fault tolerant protocols and trace spaces
play

Fault-tolerant protocols and trace spaces Eric Goubault CEA LIST, - PowerPoint PPT Presentation

Nov 25, 2022 •245 likes •1.34k views

Fault-tolerant protocols and trace spaces Eric Goubault CEA LIST, Ecole Polytechnique MMTDC, Bremen, 26th-30th of August 2013 Eric Goubault, CEA LIST, Ecole Polytechnique 1 / 68 Contents of the talk Some directed algebraic topology, in

  1. The index poset M l , n : boolean matrices with l rows and n columns. space obtained by extending X M : for every ( i , j ) such that M ( i , j ) = 1 the forbidden cube i downwards in every direction other than j t 1 t 1 t 1 0 0 0 1 1 1 t 0 t 0 t 0 � 1 � � 0 � � 1 � 0 1 0 1 0 1 0 0 1 alive alive dead Eric Goubault, CEA LIST, Ecole Polytechnique 27 / 68

  2. The index poset, combinatorially P a . V a . P b . V b | P a . V a . P b . V b | P a . V a . P b . V b t 1 t 1 t 1 t 1 1 t 2 t 2 t 2 t 2 0 t 0 t 0 t 0 t 0 � 0 � � 1 � � 0 � � 0 � 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 alive alive alive dead Eric Goubault, CEA LIST, Ecole Polytechnique 28 / 68

  3. The index poset Alive and dead? Important matrices are ◮ the dead poset D ( X ) = { M ∈ M C l , n / Ψ( M ) = 1 } . ◮ the index poset C ( X ) = { M ∈ M R l , n / Ψ( M ) = 0 } (the alive matrices). ◮ consider the entrywise ordering (0 < 1) on matrices. General results by Martin Raussen: C ( X ) D ( X ) homotopy classes of traces � � (and even more, but let us just start with that!) Eric Goubault, CEA LIST, Ecole Polytechnique 29 / 68

  4. The dead poset Proposition A matrix M ∈ M C l , n is in D ( X ) iff it satisfies i ′ ∈ R ( M ) y i ′ x i ∀ ( i , j ) ∈ [0 : l [ × [0 : n [ , M ( i , j ) = 1 ⇒ j < min j where R ( M ) : indexes of non-null rows of M. Example t 1 y 1 1 1 x 1 x 0 1 = 1 < 2 = min( y 0 1 , y 1 � 0 � 1 1 ) 1 M = y 0 x 1 0 = 2 < 3 = min( y 0 0 , y 1 1 0 0 ) 1 0 x 0 1 t 0 x 0 0 x 1 0 y 0 0 y 1 0 Eric Goubault, CEA LIST, Ecole Polytechnique 30 / 68

  5. Example, scan/update in dimension 2 3 dead matrices t 1 t 1 t 1 0 0 0 1 1 1 t 0 t 0 t 0 � 1 1 � � 0 0 � � 1 0 � 0 0 1 1 0 1 Eric Goubault, CEA LIST, Ecole Polytechnique 31 / 68

  6. The index poset Proposition A matrix M is in C ( X ) iff for every N ∈ D ( X ) , N � � M. Remark N � � M: there exists ( i , j ) s.t. N ( i , j ) = 1 and M ( i , j ) = 0 . Remark Since C ( X ) is downward closed it will be enough to compute the set C max ( X ) of maximal alive matrices. Eric Goubault, CEA LIST, Ecole Polytechnique 32 / 68

  7. Connected components Definition Two matrices M and N are connected when M ∧ N does not contain any null row. ( M ∧ N : pointwise min of M and N ) Proposition The connected components of C ( X ) are in bijection with homotopy classes of traces b → e in X. Eric Goubault, CEA LIST, Ecole Polytechnique 33 / 68

  8. Example Scan/update in dimension 2 - 1 round u . s | u . s generates a trace space made of 3 distinct points: t 1 t 1 t 1 t 0 t 0 t 0 � 1 � � 0 � � 0 � 0 1 1 M 1 = M 2 = M 3 = 1 0 0 1 1 0 Eric Goubault, CEA LIST, Ecole Polytechnique 34 / 68

  9. Some combinatorial considerations Hypergraph transversal ◮ An hypergraph H = ( V , E ) consists of a set V of vertices and a set E of edges, where an edge is a subset of V ◮ A transversal T of H is a subset of V such that T ∩ e � = ∅ for every edge e ∈ E . D ( X ) ⇒ hypergraph H : ◮ vertices: [0 : l [ × [0 : n [ ◮ hyperedges: { ( i , j ) / D ( i , j ) = 1 } ( D is a matrix in D ( X )) The sets { ( i , j ) / M ( i , j ) = 0 } , where M is a maximal matrix of C ( X ), correspond to minimal transversals (wrt inclusion order) of H . Eric Goubault, CEA LIST, Ecole Polytechnique 35 / 68

