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Abstract. We present a new method for the generation of linear invariants which reduces the problem to a non-linear constraint solving problem. Our method, based on Farkas’ Lemma, synthesizes linear invariants by extracting non-linear constraints on the coefficients of a target invariant from a program. These constraints guarantee that the linear invariant… (More)

- Sriram Sankaranarayanan, Henny B. Sipma, Zohar Manna
- POPL
- 2004

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)

S-TaLiRo is a Matlab (TM) toolbox that searches for trajectories 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)

- Sriram Sankaranarayanan, Henny B. Sipma, Zohar Manna
- VMCAI
- 2005

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)

- Xin Chen, Erika Ábrahám, Sriram Sankaranarayanan
- RTSS
- 2012

We propose an approach for verifying non-linear hybrid systems using higher-order Taylor models that are a combination of bounded degree polynomials over the initial conditions and time, bloated by an interval. Taylor models are an effective means for computing rigorous bounds on the complex time trajectories of non-linear differential equations. As a… (More)

- Sriram Sankaranarayanan, Henny B. Sipma, Zohar Manna
- HSCC
- 2004

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)

- Xin Chen, Erika Ábrahám, Sriram Sankaranarayanan
- CAV
- 2013

The tool FLOW* performs Taylor model-based flowpipe construction for non-linear (polynomial) hybrid systems. FLOW* combines well-known Taylor 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 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)

We present techniques for the analysis of infinite state probabilistic programs to synthesize probabilistic invariants and prove almost-sure termination. Our analysis is based on the notion of (super) martingales from probability theory. First, we define the concept of (super) martingales for loops in probabilistic programs. Next, we present the use of… (More)

- Houssam Abbas, Georgios E. Fainekos, Sriram Sankaranarayanan, Franjo Ivancic, Aarti Gupta
- ACM Trans. Embedded Comput. Syst.
- 2013

We present a Monte-Carlo optimization technique for finding system behaviors that falsify a metric temporal logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a falsifying behavior by exploring trajectories with smaller… (More)