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

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

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

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

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

A 4-bit counter circuit

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

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]

Boolean Invariants

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]

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

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

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

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]

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]

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