  10. Some combinatorial considerations First dead matrix: t 1 1 1 0 0 0 1 t 0 Eric Goubault, CEA LIST, Ecole Polytechnique 35 / 68

  11. Some combinatorial considerations Second dead matrix: t 1 0 0 0 1 1 1 t 0 Eric Goubault, CEA LIST, Ecole Polytechnique 35 / 68

  12. Some combinatorial considerations Third and last (minimal) dead matrix: t 1 1 0 0 0 1 1 t 0 Eric Goubault, CEA LIST, Ecole Polytechnique 35 / 68

  13. Some combinatorial considerations First (maximal) alive matrix: t 1 0 1 0 1 t 0 Eric Goubault, CEA LIST, Ecole Polytechnique 35 / 68

  14. Some combinatorial considerations Second alive matrix: t 1 1 0 1 0 t 0 Eric Goubault, CEA LIST, Ecole Polytechnique 35 / 68

  15. Some combinatorial considerations Third (and last) maximal alive matrix: t 1 0 1 1 0 t 0 Eric Goubault, CEA LIST, Ecole Polytechnique 35 / 68

  16. What is the meaning of traces? t 1 t 1 t 1 t 0 t 0 t 0 � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 1 M 2 M 3 Eric Goubault, CEA LIST, Ecole Polytechnique 36 / 68

  17. What is the meaning of traces? t 1 t 1 t 1 s t 0 t 0 t 0 u � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 1 M 2 M 3 ◮ M 1 : P 1 does its scan before P 0 does its update ◮ M 1 : P 1 does not know the current value of P 0 but P 0 does Eric Goubault, CEA LIST, Ecole Polytechnique 36 / 68

  18. What is the meaning of traces? t 1 t 1 t 1 s u t 0 t 0 t 0 u s � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 1 M 2 M 3 ◮ M 1 : P 1 does its scan before P 0 does its update ◮ M 2 : P 0 does its scan before P 1 does its update ◮ M 1 : P 1 does not know the current value of P 0 but P 0 does ◮ M 2 : P 0 does not know the current value of P 1 but P 1 does Eric Goubault, CEA LIST, Ecole Polytechnique 36 / 68

  19. What is the meaning of traces? t 1 t 1 t 1 s s u u t 0 t 0 t 0 u s u s � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 1 M 2 M 3 ◮ M 1 : P 1 does its scan before P 0 does its update ◮ M 2 : P 0 does its scan before P 1 does its update ◮ M 3 : P 0 and P 1 do update, then do there scan together ◮ M 1 : P 1 does not know the current value of P 0 but P 0 does ◮ M 2 : P 0 does not know the current value of P 1 but P 1 does ◮ M 3 : P 0 and P 1 know their values Eric Goubault, CEA LIST, Ecole Polytechnique 36 / 68

  20. Link with the protocol complex t 1 t 1 t 1 t 0 t 0 t 0 � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 Protocol complex: � 0 . 11 � 1 . 11 � 0 . 10 1 . 01 (1 . 01 (resp. 0 . 10) means P 1 (resp. P 0 ) knows only its own value; 1 . 11 (resp. 0 . 11) means P 1 (resp. P 0 ) knows all values) Eric Goubault, CEA LIST, Ecole Polytechnique 37 / 68

  21. Link with the protocol complex t 1 t 1 t 1 t 0 t 0 t 0 � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 1 Protocol complex: 1 . 01 M 1 � 0 . 11 � 1 . 11 � 0 . 10 Eric Goubault, CEA LIST, Ecole Polytechnique 37 / 68

  22. Link with the protocol complex t 1 t 1 t 1 t 0 t 0 t 0 � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 1 M 3 Protocol complex: 1 . 01 M 1 � 0 . 11 M 3 � 1 . 11 � 0 . 10 M 3 differs from M 1 by just a 1 (connected) Eric Goubault, CEA LIST, Ecole Polytechnique 37 / 68

  23. Link with the protocol complex t 1 t 1 t 1 t 0 t 0 t 0 � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 1 M 2 M 3 Protocol complex: 1 . 01 M 1 � 0 . 11 M 3 � 1 . 11 M 2 � 0 . 10 M 3 differs from M 2 by just a 1 (connected) Eric Goubault, CEA LIST, Ecole Polytechnique 37 / 68

