Automatic%20synthesis%20and%20verification%20of%20asynchronous%20interface%20controllers

1
Automatic synthesis and verification of
asynchronous interface controllers

• Jordi Cortadella Universitat Politècnica de
  Catalunya, Spain
• Michael Kishinevsky Intel Corporation, USA
• Alex Kondratyev Theseus Logic, USA
• Luciano Lavagno Università di Udine, Italy
• Enric Pastor Universitat Politècnica de
  Catalunya, Spain
• Marco A. Peña Universitat Politècnica de
  Catalunya, Spain
• Alexander Yakovlev University of Newcastle upon
  Tyne, UK

2
Specification(environment)
Implementation (circuit)
3
Why and why not?

• Asynchronous circuits robustness, modularity,
  less power consumption, low EMI, no clock skew
  and many other debatable advantages
• Designing correct async circuits is
  difficult(hazards, testing)
• Designing efficient async circuits is a nightmare
  (time comes into play)
• Design automation is crucial

4
How to make it asynchronous ?
5
Outline

• Synthesis flow with STGs
• Specification
• State graph and next-state functions
• State encoding
• Implementability conditions
• Logic decomposition
• Synthesis with relative timing assumptions
• Formal verification of timed circuits

6
Specification(STG)
Reachability analysis
State Graph
State encoding
SG withCSC
Design flow
Boolean minimization
Next-state functions
Logic decomposition
Decomposed functions
Technology mapping
Gate netlist
7
VME bus
8
STG for the READ cycle
DTACK-
DSr
LDS
LDTACK
D
DTACK
DSr-
D-
LDS-
LDTACK-
D
LDS
DSr
VME Bus Controller
LDTACK
DTACK
9
Specification(STG)
Reachability analysis
State Graph
State encoding
SG withCSC
Design flow
Boolean minimization
Next-state functions
Logic decomposition
Decomposed functions
Technology mapping
Gate netlist
10
Binary encoding of signals
DSr
DTACK-
LDS
LDTACK-
LDTACK-
LDTACK-
DSr
DTACK-
LDS-
LDS-
LDS-
LDTACK
DSr
DTACK-
D
D-
DSr-
DTACK
11
State graph
DSr
DTACK-
10000
LDS
LDTACK-
LDTACK-
LDTACK-
DSr
DTACK-
10010
LDS-
LDS-
LDS-
LDTACK
DSr
DTACK-
10110
01110
10110
D
D-
DSr-
DTACK
(DSr , DTACK , LDTACK , LDS , D)
12
Excitation / Quiescent Regions
13
Next-state function
0 ? 1
0 ? 0
1 ? 1
1 ? 0
14
Karnaugh map for LDS
LDS 1
LDS 0
-
-
-
0
1
-
0
1
-
-
-
-
-
-
-
-
1
1
1
-
-
-
-
-
0
0
0
0
0
0/1?
-
-
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Specification(STG)
Reachability analysis
State Graph
State encoding
SG withCSC
Design flow
Boolean minimization
Next-state functions
Logic decomposition
Decomposed functions
Technology mapping
Gate netlist
16
Concurrency reduction
LDS
LDS-
LDS-
LDS-
10110
10110
17
Concurrency reduction
DTACK-
DSr
LDS
LDTACK
D
DTACK
DSr-
D-
LDS-
LDTACK-
18
State encoding conflicts
LDS
LDTACK-
LDS-
LDTACK
10110
10110
19
Signal Insertion
LDTACK-
LDS
LDS-
LDTACK
101101
101100
D-
DSr-
20
Specification(STG)
Reachability analysis
State Graph
State encoding
SG withCSC
Design flow
Boolean minimization
Next-state functions
Logic decomposition
Decomposed functions
Technology mapping
Gate netlist
21
Complex-gate implementation
22
Implementability conditions

• Consistency CSC persistency
• There exists a speed-independent circuit that
  implements the behavior of the STG(under the
  assumption that ay Boolean function can be
  implemented with one complex gate)

