1,489 research outputs found
Symbolic Approximation of Weighted Timed Games
Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the accumulated weight while reaching a target. Weighted timed games are notoriously difficult and quickly undecidable, even when restricted to non-negative weights. For non-negative weights, the largest class that can be analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the value problem is undecidable, the authors show how to approximate the value by considering regions with a refined granularity. In this work, we extend this class to incorporate negative weights, allowing one to model energy for instance, and prove that the value can still be approximated, with the same complexity. In addition, we show that a symbolic algorithm, relying on the paradigm of value iteration, can be used as an approximation schema on this class
Symbolic Approximation of Weighted Timed Games
Weighted timed games are zero-sum games played by two players on a timed
automaton equipped with weights, where one player wants to minimise the
accumulated weight while reaching a target. Weighted timed games are
notoriously difficult and quickly undecidable, even when restricted to
non-negative weights. For non-negative weights, the largest class that can be
analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the
value problem is undecidable, the authors show how to approximate the value by
considering regions with a refined granularity. In this work, we extend this
class to incorporate negative weights, allowing one to model energy for
instance, and prove that the value can still be approximated, with the same
complexity. In addition, we show that a symbolic algorithm, relying on the
paradigm of value iteration, can be used as an approximation schema on this
class
Tropical Fourier-Motzkin elimination, with an application to real-time verification
We introduce a generalization of tropical polyhedra able to express both
strict and non-strict inequalities. Such inequalities are handled by means of a
semiring of germs (encoding infinitesimal perturbations). We develop a tropical
analogue of Fourier-Motzkin elimination from which we derive geometrical
properties of these polyhedra. In particular, we show that they coincide with
the tropically convex union of (non-necessarily closed) cells that are convex
both classically and tropically. We also prove that the redundant inequalities
produced when performing successive elimination steps can be dynamically
deleted by reduction to mean payoff game problems. As a complement, we provide
a coarser (polynomial time) deletion procedure which is enough to arrive at a
simply exponential bound for the total execution time. These algorithms are
illustrated by an application to real-time systems (reachability analysis of
timed automata).Comment: 29 pages, 8 figure
Quantitative reactive modeling and verification
Formal verification aims to improve the quality of software by detecting errors before they do harm. At the basis of formal verification is the logical notion of correctness, which purports to capture whether or not a program behaves as desired. We suggest that the boolean partition of software into correct and incorrect programs falls short of the practical need to assess the behavior of software in a more nuanced fashion against multiple criteria. We therefore propose to introduce quantitative fitness measures for programs, specifically for measuring the function, performance, and robustness of reactive programs such as concurrent processes. This article describes the goals of the ERC Advanced Investigator Project QUAREM. The project aims to build and evaluate a theory of quantitative fitness measures for reactive models. Such a theory must strive to obtain quantitative generalizations of the paradigms that have been success stories in qualitative reactive modeling, such as compositionality, property-preserving abstraction and abstraction refinement, model checking, and synthesis. The theory will be evaluated not only in the context of software and hardware engineering, but also in the context of systems biology. In particular, we will use the quantitative reactive models and fitness measures developed in this project for testing hypotheses about the mechanisms behind data from biological experiments
Computing Branching Distances Using Quantitative Games
We lay out a general method for computing branching distances between labeled
transition systems. We translate the quantitative games used for defining these
distances to other, path-building games which are amenable to methods from the
theory of quantitative games. We then show for all common types of branching
distances how the resulting path-building games can be solved. In the end, we
achieve a method which can be used to compute all branching distances in the
linear-time--branching-time spectrum
Computer Aided Verification
This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency
SAT Modulo Monotonic Theories
We define the concept of a monotonic theory and show how to build efficient
SMT (SAT Modulo Theory) solvers, including effective theory propagation and
clause learning, for such theories. We present examples showing that monotonic
theories arise from many common problems, e.g., graph properties such as
reachability, shortest paths, connected components, minimum spanning tree, and
max-flow/min-cut, and then demonstrate our framework by building SMT solvers
for each of these theories. We apply these solvers to procedural content
generation problems, demonstrating major speed-ups over state-of-the-art
approaches based on SAT or Answer Set Programming, and easily solving several
instances that were previously impractical to solve
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