  24. This is actually the minimal transversal hypergraph! (vertices are indexes in the matrices, hitting sets are hyper-edges): . . t 1 t 1 t 1 t 0 t 0 t 0 . . � 1 � � 0 � � 0 � 0 1 1 1 0 0 1 1 0 M 2 M 3 M 1 M 1 M 2 M 3 Eric Goubault, CEA LIST, Ecole Polytechnique 38 / 68

  25. More rounds? clean-memory/layered immediate snapshot t 1 s u s u u s u s t 0 Iterated subdivision (fractal) of the protocol complex (round 1): 1 . 01 M 1 � 0 . 11 M 3 � 1 . 11 M 2 � 0 . 10 Eric Goubault, CEA LIST, Ecole Polytechnique 39 / 68

  26. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): � 0 . 1111) � 1 . 0111 � 0 . 1101 � 1 . 1101 1 . 0101 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  27. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): 11 � 0 . 1111) 1 � 1 . 0111 1 � 0 . 1101 � 1 . 1101 1 . 0101 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  28. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): 11 � 0 . 1111) 13 � 1 . 0111 1 � 0 . 1101 � 1 . 1101 1 . 0101 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  29. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): 11 � 0 . 1111) 13 � 1 . 0111 12 � 0 . 1101 � 1 . 1101 1 . 0101 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  30. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): 31 � 1 . 1101 � 0 . 1111) � 1 . 0111 � 0 . 1101 1 . 0101 3 3 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  31. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): 31 � 1 . 1101 � 0 . 1111) � 1 . 0111 � 0 . 1101 1 . 0101 33 3 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  32. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): 31 � 1 . 1101 � 0 . 1111) � 1 . 0111 � 0 . 1101 1 . 0101 33 32 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  33. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): � 0 . 1111) � 1 . 0111 � 0 . 1101 � 1 . 1101 1 . 0101 2 2 21 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  34. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): � 0 . 1111) � 1 . 0111 � 0 . 1101 � 1 . 1101 1 . 0101 2 23 21 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  35. � � � � � Clean-memory model t 1 t 0 Iterated subdivision (fractal) of the protocol complex (round 2): � 0 . 1111) � 1 . 0111 � 0 . 1101 � 1 . 1101 1 . 0101 22 23 21 0 . 0101 1 . 1111 0 . 0111 1 . 1101 0 . 1111 Eric Goubault, CEA LIST, Ecole Polytechnique 40 / 68

  36. Hence Theorem The clean memory model for n processes at round r produces a subdivided n simplex (up to some “flares” which do not affect ( n − 1)-connectedness) (The flares are ruled out, classically, by the layered execution requirement) ◮ Clear relation with underlying geometric semantics ◮ All is fine, but is there a new result here? Not yet... Eric Goubault, CEA LIST, Ecole Polytechnique 41 / 68

  37. Example: same-memory model Much more complicated! But fits in our framework perfectly t 1 t 0 Eric Goubault, CEA LIST, Ecole Polytechnique 42 / 68

  38. Example: same-memory model Much more complicated! But fits in our framework perfectly t 1 t 0 → each block (1 unfolding) creates an ( n − 1)-connected complex Eric Goubault, CEA LIST, Ecole Polytechnique 42 / 68

  39. Example: same-memory model Much more complicated! But fits in our framework perfectly t 1 t 0 → each block (1 unfolding) creates an ( n − 1)-connected complex → glued under some recurrence relation Eric Goubault, CEA LIST, Ecole Polytechnique 42 / 68

  40. Example: same-memory model Much more complicated! But fits in our framework perfectly t 1 t 0 → each block (1 unfolding) creates an ( n − 1)-connected complex → glued under some recurrence relation → whose relations make it a contractible scheme for pasting blocks Eric Goubault, CEA LIST, Ecole Polytechnique 42 / 68

  41. Example: same-memory model Much more complicated! But fits in our framework perfectly t 1 t 0 → each block (1 unfolding) creates an ( n − 1)-connected complex → glued under some recurrence relation → whose relations make it a contractible scheme for pasting blocks → hence (nerve lemma), creates an ( n − 1)-connected protocol complex! (not previously described, as this does not create an iterated subdivided simplex) Eric Goubault, CEA LIST, Ecole Polytechnique 42 / 68

