Implementation of an Interleaving Semantics for TLDA
1. Implementation of an
Interleaving Semantics for TLDA
Luhme XI
Niels Lohmann
nlohmann@informatik.hu-berlin.de
http://www.informatik.hu-berlin.de/~nlohmann/arbeit
7 May 2005
2. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
2
3. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts: Implementation
Examples
Outlook
2
4. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts: Implementation
Examples
! transitions update values Outlook
2
5. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
! Luhme XI
idle t1 pending critical idle
t2
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts: Implementation
Examples
! transitions update values Outlook
! …0f involved variables
2
6. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
! Luhme XI
idle t1 pending critical idle
t2
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts: Implementation
Examples
! transitions update values Outlook
! …0f involved variables
dom(t1)={agent1} dom(t2)={agent1, sem}
2
7. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
C
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts (continued): Implementation
Examples
Outlook
3
8. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
C
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts (continued): Implementation
Examples
! a cut can be understood as a global state Outlook
3
9. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
C0 C
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts (continued): Implementation
Examples
! a cut can be understood as a global state Outlook
! every run has an initial cut
3
10. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
C C'
! Luhme XI
idle t1 pending critical idle
1 0 1 0
idle t2 pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts (continued): Implementation
Examples
Outlook
4
11. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
C C'
! Luhme XI
idle t1 pending critical idle
1 0 1 0
idle t2 pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts (continued): Implementation
Examples
! when all possible transitions occur, the Outlook
successor cut C' is reached
4
12. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
C C'
! Luhme XI
idle t1 pending critical idle
1 0 1 0
idle t2 pending critical
Introduction to
§ TLDA
Semantics
Transition System
basic concepts (continued): Implementation
Examples
! when all possible transitions occur, the Outlook
successor cut C' is reached
! cuts C, C' and the occurred transitions
form a step 4
13. Introduction to TLDA
semantic model and basic concepts
The semantic model of TLDA is a run.
C C'
! Luhme XI
idle t1 pending critical idle
1 0 1 0
idle t2 pending critical
Introduction to
§
this cut cannot be reached with steps TLDA
Semantics
Transition System
basic concepts (continued): Implementation
Examples
! when all possible transitions occur, the Outlook
successor cut C' is reached
! cuts C, C' and the occurred transitions
form a step 4
14. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
constants
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
5
15. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
variables describing
values in current cut Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
5
16. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
! flexible variables ( )
Introduction to
TLDA
Semantics
variables describing values in successor cut
Transition System
Implementation
Examples
Outlook
5
17. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
! flexible variables ( )
Introduction to
! primed flexible variables ( ) TLDA
Semantics
variables describing Transition System
involvedness of sets Implementation
of flexible variables
Examples
Outlook
5
18. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
! flexible variables ( )
Introduction to
! primed flexible variables ( ) TLDA
Semantics
! ~-variables ( ) Transition System
Implementation
Examples
Outlook
5
19. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
! flexible variables ( )
Introduction to
! primed flexible variables ( ) TLDA
Semantics
! ~-variables ( ) Transition System
Implementation
! formulas Examples
Outlook
formulas evaluated in steps of a run
5
20. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
! flexible variables ( )
Introduction to
! primed flexible variables ( ) TLDA
Semantics
! ~-variables ( ) Transition System
Implementation
! formulas Examples
! step formulas Outlook
step formulas with only flexible variables
5
21. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
! flexible variables ( )
Introduction to
! primed flexible variables ( ) TLDA
Semantics
! ~-variables ( ) Transition System
Implementation
! formulas Examples
! step formulas Outlook
! state predicate step formulas with only flexible variables
5
22. Introduction to TLDA
syntax
syntactic elements:
! variables Luhme XI
! rigid variables ( )
! flexible variables ( )
Introduction to
! primed flexible variables ( ) TLDA
Semantics
! ~-variables ( ) Transition System
Implementation
! formulas Examples
! step formulas Outlook
! state predicate
! run formulas formulas evaluated in a whole run
5
23. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
6
24. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
6
25. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
6
26. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
6
27. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
6
28. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
Is there a transition
occurring in SC involving
both agent1 and sem?
