# Reachability Analysis of Lazy Linear Hybrid Automata

### Susmit Kumar Jha

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2011-112

October 17, 2011

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-112.pdf

Lazy linear hybrid automata (LLHA) model the discrete time behavior of control systems containing finite-precision sensors and actuators interacting with their environment under bounded inertial delays. In this report, we present a symbolic technique for reachability analysis of lazy linear hybrid automata. The model permits invariants and guards to be nonlinear predicates but requires flow values to be constants. Assuming finite precision, flows represented by uniform linear predicates can be reduced to those containing values from a finite set of constants. We present an abstraction hierarchy for LLHA. Our verification technique is based on bounded model checking and k-induction for reachability analysis at different levels of the abstraction hierarchy within an abstraction-refinement framework. The counterexamples obtained during BMC are used to construct refinements in each iteration. Our technique is practical and compares favorably with state-of-the-art tools, as demonstrated on examples that include the Air Traffic Alert and Collision Avoidance System (TCAS).

**Advisor:** Sanjit A. Seshia

BibTeX citation:

@mastersthesis{Jha:EECS-2011-112, Author = {Jha, Susmit Kumar}, Title = {Reachability Analysis of Lazy Linear Hybrid Automata}, School = {EECS Department, University of California, Berkeley}, Year = {2011}, Month = {Oct}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-112.html}, Number = {UCB/EECS-2011-112}, Abstract = {Lazy linear hybrid automata (LLHA) model the discrete time behavior of control systems containing finite-precision sensors and actuators interacting with their environment under bounded inertial delays. In this report, we present a symbolic technique for reachability analysis of lazy linear hybrid automata. The model permits invariants and guards to be nonlinear predicates but requires flow values to be constants. Assuming finite precision, flows represented by uniform linear predicates can be reduced to those containing values from a finite set of constants. We present an abstraction hierarchy for LLHA. Our verification technique is based on bounded model checking and k-induction for reachability analysis at different levels of the abstraction hierarchy within an abstraction-refinement framework. The counterexamples obtained during BMC are used to construct refinements in each iteration. Our technique is practical and compares favorably with state-of-the-art tools, as demonstrated on examples that include the Air Traffic Alert and Collision Avoidance System (TCAS).} }

EndNote citation:

%0 Thesis %A Jha, Susmit Kumar %T Reachability Analysis of Lazy Linear Hybrid Automata %I EECS Department, University of California, Berkeley %D 2011 %8 October 17 %@ UCB/EECS-2011-112 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-112.html %F Jha:EECS-2011-112