23
Specification(STG)
Reachability analysis
State Graph
State encoding
SG withCSC
Design flow
Boolean minimization
Next-state functions
Logic decomposition
Decomposed functions
Technology mapping
Gate netlist
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No Hazards
25
Decomposition May Lead to Hazards
1000
1100
1100
0100
0110
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Decomposition example
27
x
y-
w
y
1001
1011
z-
z
w-
y
1000
0001
w
y
z
x
w-
z-
x
w
1010
0000
0101
0011
w-
z-
y
x
w
y
z
0010
0100
x-
z
y
x
z
y
0110
0111
x
z
y
28
s1
x
y-
w
s
1001
1011
y
z-
s-
z
w
1001
1000
z-
s-
y
w-
x
w
0011
0001
1000
1010
y
s-
x
w-
z-
w
x-
y
z
0000
0101
1010
z
w-
z-
y
x
0111
0010
0100
y
s
y
x
x
z
s0
z
0111
y
0110
29
s1
y-
y-
1001
1011
z-
s-
s-
w
1001
1000
z-
s-
y
w-
z-
w-
w
0011
0001
1000
1010
y
s-
x
w-
z-
x-
0000
0101
1010
y
x
x-
w-
z-
y
x
0111
0010
0100
s
s
y
x
z
s0
z
0111
0110
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Adding timing assumptions
DTACK-
DSr
LDS
LDTACK
D
DTACK
DSr-
D-
LDS-
LDTACK-
D
DTACK
LDS
map
csc
DSr
LDTACK
31
Bus
Data Transceiver
Device
D
LDS
DSr
VME Bus Controller
LDTACK
DTACK
D
DTACK
LDS
map
csc
DSr
LDTACK
32
Adding timing assumptions
DTACK-
DSr
LDS
LDTACK
D
DTACK
DSr-
D-
LDS-
LDTACK-
D
DTACK
LDS
map
csc
DSr
LDTACK
33
Adding timing assumptions
DTACK-
DSr
LDS
LDTACK
D
DTACK
DSr-
D-
LDS-
LDTACK-
D
DTACK
LDS
map
csc
DSr
LDTACK
34
State space domain
DSr
LDTACK-
35
State space domain
DSr
LDTACK-
36
State space domain
DSr
LDTACK-
Two more unreachable states
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Boolean domain
LDS 1
LDS 0
-
-
-
0
1
-
0
1
-
-
-
-
-
-
-
-
1
1
1
-
-
-
-
-
0
0
0
0
0
0/1?
-
-
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Boolean domain
LDS 1
LDS 0
-
-
-
0
1
-
0
1
-
-
-
-
-
-
-
-
1
1
1
-
-
-
-
-
0
0
-
0
0
1
-
-
One more DC vector for all signals
One state conflict is removed
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Netlist with one timing constraint
DTACK-
DSr
LDS
LDTACK
D
DTACK
DSr-
D-
LDS-
LDTACK-
D
DTACK
LDS
map
csc
DSr
LDTACK
40
Netlist with one timing constraint
DTACK-
DSr
LDS
LDTACK
D
DTACK
DSr-
D-
LDS-
LDTACK-
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Types of timing assumptions

• Environment slower (or faster) than the circuit
• Gate delay shorter than another gate delay
• Speculative enabling (events enabled beforethey
  must actually occur)
• Indistiguishable firing times of different
  events
• . . .

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Formal verification

• Implementability properties
• Consistency, persistency, state coding
• Behavioral properties (safeness, liveness)
• Mutual exclusion, ack after req,
• Equivalence checking
• Circuit ? Specification
• Circuit lt Specification

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x

• Property
• g must fire before d after having fired x

a
b
b
g
a
c
c
g
b
c
a
b
c
g
c
b
d
g
y
d
g
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Verifying asynchronous circuits

• Internal signals cannot be abstracted out(many
  more state signals and states)
• If delays must be taken into account, each gate
  is a component with delay
• Verification with timed automata results
  unmanageable (BDDs do not work) Gate
  counter state signal
• We need clever strategies to do symbolic model
  checking

45
x

• Timed Transition System
• (Manna, Pnueli)
• Transition System
• Min/Max Delays

a
b
b
g
a
c
c
b
c
c
g
d(a) ? 1,2 d(b) ? 1,2 d(c) ? 2.5,3 d(g) ?
0.5,0.5 d(d,x,y) ? 0,?)
c
y
d
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x
a
b
b
g
a
c
c
g
b
c
a
b
c
g
c
b
d
g
y
d
g
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x
x
a
b
a
g
c
b
c
d
d
g
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Maximum Time Separation (McMillan Dill, 1992)
x
1,2
1,2
a
b
0.5,0.5
2.5,3
g
c
0,?)
0,?)
d
max t(g) - t(d)
-2
49
Maximum Time Separation (McMillan Dill, 1992)
x
From absolute to relative timing
a
b
g
c
d
max t(g) - t(d)
-2
50
x
x
a
b
a
b
b
g
a
c
c
g
g
c
b
c
a
b
c
g
d
c
b
d
g
y
d
g
51
x
a
b
b
g
a
c
c
g
b
c
c
a
b
c
g
g
c
c
b
d
d
g
g
y
y
d
d
g
g
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x
x
a
a
b
b
g
c
g
g
c
b
c
b
c
g
d
c
b
d
g
d
g
53
x
x
a
a
b
b
g
c
g
c
b
c
c
g
d
c
d
54
x
a
b
b
g
a
c
b
c
a
g
g
c
c
d
g
y
y
d
d
g
55
x
b
x
a
c
a
b
c
a
g
g
c
c
d
g
d
d
g
56
x
b
x
a
c
a
b
c
g
g
c
c
d
d
57
x
a
b
b
g
a
b
g
g
c
c
y
y
d
d
58
x
a
b
b
g
a
b
g
g
c
c
y
y
d
d
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Border of failure states

• Failure trace

• Event structure

• Timing analysis

• Composition

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• Failure trace

• Event structure

• Timing analysis

• Composition

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Backannotation (sufficient timing constraints)
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Conclusions

• An asynchronous circuit is a concurrent system
  with processes (gates) and communication (wires)
• The synthesis and formal verification of
  asynchronous control circuits can be totally
  automated
• The theory of concurrency is crucial to formalize
  automatic synthesis and verification methods
• Existing tools at academia petrify, 3D, ATACS,
  Kronos, versify, etc.
• Industry starting to try Intel, Theseus,
  Cogency, IBM, ...