Linear Model Measurements with Application to Bird Flocking Scott A. Smolka Linear Model Measurements with Application to Bird Flocking Scott A. Smolka Stony Brook University Joint work with Radu Grosu, Doron Peled, C.R. Ramakrishnan, Scott Stoller, Junxing Yang

Congratulations Ed! I first met Ed at Harvard in 1980, on occasion of visit by Amir Pnueli Closely followed Ed’s work throughout his illustrious career Finally got to work with Ed in 2009 with launch of NSF CMACS Expedition in Computing Ed is mentor, friend, colleague, and inspiration!

Talk Outline Flocking Model Neighborhood-based Measurements Path-based Measurements Application to Flocking Goal: Model-measurement framework provides fitness values for parameter-optimization framework

Flocking Model Cucker’s modelReynold’s model

Velocity Matching Measures how well the velocities are aligned: LTL property to be “measured”:

Neighborhood-Based Measurement State space is a tuple is finite set of states is initial state is transition relation Components in each state Tuple of measurement variables Well-founded value set Expressions based on that result in values from Constants Update function

Measurement Algorithm With each clock tick, execute in each state If is not minimal, then do Send to all neighbors Receive from neighbors Update decreasing

Example Measurements Find maximal value in a graph Well-founded domain is the natural numbers with usual < Decreasing expression E assigned to each state is simply d current maximal counter, initialized to width of the structure

Example Measurements (contd.) LTL Model Checking: Let. Measure linear combination of how fast becomes true in + average value of VM while is true. CTL Model Checking Variable for each subformula Two counters: phase-counter and down-counter For sub-formula e.g. :

Path Measurements 1.Paths may be infinite. 2.Multiple paths in the structure (possibly infinite). Assume measurements are affected mainly by a finite prefix of sequences. Impose a limit on the length. Use generalized Monte Carlo measurements to conclude that a large enough number of executions has guaranteed some measurement threshold.

Generalized Monte-Carlo Measurements Obtain joint estimate of mean values of Boolean-real pairs Additive approximation (AAA algorithm): Multiplicative approximation (SRA and OAA algorithms):

Experimental Results Runs μRμR N Avg Std2.7e Table 1. Results obtained from OAA Runs μRμR N Avg Std Table 2. Results obtained from AAA Figure 1. Birds’ positions and velocities after 50 steps of simulation

V-formation Figure 2. Birds’ positions and velocities after 500 steps of simulation Model measurements as fitness in Genetic Algorithm To achieve V-formation, measure clear view + upwash benefit