TY - CONF
AB - A Rapidly-exploring Random Tree (RRT) is an algorithm which can search a non-convex region of space by incrementally building a space-filling tree. The tree is constructed from random points drawn from system’s state space and is biased to grow towards large unexplored areas in the system. RRT can provide better coverage of a system’s possible behaviors compared with random simulations, but is more lightweight than full reachability analysis. In this paper, we explore some of the design decisions encountered while implementing a hybrid extension of the RRT algorithm, which have not been elaborated on before. In particular, we focus on handling non-determinism, which arises due to discrete transitions. We introduce the notion of important points to account for this phenomena. We showcase our ideas using heater and navigation benchmarks.
AU - Bak, Stanley
AU - Bogomolov, Sergiy
AU - Henzinger, Thomas A
AU - Kumar, Aviral
ED - Abate, Alessandro
ED - Bodo, Sylvie
ID - 633
SN - 978-331963500-2
TI - Challenges and tool implementation of hybrid rapidly exploring random trees
VL - 10381
ER -
TY - CONF
AB - Signal regular expressions can specify sequential properties of real-valued signals based on threshold conditions, regular operations, and duration constraints. In this paper we endow them with a quantitative semantics which indicates how robustly a signal matches or does not match a given expression. First, we show that this semantics is a safe approximation of a distance between the signal and the language defined by the expression. Then, we consider the robust matching problem, that is, computing the quantitative semantics of every segment of a given signal relative to an expression. We present an algorithm that solves this problem for piecewise-constant and piecewise-linear signals and show that for such signals the robustness map is a piecewise-linear function. The availability of an indicator describing how robustly a signal segment matches some regular pattern provides a general framework for quantitative monitoring of cyber-physical systems.
AU - Bakhirkin, Alexey
AU - Ferrere, Thomas
AU - Maler, Oded
AU - Ulus, Dogan
ED - Abate, Alessandro
ED - Geeraerts, Gilles
ID - 636
SN - 978-331965764-6
TI - On the quantitative semantics of regular expressions over real-valued signals
VL - 10419
ER -
TY - GEN
ED - Bogomolov, Sergiy
ED - Martel, Matthieu
ED - Prabhakar, Pavithra
ID - 638
TI - Numerical Software Verification
VL - 10152
ER -
TY - GEN
AB - Synchronous programs are easy to specify because the side effects of an operation are finished by the time the invocation of the operation returns to the caller. Asynchronous programs, on the other hand, are difficult to specify because there are side effects due to pending computation scheduled as a result of the invocation of an operation. They are also difficult to verify because of the large number of possible interleavings of concurrent asynchronous computation threads. We show that specifications and correctness proofs for asynchronous programs can be structured by introducing the fiction, for proof purposes, that intermediate, non-quiescent states of asynchronous operations can be ignored. Then, the task of specification becomes relatively simple and the task of verification can be naturally decomposed into smaller sub-tasks. The sub-tasks iteratively summarize, guided by the structure of an asynchronous program, the atomic effect of non-atomic operations and the synchronous effect of asynchronous operations. This structuring of specifications and proofs corresponds to the introduction of multiple layers of stepwise refinement for asynchronous programs. We present the first proof rule, called synchronization, to reduce asynchronous invocations on a lower layer to synchronous invocations on a higher layer. We implemented our proof method in CIVL and evaluated it on a collection of benchmark programs.
AU - Henzinger, Thomas A
AU - Kragl, Bernhard
AU - Qadeer, Shaz
ID - 6426
SN - 2664-1690
TI - Synchronizing the asynchronous
ER -
TY - CONF
AB - Despite researchers’ efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract the original system and find an invariant for the abstraction. In this paper, we propose an approach to constructing a new kind of abstraction called conic abstraction for affine hybrid systems, and to computing reachable sets based on this abstraction. The essential feature of a conic abstraction is that it partitions the state space of a system into a set of convex polyhedral cones which is derived from a uniform conic partition of the derivative space. Such a set of polyhedral cones is able to cut all trajectories of the system into almost straight segments so that every segment of a reach pipe in a polyhedral cone tends to be straight as well, and hence can be over-approximated tightly by polyhedra using similar techniques as HyTech or PHAVer. In particular, for diagonalizable affine systems, our approach can guarantee to find an invariant for unbounded reachable sets, which is beyond the capability of bounded-time reachability analysis tools. We implemented the approach in a tool and experiments on benchmarks show that our approach is more powerful than SpaceEx and PHAVer in dealing with diagonalizable systems.
AU - Bogomolov, Sergiy
AU - Giacobbe, Mirco
AU - Henzinger, Thomas A
AU - Kong, Hui
ID - 647
SN - 978-331965764-6
TI - Conic abstractions for hybrid systems
VL - 10419
ER -