6
29. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
Is there a transition
occurring in SC involving
both agent1 and sem?
6
30. Introduction to TLDA
evaluating formulas
evaluating step formulas:
C C'
! Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
6
31. Introduction to TLDA
evaluating formulas
evaluating step formulas:
There is no transition
C C'
! involving agent2. Luhme XI
idle pending critical idle
t
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Transition System
Implementation
Examples
Outlook
6
32. Introduction to TLDA
evaluating formulas
evaluating run formulas:
! Luhme XI
idle pending critical idle
t1 t2
1 0 1
idle pending
Introduction to
§ TLDA
Semantics
Transition System
? Implementation
Examples
Outlook
7
33. Introduction to TLDA
evaluating formulas
evaluating run formulas:
! Luhme XI
idle pending critical idle
t1 t2
1 0 1
idle pending
Introduction to
§ TLDA
Semantics
Transition System
? Implementation
Examples
Outlook
7
34. Introduction to TLDA
evaluating formulas
evaluating run formulas:
C0 C1 C2 C3
! Luhme XI
idle pending critical idle
t1 t2
1 0 1
idle pending
Introduction to
§ TLDA
Semantics
Transition System
? Implementation
Examples
Outlook
7
35. Introduction to TLDA
evaluating formulas
evaluating run formulas:
C0 C1 C2 C3
! Luhme XI
idle pending critical idle
t1 t2
1 0 1
idle pending
Introduction to
§ TLDA
Semantics
Transition System
? Implementation
Examples
Outlook
7
36. Introduction to TLDA
evaluating formulas
evaluating run formulas:
C0 C1 C2 C3
! Luhme XI
idle pending critical idle
t1 t2
1 0 1
idle pending
Introduction to
§ TLDA
Semantics
!
?
Transition System
Implementation
Examples
Outlook
7
37. Semantics
partial ordered semantics
! TLDA: partial order semantics
! transitions are partially ordered Luhme XI
1 u1 0 u2 1
Introduction to
u1 occurs before u2 TLDA
Semantics
Transition System
! concurrent transitions have no order Implementation
Examples
Outlook
idle pending Which
t1
transition
idle t2 pending occurs first?
8
38. Semantics
interleaving semantics
! other formalisms (e.g. TLA):
interleaving semantics Luhme XI
! all possible interleavings of transitions
idle t1 pending t2 pending First t1,
idle idle pending then t2! Introduction to
TLDA
idle t2 idle t1 pending Semantics
idle pending pending First t2, Transition System
then t1! Implementation
idle {t1, t2} pending Examples
idle pending Outlook
t1 and t2 occur
concurrently!