  42. In general...: interval posets and schedules Interval posets ◮ Let S be a set of closed intervals in R (i.e. of elements of the form [ a , b ], a , b in R ) ◮ We define the partial order: [ a , b ] � [ c , d ] ⇔ b � c ◮ ( S , � ) is called an interval poset ◮ Are very well described, combinatorially ◮ For instance Fishburn’s theorem (equivalence with (2+2)-free posets) ◮ And number of such posets on n elements is well known, example: 1,3,19,207,3451, . . . (this is A079144 on OEIS) Eric Goubault, CEA LIST, Ecole Polytechnique 43 / 68

  43. Theorem The dihomotopy classes of maximal paths, for the 1-round scan/update model for n processes, is in bijection with the interval posets on n elements. The bijection associates to each dihomotopy class [ p ] the set of intervals in [0 , 1] ( p ◦ π i ) − 1 ([ u i , s i ]) ( i = 1 , . . . , n ) Proof relies on the characterization of dihomotopy classes through alive matrices, hence dead matrices - recall condition on being dead, as some interval inequalities! Eric Goubault, CEA LIST, Ecole Polytechnique 44 / 68

  44. Example, in dimension 2 t 1 t 1 t 1 s 2 s 2 s 2 0 0 0 u 2 u 2 u 2 1 1 1 t 0 t 0 t 0 u 1 s 1 u 1 s 1 u 1 s 1 [ u 2 , s 2 ] < [ u 1 , s 1 ] [ u 1 , s 1 ] , [ u 2 , s 2 ] [ u 2 , s 2 ] < [ u 1 , s 1 ] Eric Goubault, CEA LIST, Ecole Polytechnique 45 / 68

  45. What is the structure of the protocol complex now? Extension order on posets Let ( S 1 � 1 ) and ( S 2 , � 2 ) be two partial order on some sets S 1 ⊆ S 2 . We say that � 1 ⇒ � 2 if ∀ s , t ∈ S 1 , s � 1 t ⇒ s � 2 t . When S 1 = S 2 , this is the linearization order. Importance of the extension order for our purpose Let � 1 and � 2 be interval orders on the same set of cardinal n + 1. If � 1 is a linearization of � 2 then the corresponding n -simplexes share a common ( n − 1) face. In fact, the face poset of the protocol complex is given by the extension order on interval posets up to n elements Eric Goubault, CEA LIST, Ecole Polytechnique 46 / 68

  46. Structure of the protocol complex Corollary The protocol complex for scan/update in dimension n , for one round, is homotopy equivalent to the order complex for the extension order on interval posets up to n elements. (since the order complex of the face poset is just the barycentric subdivision) Theorem The protocol complex for the scan/update model, in dimension n , for one round, is an ( n − 1)-connected simplicial set. It is a subdivision of ∆[ n ] plus some extra contractible “flares”. The flares are ruled out, classically, by the layered execution requirement Eric Goubault, CEA LIST, Ecole Polytechnique 47 / 68

  47. Trace space 19 maximal alive matrices (for 53 dead ones) 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 Eric Goubault, CEA LIST, Ecole Polytechnique 48 / 68

  48. Reorganizing things a bit... 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 4 2 0 3 3 0 2 3 1 2 4 0 1 4 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 4 1 1 3 2 1 3 1 2 2 2 2 1 3 2 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 4 2 1 2 3 0 3 3 4 0 2 3 0 3 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 2 1 3 2 0 4 1 1 4 0 2 4 Eric Goubault, CEA LIST, Ecole Polytechnique 49 / 68

  49. 1 of symmetry type (2,2,2) 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 4 2 0 3 3 0 2 3 1 2 4 0 1 4 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 4 1 1 3 2 1 3 1 2 2 2 2 1 3 2 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 4 2 1 2 3 0 3 3 4 0 2 3 0 3 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 2 1 3 2 0 4 1 1 4 0 2 4 Eric Goubault, CEA LIST, Ecole Polytechnique 50 / 68

  50. 6 of symmetry type (3,2,1) 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 4 2 0 3 3 0 2 3 1 2 4 0 1 4 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 4 1 1 3 2 1 3 1 2 2 2 2 1 3 2 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 4 2 1 2 3 0 3 3 4 0 2 3 0 3 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 2 1 3 2 0 4 1 1 4 0 2 4 Eric Goubault, CEA LIST, Ecole Polytechnique 51 / 68

  51. 3 of symmetry type (3,3,0) 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 4 2 0 3 3 0 2 3 1 2 4 0 1 4 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 4 1 1 3 2 1 3 1 2 2 2 2 1 3 2 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 4 2 1 2 3 0 3 3 4 0 2 3 0 3 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 2 1 3 2 0 4 1 1 4 0 2 4 Eric Goubault, CEA LIST, Ecole Polytechnique 52 / 68

