EE 5940: Circuits, Computation and Biology

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EE 5940 Circuits, Computation and Biology
Marc D. Riedel
Assistant Professor, ECE University of Minnesota
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Analysis of Digital Circuits
Large domain, small range.
inputs
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Analysis of Digital Circuits
Large domain, small range.
inputs
2m possibilities
2 possibilities
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Data Structures
Truth Tables
Example
4 rows
2 variables
8 rows
3 variables
264 rows
64 variables
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Data Structures
Decision Diagrams
Example
x1
x2
x3
f
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Data Structures
Decision Diagrams
Optimize by merging nodes
x3
x3
x3
x3
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Data Structures
Decision Diagrams
S
Optimize by merging nodes
x1
1
0
x2
1
x3
x3
x3
0
1
0
1
1
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Data Structures
Decision Diagrams
Optimize by merging nodes
x2
x2
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Data Structures
Decision Diagrams
S
Optimize by merging nodes
x1
0
x2
1
0
x3
1
0
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Data Structures
Logic Operations

AND
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Decision Diagrams
Vibrant area of research

• Introduced by Lee (1959), popularized by Bryant
  (1986)
• Used in logic design, verification, artificial
  intelligence, etc.

Properties

• Canonical unique up to variable ordering
• Compact represent functions of up to 1000
  variables
• Efficient perform logic operations in
  linear-time

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Analysis of Systems of Chemical Equations
Large domain, small range?
For m species, each with max. quantity N
inputs
?
Yes/No
Nm possibilities
Yes/No possibilities
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System of Chemical Equations
Discrete Quantities of Molecular Species
Types of Questions

• Can a certain state, S1, be transformed into
  another state, S2? If so, in how many different
  ways? S2

• Can S1 be transformed into S2 without passing
  through a third state S3?

• Can S1 be reached from at least one state in a
  set of states T? From all the states in a set of
  states U?

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Decision Diagrams
e.g., set of possible initial states
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Decision Diagrams
e.g., set of possible initial states
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System of Chemical Equations
State Evolution
R1 occurs
or
R2 occurs
state before
state after
or
R3 occurs
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Decision Diagrams
reaction 1 occurs
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Decision Diagrams
reaction 2 occurs
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Decision Diagrams
reaction 3 occurs
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Decision Diagrams
Reachable States After The Next Reaction
S1
or
S2
or
S3
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Decision Diagrams
Evolution of Reachable States
S
Track evolution of a large number of states in
parallel.
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Yes/No Questions
Can ask (and answer) arbitrarily complicated
yes/no questions pertaining to reachability
C1 state S is reachable after 100 reactions
C2 state T is reachable from state U or
from state V but not from both
C3 state X is never reachable