! totally ordered
! exponential number of interleavings
and intermediate states 9
39. Semantics for TLDA
interleaving semantics
first subject of my work: development of
an interleaving semantics for TLDA Luhme XI
! model checking:
! few experiences with partial order
semantics (complicated data structures) Introduction to
TLDA
! interleavings can be easily represented by a Semantics
Transition System
labelled graph (transition system) Implementation
Examples
! explicit model checkers (LoLA, Spin) base Outlook
on graph search in a transition system
! Next subject: build a transition system 10
40. Transition System
definition
formally a quintuple TS = (S, S0, Act, R, L)
Luhme XI
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
sem ! 1 sem ! 0 sem ! 1
s0 s1 s2
11
41. Transition System
definition
formally a quintuple TS = (S, S0, Act, R, L)
! S: nonempty set of states Luhme XI
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
sem ! 1 sem ! 0 sem ! 1
s0 s1 s2
11
42. Transition System
definition
formally a quintuple TS = (S, S0, Act, R, L)
! S: nonempty set of states Luhme XI
! S0 " S: nonempty set of initial states
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
sem ! 1 sem ! 0 sem ! 1
s0 s1 s2
11
43. Transition System
definition
formally a quintuple TS = (S, S0, Act, R, L)
! S: nonempty set of states Luhme XI
! S0 " S: nonempty set of initial states
! Act: finite set of actions Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
{a2, a3}
sem ! 1 sem ! 0 sem ! 1
{a0} {a1}
s0 s1 s2
11
44. Transition System
definition
formally a quintuple TS = (S, S0, Act, R, L)
! S: nonempty set of states Luhme XI
! S0 " S: nonempty set of initial states
! Act: finite set of actions Introduction to
TLDA
! R " S # (Act) # S: transition relation, labeled Semantics
with a nonempty set of actions Transition System
Implementation
Examples
Outlook
{a2, a3}
sem ! 1 sem ! 0 sem ! 1
{a0} {a1}
s0 s1 s2
11
45. Transition System
definition
formally a quintuple TS = (S, S0, Act, R, L)
! S: nonempty set of states Luhme XI
! S0 " S: nonempty set of initial states
! Act: finite set of actions Introduction to
TLDA
! R " S # (Act) # S: transition relation, labeled Semantics
with a nonempty set of actions Transition System
Implementation
! L: S " (Var " Val): function to label states Examples
with a mapping variables/values Outlook
{a2, a3}
sem ! 1 sem ! 0 sem ! 1
{a0} {a1}
s0 s1 s2
11
46. Transition System
construction
We can construct a transition system TS!
for TLDA specifications ! in normal form: Luhme XI
! Definition: normal form: Introduction to
TLDA
! , Init $ Next $ Progress Semantics
Transition System
state predicate step formula ignored right now Implementation
Examples
Outlook
! Actions:
Act is the set of the clauses of the
disjunctive normal form of Next. 12
47. Transition System
construction
! States, initial states, labels
C0
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
For each cut reachable with steps from C0, Transition System
Implementation
add a new state and label it. Examples
sC Outlook
0
13
48. Transition System
construction
! States, initial states, labels
C0 C1
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
For each cut reachable with steps from C0, Transition System
Implementation
add a new state and label it. Examples
sC sC Outlook
0 1
13
49. Transition System
construction
! States, initial states, labels
C0 C1 C2
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
For each cut reachable with steps from C0, Transition System
Implementation
add a new state and label it. Examples
sC sC sC Outlook
0 1 2
Repeat this for all runs of !. 13
50. Transition System
construction
! Transition relation:
C0 C1 C2
! Luhme XI
idle pending critical idle
1 0 1 0
idle pending critical
Introduction to
§ TLDA
Semantics
Each step fulfils a set of clauses Ai of Next. Transition System
Implementation
Label the new transition relation with Ai (Ai " Act). Examples
sC sC sC Outlook
0 1 2
A0 A1
Repeat this for all runs of !. 14
51. Transition System
properties
properties of TS!:
Luhme XI
! For all runs of !, for all cuts C reachable
with steps from the initial cut, there Introduction to
exists a corresponding state sC in TS! TLDA
Semantics
reachable from an initial state. Transition System
Implementation
! For all states sC in TS! reachable from Examples
Outlook
an initial state, there exists a run of !
with a corresponding cut C reachable
with steps from the initial cut.
15
52. Transition System
properties
Do we reach all cuts with steps from C0?
Luhme XI
!* C0 C1 C2 C3
idle t1 pending critical idle
t2 t4 Introduction to
1 0 1 0 TLDA
t5
idle t3 pending critical Semantics
§ Transition System
" u1 " u2 " " Implementation
Examples
Outlook
16
53. Transition System
properties
Do we reach all cuts with steps from C0?
Luhme XI
!* C0 C1 C2 C* C3
idle t1 pending critical idle
t2 t4 Introduction to
1 0 1 0 TLDA
t5
idle t3 pending critical Semantics
§ Transition System
" u1 " u2 " " Implementation
Examples
Outlook
16
54. Transition System
properties
Do we reach all cuts with steps from C0?
