Learn More
S-TaLiRo is a Matlab (TM) toolbox that searches for tra-jectories of minimal robustness in Simulink/Stateflow diagrams. It can analyze arbitrary Simulink models or user defined functions that model the system. At the heart of the tool, we use randomized testing based on stochastic optimization techniques including Monte-Carlo methods and Ant-Colony(More)
We present a new method for the generation of linear in-variants which reduces the problem to a non-linear constraint solving problem. Our method, based on Farkas' Lemma, synthesizes linear in-variants by extracting non-linear constraints on the coefficients of a target invariant from a program. These constraints guarantee that the linear invariant is(More)
We present a method for generating linear invariants for large systems. The method performs forward propagation in an abstract domain consisting of arbitrary polyhedra of a predefined fixed shape. The basic operations on the domain like abstraction, intersection, join and inclusion tests are all posed as linear optimization queries, which can be solved(More)
The tool FLOW* performs Taylor model-based flowpipe construction for non-linear (polynomial) hybrid systems. FLOW* combines well-known Tay-lor model arithmetic techniques for guaranteed approximations of the continuous dynamics in each mode with a combination of approaches for handling mode invariants and discrete transitions. FLOW* supports a wide variety(More)
We present a new technique for the generation of non-linear (algebraic) invariants of a program. Our technique uses the theory of ideals over polynomial rings to reduce the non-linear invariant generation problem to a numerical constraint solving problem. So far, the literature on invariant generation has been focussed on the construction of linear(More)
We present a new method for generating algebraic invariants of hybrid systems. The method reduces the invariant generation problem to a constraint solving problem using techniques from the theory of ideals over polynomial rings. Starting with a template invariant – a polynomial equality over the system variables with unknown coefficients – constraints are(More)
We propose an approach for the static analysis of probabilistic programs that sense, manipulate, and control based on uncertain data. Examples include programs used in risk analysis, medical decision making and cyber-physical systems. Correctness properties of such programs take the form of queries that seek the probabilities of assertions over program(More)
Lyapunov functions are used to prove stability and to obtain performance bounds on system behaviors for nonlinear and hybrid dynamical systems, but discovering Lyapunov functions is a difficult task in general. We present a technique for discovering Lyapunov functions and barrier certificates for nonlinear and hybrid dynamical systems using a search-based(More)
The convexity of numerical domains such as polyhedra, octagons , intervals and linear equalities enables tractable analysis of software for buffer overflows, null pointer dereferences and floating point errors. However, convexity also causes the analysis to fail in many common cases. Powerset extensions can remedy this shortcoming by considering(More)
We propose a novel integration of interval constraint propagation (ICP) with SMT solvers for linear real arithmetic (LRA) to decide nonlinear real arithmetic problems. We use ICP to search for interval solutions of the nonlinear constraints, and use the LRA solver to either validate the solutions or provide constraints to incrementally refine the search(More)