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 - 03029743
T2 - Models, Algorithms, Logics and Tools
TI - The cost of exactness in quantitative reachability
VL - 10460
ER -
TY - CONF
AB - Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples. We show that for the class of convex hybrid automata, i.e., hybrid automata with (possibly nonlinear) convex constraints on derivatives, such directions always exist and can be found using convex optimization. We embed our method inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible. We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata.
AU - Bogomolov, Sergiy
AU - Frehse, Goran
AU - Giacobbe, Mirco
AU - Henzinger, Thomas A
ID - 631
SN - 978-366254576-8
TI - Counterexample guided refinement of template polyhedra
VL - 10205
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
ED - Bogomolov, Sergiy
ED - Martel, Matthieu
ED - Prabhakar, Pavithra
ID - 638
TI - Numerical Software Verification
VL - 10152
ER -