TY - CHAP AB - In the analysis of reactive systems a quantitative objective assigns a real value to every trace of the system. The value decision problem for a quantitative objective requires a trace whose value is at least a given threshold, and the exact value decision problem requires a trace whose value is exactly the threshold. We compare the computational complexity of the value and exact value decision problems for classical quantitative objectives, such as sum, discounted sum, energy, and mean-payoff for two standard models of reactive systems, namely, graphs and graph games. AU - Chatterjee, Krishnendu AU - Doyen, Laurent AU - Henzinger, Thomas A ED - Aceto, Luca ED - Bacci, Giorgio ED - Ingólfsdóttir, Anna ED - Legay, Axel ED - Mardare, Radu ID - 625 SN - 0302-9743 T2 - Models, Algorithms, Logics and Tools TI - The cost of exactness in quantitative reachability VL - 10460 ER - 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 AB - This book constitutes the refereed proceedings of the 9th InternationalWorkshop on Numerical Software Verification, NSV 2016, held in Toronto, ON, Canada in July 2011 - colocated with CAV 2016, the 28th International Conference on Computer Aided Verification. The NSV workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability. ED - Bogomolov, Sergiy ED - Martel, Matthieu ED - Prabhakar, Pavithra ID - 638 SN - 0302-9743 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 -