1. Department of Computer Science
Formal Methods
Debashis Sahoo
Department of Computer Science
CSE291 – H00 – Lecture 14

2. Formal Models Broad View Narrow View
application of discrete mathematics to software engineering
Narrow View
Use of a formal language
a set of strings over some well-defined alphabet, with rules for distinguishing which strings belong to the language
Formal reasoning about formulae in the language
E.g. formal proofs: use axioms and proof rules to demonstrate that some formula is in the language
What I would like to cover are these points:
More formal
Basic intro to boolean logic
Describe with example
Show how these are applied
Markers vs cell types
Normal vs cancer

3. Formal Models A finite state machine (FSM) description
State Transition Table, Initial State
Petri nets
State charts
A set of properties
Invariants
Temporal logic formulas
What I would like to cover are these points:
More formal
Basic intro to boolean logic
Describe with example
Show how these are applied
Markers vs cell types
Normal vs cancer

4. Finite State Machine A set of states An initial state
A set of transitions
A set of final states

5. Finite State Machine A set of input variables A set of state variables
State variables are logical functions of input and previous states.

6. A 4-bit counter circuit

7. Analysis of Digital Systems
Boolean state space
exploration
Property p holds in this path

8. Six Boolean Implications
Sparse quadrants are highlighted.
Prepare a comparison slides.
Correlation vs Boolean
If then
Get rid of slide numbers
Divide the pictures:
Two slides
First show Asymmetric
Symmetric
[Sahoo et al. Genome Biology 08]

9. Boolean Invariants

10. MiDReG Algorithm MiDReG = (Mining Developmentally Regulated Genes)
Boolean Implications
A high => B low
Differentiation
Expression
Gene A
Gene B
Replace seed with Gene A
Same slides with and without gene X
Just Differentiation
Make the arrow visible
Spell MiDReG
[Sahoo et al. PNAS 2010]

11. MiDReG Algorithm MiDReG = (Mining Developmentally Regulated Genes)
[Sahoo et al. PNAS 2010]

12. MiDReG Algorithm MiDReG = (Mining Developmentally Regulated Genes)
[Sahoo et al. PNAS 2010]

13. More B Cell Genes
[Sahoo et al. PNAS 2010]

14. Validation of B Cell Genes
So far we have confirmed 15 genes by qPCR.
[Weissman Lab] Jun Seita, Deepta Bhattacharya
[Sahoo et al. PNAS 2010]

15. Analysis of Predicted Genes
41 mice knockout available out of 62 predicted B cell genes
26/41 have defects in B cell function and differentiation
[Sahoo et al. PNAS 2010]

16. The Branchpoint between B and T Cell Development
[Inlay*, Bhattacharya*, Sahoo* et al. Genes Dev 09]
[Weissman Lab] Matthew A. Inlay