Boolean Analysis Debashis Sahoo Department of Computer Science
Boolean Analysis Debashis Sahoo Department of Computer Science CSE 291 – H 00 – Lecture 13
Boolean Implication GABRB 1 45, 000 Affymetrix microarrays • Pair of genes. • Four quadrants. • Sparse quadrants. • Boolean relationships. If ACPP high, then GABRB 1 low If GABRB 1 high, then ACPP low ACPP
CDH expression Threshold Calculation High Intermediate Low Threshold • Threshold for each gene • Sort expression values • Step. Miner Sorted arrays [Sahoo et al. 07]
Boolean. Net Statistics B a 01 a 11 a 00 a 10 A n. Alow = (a 00+ a 01), n. Blow = (a 00+ a 10) total = a 00+ a 01+ a 10+ a 11, observed = a 00 expected = (n. Alow/ total * n. Blow/ total) * total (expected – observed) statistic = error rate = 1 2 √ a 00 ( (a + a ) 00 01 + expected a 00 (a 00+ a 10) ) Boolean Implication = (statistic > 3, error rate < 0. 1) [Sahoo et al. Genome Biology 08]
Six Boolean Implications [Sahoo et al. Genome Biology 08]
Boolean Invariants
Formal Models • Broad 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
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
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
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