Luhme XI
!* C0 C1 C2 C* C3
idle t1 pending critical idle
t2 t4 Introduction to
1 0 1 0 TLDA
t5
idle t3 pending critical Semantics
§ Transition System
" u1 " u2 " " Implementation
Examples
Outlook
16
55. Transition System
properties
Do we reach all cuts with steps from C0?
Luhme XI
!* C0 C1 C2 C*
idle t1 pending critical idle
t2 t4 Introduction to
1 0 1 0 TLDA
t5
idle t3 pending critical Semantics
Transition System
" u1 " u2 " " Implementation
Examples
§
Outlook
16
56. Transition System
properties
Do we reach all cuts with steps from C0? !
Luhme XI
!* C0 C1 C2 C*
idle t1 pending critical idle
t2 t4 Introduction to
1 0 1 0 TLDA
t5
idle t3 pending critical Semantics
Transition System
" u1 " u2 " " Implementation
Examples
§
Outlook
16
57. Transition System
properties
Does "# ⊨ ! hold? Not necessarily!
Luhme XI
But it always holds for environment
invariant formulas. Introduction to
TLDA
Semantics
Transition System
Can be understood literally: Implementation
A formula ! is called environment invariant Examples
Outlook
i! for all runs " with " ⊨ ! holds:
when "# has the same restrictions on the
system variables as ", then "# ⊨ !.
17
58. Transition System
properties revised
Properties of TS! (! environment
invariant): Luhme XI
! For all runs of !, for all cuts C reachable
with steps from the initial cut, there Introduction to
exists a corresponding state sC in TS! TLDA
Semantics
reachable from an initial state. Transition System
Implementation
! For all states sC in TS! reachable from Examples
Outlook
an initial state, there exists a run of !
with a corresponding cut C reachable
with steps from the initial cut.
18
59. Transition System
propositions
Properties of TS! (! environment
invariant): Luhme XI
1. Every cut is represented by a state.
2. Every run is represented by a sequence of Introduction to
states beginning at an initial state. TLDA
Semantics
3. Every state represents a cut. Transition System
Implementation
4. Every sequence of states beginning at an Examples
initial state represents a run. Outlook
All interleavings of ! are contained in TS!.
! TS! is a TLDA interleaving semantics. 19
60. Implementation
overview
second subject of my work:
the prototypic implementation “TLDC” Luhme XI
! present features:
! parse a TLDA specification
Introduction to
! build a DNF-tree TLDA
Semantics
! discard irrelevant/contradicting actions Transition System
! create C-code to build the transition system Implementation
Examples
! future: Outlook
! better heuristics
! TLDA model checking
! reduction techniques 20
61. Implementation
pruning heuristics
creation of actions/pruning of contradictions
Luhme XI
DNF-tree (n=4)
Introduction to
TLDA
" "
Semantics
Transition System
" " Implementation
Examples
Outlook
" "
21
62. Implementation
pruning heuristics
creation of actions/pruning of contradictions
Luhme XI
DNF-tree (n=4)
Introduction to
TLDA
" "
Semantics
Transition System
" " Implementation
Examples
Outlook
" "
21
63. Implementation
pruning heuristics
creation of actions/pruning of contradictions
Luhme XI
DNF-tree (n=4)
Introduction to
TLDA
" "
Semantics
Transition System
" " Implementation
Examples
Outlook
" "
21
64. Implementation
pruning heuristics
creation of actions/pruning of contradictions
Luhme XI
DNF-tree (n=4)
Introduction to
TLDA
" "
Semantics
Transition System
" " Implementation
Examples
Outlook
" "
21
65. Implementation
pruning heuristics
creation of actions/pruning of contradictions
Luhme XI
DNF-tree (n=4)
Introduction to
TLDA
" "
Semantics
Transition System
" " Implementation
Examples
Outlook
" "
21
66. Implementation
pruning heuristics
creation of actions/pruning of contradictions
Luhme XI
DNF-tree (n=4)
# " "
Introduction to
TLDA
Semantics
Transition System
" " Implementation
Examples
Outlook
" "
21
67. Implementation
pruning heuristics
creation of actions/pruning of contradictions
Luhme XI
DNF-tree (n=4)
Introduction to
TLDA
" "
Semantics
Transition System
" " Implementation
Examples
continue here… Outlook
" "
21
68. Implementation
gaining knowledge
treating ~-variables
! most actions contradict because of Luhme XI
~-variables
! ! “the more, the better”
Introduction to
! a lot of knowledge can be gained: TLDA
Semantics
! d Transition System
Implementation
! Examples
Outlook
!