  52. 3 of symmetry type (4,1,1) 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 4 2 0 3 3 0 2 3 1 2 4 0 1 4 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 4 1 1 3 2 1 3 1 2 2 2 2 1 3 2 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 4 2 1 2 3 0 3 3 4 0 2 3 0 3 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 2 1 3 2 0 4 1 1 4 0 2 4 Eric Goubault, CEA LIST, Ecole Polytechnique 53 / 68

  53. 6 of symmetry type (4,2,0) 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 4 2 0 3 3 0 2 3 1 2 4 0 1 4 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 4 1 1 3 2 1 3 1 2 2 2 2 1 3 2 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 4 2 1 2 3 0 3 3 4 0 2 3 0 3 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 2 1 3 2 0 4 1 1 4 0 2 4 Eric Goubault, CEA LIST, Ecole Polytechnique 54 / 68

  54. Corresponding to the labelled interval posets on 3 elements (19 of them) (2,2,2) a b c Eric Goubault, CEA LIST, Ecole Polytechnique 55 / 68

  55. Corresponding to the labelled interval posets on 3 elements (19 of them) (3,2,1) a c a b a b c b c a b c b a c c b b a c a Eric Goubault, CEA LIST, Ecole Polytechnique 55 / 68

  56. Corresponding to the labelled interval posets on 3 elements (19 of them) (3,3,0) a c a b a b c b c a b c b a c c a c b b c a b b a b c a a c Eric Goubault, CEA LIST, Ecole Polytechnique 55 / 68

  57. Corresponding to the labelled interval posets on 3 elements (19 of them) (4,1,1) a c a b a b c b c a b c b a c c a c b b c a b b a b c a a c a c b b c a b a c Eric Goubault, CEA LIST, Ecole Polytechnique 55 / 68

  58. Corresponding to the labelled interval posets on 3 elements (19 of them) (4,2,0) a c a b a b c b c a b c b a c c a c b b c a b b a b c a a c c b a c b b c b c a b a c a a c a a b a c b a b b c c Eric Goubault, CEA LIST, Ecole Polytechnique 55 / 68

  59. Example, in dimension 3 Hasse diagram of the corre- t 1 sponding interval poset: [ u 0 , s 0 ] [ u 1 , s 1 ] [ u 2 , s 2 ] (let us call a = [ u 0 , s 0 ], b = t 0 [ u 1 , s 1 ], c = [ u 2 , s 2 ] for the se- t 2 quel) Eric Goubault, CEA LIST, Ecole Polytechnique 56 / 68

  60. Example: in dimension 3 (the 18 other schedules) t 1 t 1 t 1 t 0 t 0 t 0 t 2 t 2 t 2 t 1 t 1 t 1 t 0 t 0 t 0 t 2 t 2 t 2 Eric Goubault, CEA LIST, Ecole Polytechnique 57 / 68

  61. Example: in dimension 3 (the 18 other schedules) t 1 t 1 t 1 t 0 t 0 t 0 t 2 t 2 t 2 t 1 t 1 t 1 t 0 t 0 t 0 t 2 t 2 t 2 Eric Goubault, CEA LIST, Ecole Polytechnique 58 / 68

  62. Example: in dimension 3 (the 18 other schedules) t 1 t 1 t 1 t 0 t 0 t 0 t 2 t 2 t 2 t 1 t 1 t 1 t 0 t 0 t 0 t 2 t 2 t 2 Eric Goubault, CEA LIST, Ecole Polytechnique 59 / 68

  63. Logical interpretation Each interval can be interpreted in terms of “knowledge”, hence the structure of the protocol complex... a c b a b c b c a b a c { 0 . 111 , 1 . 111 , 2 . 111 } { 0 . 111 , 1 . 011 , 2 . 011 } { 0 . 110 , 1 . 110 , 2 . 111 } { 0 . 101 , 1 . 111 , 2 . 101 } a c b b c c b b a c a a { 0 . 111 , 1 . 011 , 2 . 011 } { 0 . 110 , 1 . 110 , 2 . 111 } { 0 . 101 , 1 . 111 , 2 . 101 } { 0 . 100 , 1 . 111 , 2 . 111 } a c a a b b b b c c a c { 0 . 111 , 1 . 010 , 2 . 111 } { 0 . 111 , 1 . 011 , 2 . 011 } { 0 . 111 , 1 . 111 , 2 . 001 } { 0 . 101 , 1 . 111 , 2 . 101 } etc. Eric Goubault, CEA LIST, Ecole Polytechnique 60 / 68

