'm back late on Friday 16th.
I may or may not have email or phone access there. In theory, they will have WiFi piped through ISDN, so I should hopefully still be able to (slowly) check email.
I'm giving a paper at the workshop. I haven't even started doing the slides yet. Bad me. The paper details the proof I ended up at accidentally a couple of months ago that shows that it is, surprisingly to me, impossible to build a delay-insensitive circuit that is capable of rejecting all possible glitches at its inputs. The proof falls out of the wierd maths that itself falls out of my transitional logic. Basically, ordinary 2-value Boolean logics are well behaved in terms of group theory, so they are effectively algebras that do all the expected stuff. You can kind-of think of AND as multiplication, and OR as addition, and everything kind-of works the way you'd expect. Kind-of. However, if you take time into account, as my extended logic does, you find that this only holds for steady states -- if values change their truth status over time, you end up with algebraic laws that look quite a bit different. You don't get groups. You probably get something a bit like a very degenerate group, which someone who knows more group theory than I could no doubt name. I vaguely remember thinking it was probably a semigroup, but I'm not certain about that. My supervisor thought it wasn't, although it seemed to fit with what I'd read in my group theory textbook. Anyway. Going back to what I was doing, I was trying to prove the correctness of the classic triple modular redundancy voting logic circuit that is commonly used in lots of aerospace applications. I was initially pretty sure that it would come out correct, and that it would make for a nice, clean, friendly example for my thesis. What I found, in contrary, was that the standard digital voting logic circuit (e.g. (a & b) | (a & c) | (b & c) ) is not actually correct at all, in the sense that under certain circumstances it not only passes on glitches, but can actually multiply them! I then had a go at generalising the result, and found that I could do a neat bit of induction to show that the conditions necessary for a correct circuit can not be achieved by any possible delay insensitive circuit, regardless of its size or topology. Even infinitely large circuits don't get a get-out-of-glitchiness-free card. It all falls out of algebraic properties of the transitional logic, which itself is already known to be properly predictive of the real world thanks to a nifty series of proofs from my SAS'04 paper that showed a Galois insertion to exist between the concrete and abstract worlds, and that my operators (AND, OR, NOT and a couple of different kinds of delay) are also sound and in many cases complete. (This is an abstract interpretation definition of 'sound' and 'complete', which differs a bit from the definitions used by logicians, so don't shoot me, I've not cured anything fundamental about classical logic here!)
Whoops, rambled on a bit there. I'm currently at the CL, so I'd better go and feed myself, go home and pack for leaving in the morning. (Like a plank, I booked the plane a day too early because I believed the conference web site when it said that the summer school starts on Thursday, whereas in fact it actually starts Friday, and Thursday was arrival and registration only).
In other news, my LifeDrive arrived. Very very shiny. Does a good impersonation of an iPod. I've not watched a movie on it yet, so more on that when I have tried it. Best of all, like all Palms, it is totally wonderful for calendar and to-do-list stuff, and it has already helped reduce my stress levels due to getting all my stuff organised. Maybe I'll take 'Getting Things Done' (thanks for the pointer,
keithlard) with me and finally finish reading the damned thing! Otherwise, I'll probably continue reading Harry Potter et le Prisonnier d'Azkaban, which is way more fun than real French homework. I should really brush up on my German a bit, under the circumstances. Maybe on the plane on the way there. We shall see if I am good and avoid just buying a crappy airport adventure novel like I usually seem to.See you all in a couple of weeks!