!
! "
22
69. Examples
mutual exclusion
Luhme XI
requesting1 requesting2
Introduction to
TLDA
critical1 critical2 Semantics
Transition System
semaphore Implementation
idle1 idle2 Examples
Outlook
23
70. Examples
mutual exclusion
First example: mutual exclusion
! Petri net Luhme XI
requesting1 requesting2
Introduction to
TLDA
critical1 critical2 Semantics
Transition System
semaphore Implementation
idle1 idle2 Examples
Outlook
! TLDA: three components/variables 23
71. Examples
mutual exclusion
Luhme XI
Introduction to
TLDA
Semantics
Transition System
Tool demonstration #1 Implementation
Examples
Outlook
24
72. Examples
mutual exclusion
Luhme XI
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
state inscriptions:
agent1 agent2 semaphore
25
73. Examples
mutual exclusion
Luhme XI
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
state inscriptions:
agent1 agent2 semaphore
25
74. Examples
mutual exclusion
Luhme XI
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
state inscriptions:
agent1 agent2 semaphore
25
75. Examples
crossing the river
! Second example:
! farmer bought a wolf, a goat and cabbage Luhme XI
! all have to cross a river with a small boat
! the farmer can only take one thing with him
Introduction to
! left unattended, the goat eats the cabbage TLDA
Semantics
! left unattended, the wolf eats the goat Transition System
Implementation
Examples
Outlook
Can they cross the river safely? 26
76. Examples
crossing the river
Luhme XI
Introduction to
TLDA
Semantics
Transition System
Tool demonstration #2 Implementation
Examples
Outlook
27
77. Examples
crossing the river
state inscriptions:
Luhme XI
farmer goat wolf cabbage
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
28
78. Examples
crossing the river
initial state (all at east side of the river)
state inscriptions:
Luhme XI
farmer goat wolf cabbage
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
28
79. Examples
crossing the river
initial state (all at east side of the river)
state inscriptions:
Luhme XI
farmer goat wolf cabbage
Introduction to
TLDA
Semantics
Transition System
Implementation
Examples
Outlook
goal state
(all at west
side of the river) 28
80. Outlook
problems
! many exponential problems:
! disjunctive normal form: Luhme XI
Peterson’s Mutex-algorithm could not yet
be modelled: few lines of TLDA end up in
milliards of actions. (pruning at its limits) Introduction to
TLDA
! ~-variables: Semantics
Dining philosophers’ problem could not Transition System
Implementation
yet be modelled: 5 forks and 5 philosophers Examples
lead to 1023 ~-variables and 2046 variables Outlook
in C++. (a new data structure might help)
! actions:
step-explosion (Stephan Roch’s work)
29
81. Outlook
future/further work
! TLDA inapplicable for explicit model
checking? Luhme XI
! Would symbolic model checking help?
Introduction to
TLDA
Semantics
! Any solutions for open problems? Transition System
Implementation
Examples
Outlook
! Any questions about my Studienarbeit?
! Ideas for subjects for a Diplomarbeit? 30
82. Implementation of an
Interleaving Semantics for TLDA
Thank you!
Niels Lohmann
nlohmann@informatik.hu-berlin.de
http://www.informatik.hu-berlin.de/~nlohmann/arbeit
7 May 2005