  64. Construction of the protocol complex Eric Goubault, CEA LIST, Ecole Polytechnique 61 / 68

  65. Construction of the protocol complex These are ruled out under the layered execution model Eric Goubault, CEA LIST, Ecole Polytechnique 61 / 68

  66. Construction of the protocol complex Eric Goubault, CEA LIST, Ecole Polytechnique 61 / 68

  67. Construction of the protocol complex Eric Goubault, CEA LIST, Ecole Polytechnique 61 / 68

  68. Construction of the protocol complex Eric Goubault, CEA LIST, Ecole Polytechnique 61 / 68

  69. Trace spaces: prodsimplicial structure ◮ A prod-simplicial space is just a space made up of simplices, and products of simplices, glued together along their faces (natural generalization of cubical and simplicial sets) Eric Goubault, CEA LIST, Ecole Polytechnique 62 / 68

  70. Trace spaces: prodsimplicial structure ◮ A prod-simplicial space is just a space made up of simplices, and products of simplices, glued together along their faces (natural generalization of cubical and simplicial sets) ◮ Example: Eric Goubault, CEA LIST, Ecole Polytechnique 62 / 68

  71. The prodsimplicial structure of trace spaces Each matrix of C represents a prod-simplex, product of one n -simplex per line, n =number of 1 per line minus 1... Recall: t 1 t 0 � 0 � 1 M 3 = 1 0 product of 2 0-simplices = point! Eric Goubault, CEA LIST, Ecole Polytechnique 63 / 68

  72. The prodsimplicial structure of trace spaces Each matrix of C represents a prod-simplex, product of one n -simplex per line, n =number of 1 per line minus 1... ◮ D ( X )(0 , 1) = { (111) } ◮ C ( X )(0 , 1) = { (110) , (101) , (011) } ◮ (0 1 1) (1 0 1) (1 1 0) Eric Goubault, CEA LIST, Ecole Polytechnique 63 / 68

  73. The prodsimplicial structure of trace spaces Each matrix of C represents a prod-simplex, product of one n -simplex per line, n =number of 1 per line minus 1... ◮ C ( X )(0 , 1) = { (110) , (101) , (011) } ◮ and common faces are meet of matrices (0 0 1) (0 1 1) (1 0 1) (0,1,0) (1 0 0) (1 1 0) Eric Goubault, CEA LIST, Ecole Polytechnique 63 / 68

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

BFTCBFTP: BYZANTINE-FAULT -TOLERANT CONSTRUCTION OF BFT PROTOCOLS EDWARD TREMEL SIGSEGV 2019

BFTCBFTP: BYZANTINE-FAULT -TOLERANT CONSTRUCTION OF BFT PROTOCOLS EDWARD TREMEL SIGSEGV 2019

BFTCBFTP: BYZANTINE-FAULT -TOLERANT CONSTRUCTION OF BFT PROTOCOLS EDWARD TREMEL SIGSEGV 2019 BYZANTINE FAULT TOLERANCE Long-standing problem in systems Byzantine (adj): excessively complicated, and typically involving a great deal of

685 views • 19 slides
Lecture 10: Fault Tolerance Fault Tolerant Concurrent Computing The main principles of fault

Lecture 10: Fault Tolerance Fault Tolerant Concurrent Computing The main principles of fault

Lecture 10: Fault Tolerance Fault Tolerant Concurrent Computing The main principles of fault tolerant programming are: Fault Detection - Knowing that a fault exists Fault Recovery - having atomic instructions that can be rolled back in

361 views • 18 slides
Fault-tolerant techniques Fault-tolerant techniques What causes component faults? What are the

Fault-tolerant techniques Fault-tolerant techniques What causes component faults? What are the

EDA421/DIT171 - Parallel and Distributed Real-Time Systems, Chalmers/GU, 2011/2012 Lecture #14 Updated May 2, 2012 Fault-tolerant techniques Fault-tolerant techniques What causes component faults? What are the effects if the

374 views • 9 slides
FAULT-TOLERANT CONTROL Is it possible? JAN MACIEJOWSKI Fault- tolerant control. DPS09,

FAULT-TOLERANT CONTROL Is it possible? JAN MACIEJOWSKI Fault- tolerant control. DPS09,

FAULT-TOLERANT CONTROL Is it possible? JAN MACIEJOWSKI Fault- tolerant control. DPS09, Gdask Canonical Control Engineering Problem Disturbance Controlled output Set-point Filter Controller Plant Sensor Noise This problem is

639 views • 29 slides
On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols ICDCS 2017 Giuseppe Antonio Di Luna, Paola Flocchini, Taisuke Izumi, Tomoko Izumi, Nicola Santoro, Giovanni Viglietta Atlanta June 8, 2017

831 views • 46 slides
Adaptive Fault Tolerant Systems: Adaptive Fault Tolerant Systems: Reflective Design and

Adaptive Fault Tolerant Systems: Adaptive Fault Tolerant Systems: Reflective Design and

1 Adaptive Fault Tolerant Systems: Adaptive Fault Tolerant Systems: Reflective Design and Validation Reflective Design and Validation Marc-Olivier Killijian Dependable Computing and Fault Tolerance Research Group Toulouse - France 2

865 views • 50 slides
Presentation of the paper Proof-of-Execution: Reaching Consensus through Fault-Tolerant

Presentation of the paper Proof-of-Execution: Reaching Consensus through Fault-Tolerant

Presentation of the paper Proof-of-Execution: Reaching Consensus through Fault-Tolerant Speculation Presenter: Haojun (Howard) Zhu Background Due to time-tested safe design of PBFT and due to the limiting designs of other BFT protocols,

536 views • 26 slides
Making Byzantine Fault Tolerant Systems Tolerate Byzantine Faults Dian Yu 1/16 Comparison with

Making Byzantine Fault Tolerant Systems Tolerate Byzantine Faults Dian Yu 1/16 Comparison with

Making Byzantine Fault Tolerant Systems Tolerate Byzantine Faults Dian Yu 1/16 Comparison with PBFT (Traditional BFT protocols) Similarities: Build practical Byzantine fault tolerance systems Protocol: Clients Primary Replicas

493 views • 18 slides
Overview Introduction and basic concept ECE 753: FAULT-TOLERANT Fault model and fault

Overview Introduction and basic concept ECE 753: FAULT-TOLERANT Fault model and fault

4/1/2014 Overview Introduction and basic concept ECE 753: FAULT-TOLERANT Fault model and fault coverage COMPUTING Checkpointing and backward error recovery (rollback) Kewal K.Saluja General principles General principles

259 views • 3 slides
Fault-Tolerant Data Collection in Fault-Tolerant Data Collection in Heterogeneous Intelligent

Fault-Tolerant Data Collection in Fault-Tolerant Data Collection in Heterogeneous Intelligent

Fault-Tolerant Data Collection in Fault-Tolerant Data Collection in Heterogeneous Intelligent Monitoring Networks Networks Heterogeneous Intelligent Monitoring Jing Deng Department of Computer Science University of North Carolina at

335 views • 18 slides
A Fault-Tolerant Alternative to Lockstep Triple Modular Redundancy Andrew L. Baldwin, BS 09,

A Fault-Tolerant Alternative to Lockstep Triple Modular Redundancy Andrew L. Baldwin, BS 09,

A Fault-Tolerant Alternative to Lockstep Triple Modular Redundancy Andrew L. Baldwin, BS 09, MS 12 W. Robert Daasch, Professor Integrated Circuits Design and Test Laboratory Problem Statement In a fault tolerant system containing

478 views • 35 slides
Overview ECE 753: FAULT-TOLERANT Fault Modeling COMPUTING References Introduction

Overview ECE 753: FAULT-TOLERANT Fault Modeling COMPUTING References Introduction

1/21/2014 Overview ECE 753: FAULT-TOLERANT Fault Modeling COMPUTING References Introduction Kewal K.Saluja Kewal K Saluja Fault models at different levels (HW) Department of Electrical and Computer Engineering Error

304 views • 5 slides
4/22/2009 Designing highly available systems Incorporate elements of fault-tolerant design

4/22/2009 Designing highly available systems Incorporate elements of fault-tolerant design

4/22/2009 Designing highly available systems Incorporate elements of fault-tolerant design Replication, TMR Distributed Systems Fully fault tolerant system will offer non-stop availability Clusters You cant achieve this! Problem:

458 views • 11 slides
Verification and Validation of a Verification and Validation of a Fault- -Tolerant Architectural

Verification and Validation of a Verification and Validation of a Fault- -Tolerant Architectural

Verification and Validation of a Verification and Validation of a Fault- -Tolerant Architectural Abstraction Tolerant Architectural Abstraction Fault Patrick H. S. Brito - Unicamp, Brazil Rogrio de Lemos - University of Kent, UK Eliane

381 views • 21 slides
REVIEW OF FAULT TOLERANT TECHNIQUES FOR DIFFERENT TYPES OF GRAPHS BY- HATEM NASSRAT TARAK

REVIEW OF FAULT TOLERANT TECHNIQUES FOR DIFFERENT TYPES OF GRAPHS BY- HATEM NASSRAT TARAK

REVIEW OF FAULT TOLERANT TECHNIQUES FOR DIFFERENT TYPES OF GRAPHS BY- HATEM NASSRAT TARAK SHINGNE Outline General view of Fault Tolerance Ft-Design approaches Trees Meshes &amp; Hypercubes conclusion Introduction Fault

584 views • 44 slides
Idealised Fault Tolerant Idealised Fault Tolerant Architectural Element Architectural Element

Idealised Fault Tolerant Idealised Fault Tolerant Architectural Element Architectural Element

Idealised Fault Tolerant Idealised Fault Tolerant Architectural Element Architectural Element Rog rio rio de Lemos de Lemos Rog University of Kent, UK University of Kent, UK Motivation architectural fault tolerance; iFTE

350 views • 16 slides
Comparative Causality: Explaining the Differences Between Executions William N. Sumner Xiangyu

Comparative Causality: Explaining the Differences Between Executions William N. Sumner Xiangyu

Comparative Causality: Explaining the Differences Between Executions William N. Sumner Xiangyu Zhang {wsumner,xyzhang} @ cs.purdue.edu ICSE 2013 22 May 2013 Background Debugging requires understanding how a program behaves. Background

1.41k views • 122 slides
Dataflow Testing Chapter 10 Dataflow Testing Testing All-Nodes and All-Edges in a control

Dataflow Testing Chapter 10 Dataflow Testing Testing All-Nodes and All-Edges in a control

Dataflow Testing Chapter 10 Dataflow Testing Testing All-Nodes and All-Edges in a control flow graph may miss significant test cases Testing All-Paths in a control flow graph is often too time- consuming Can we select a subset of

682 views • 24 slides
Fault-tolerant quantum computing with color codes Andrew J. Landahl with Jonas T. Anderson and

Fault-tolerant quantum computing with color codes Andrew J. Landahl with Jonas T. Anderson and

' !&quot; ' !&quot; !* !* !! !! % $ !# ) !# ( !&amp; !&amp; !+' *+!&quot; !&quot;#$#%&amp;'()*+,&amp;-.&amp;&quot;#/-0#.$)(&amp;'#%-1#.&amp;&amp; &quot;#$% &amp; !% !$ !% !$ &amp;+!! #+!* % $ % $

325 views • 13 slides
An Empirical Study of Fault Localization Families and Their Combinations Daming Zou, Jingjing

An Empirical Study of Fault Localization Families and Their Combinations Daming Zou, Jingjing

An Empirical Study of Fault Localization Families and Their Combinations Daming Zou, Jingjing Liang, Yingfei Xiong, Michael D. Ernst, and Lu Zhang ESEC/FSE 2019 Journal First Paper on TSE Tallinn, Estonia 29 Aug 2019 Fault Localization (FL)

479 views • 16 slides
Recursive Restarts for HA We have crash-only components now what? Reduce recovery time

Recursive Restarts for HA We have crash-only components now what? Reduce recovery time

1/14/2003 Recursive Restarts for HA We have crash-only components now what? Reduce recovery time by doing partial restarts: attempt recovery of a minimal subset of components What if restart ineffective? recover progressively

324 views • 3 slides
Inferring Test Models from Kates Bug Reports using Multi-objective Search Yuanyuan Zhang

Inferring Test Models from Kates Bug Reports using Multi-objective Search Yuanyuan Zhang

Inferring Test Models from Kates Bug Reports using Multi-objective Search Yuanyuan Zhang Mark Harman Yue Jia and Federica Sarro University College London SSBSE 2015 Challenge Track Paper Which page should we put more effort to proofread?

589 views • 28 slides
hhhh Agenda O/S Applications RMS System management Troubleshooting tools

hhhh Agenda O/S Applications RMS System management Troubleshooting tools

1 Bruce Ellis &amp; Guy Peleg bruce.ellis@bruden.com guy.peleg@bruden.com BRUDEN-OSSG hhhh Agenda O/S Applications RMS System management Troubleshooting tools Simulators 2 Si vous naimez pas ma conduite,

631 views • 62 slides
Swapping Segmented paging allows us to have non- contiguous allocations But it still

Swapping Segmented paging allows us to have non- contiguous allocations But it still

Swapping Segmented paging allows us to have non- contiguous allocations But it still limits us to the size of physical RAM How can we avoid that? By keeping some segments somewhere else Where? Maybe on a disk Lecture 9 CS

393 views • 16 slides

More recommend