44,921 research outputs found
Counterexample Generation in Probabilistic Model Checking
Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol
A Trichotomy for Regular Trail Queries
Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class T_tract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan et al. [Bagan et al., 2013]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice
Equivalence of Deterministic One-Counter Automata is NL-complete
We prove that language equivalence of deterministic one-counter automata is
NL-complete. This improves the superpolynomial time complexity upper bound
shown by Valiant and Paterson in 1975. Our main contribution is to prove that
two deterministic one-counter automata are inequivalent if and only if they can
be distinguished by a word of length polynomial in the size of the two input
automata
Minimizing Running Costs in Consumption Systems
A standard approach to optimizing long-run running costs of discrete systems
is based on minimizing the mean-payoff, i.e., the long-run average amount of
resources ("energy") consumed per transition. However, this approach inherently
assumes that the energy source has an unbounded capacity, which is not always
realistic. For example, an autonomous robotic device has a battery of finite
capacity that has to be recharged periodically, and the total amount of energy
consumed between two successive charging cycles is bounded by the capacity.
Hence, a controller minimizing the mean-payoff must obey this restriction. In
this paper we study the controller synthesis problem for consumption systems
with a finite battery capacity, where the task of the controller is to minimize
the mean-payoff while preserving the functionality of the system encoded by a
given linear-time property. We show that an optimal controller always exists,
and it may either need only finite memory or require infinite memory (it is
decidable in polynomial time which of the two cases holds). Further, we show
how to compute an effective description of an optimal controller in polynomial
time. Finally, we consider the limit values achievable by larger and larger
battery capacity, show that these values are computable in polynomial time, and
we also analyze the corresponding rate of convergence. To the best of our
knowledge, these are the first results about optimizing the long-run running
costs in systems with bounded energy stores.Comment: 32 pages, corrections of typos and minor omission
Individual Adaption in a Path-Based Simulation of the Freeway Network of Northrhine-Westfalia
Traffic simulations are made more realistic by giving individual drivers
intentions, i.e. an idea of where they want to go. One possible implementation
of this idea is to give each driver an exact pre-computed path, that is, a
sequence of roads this driver wants to follow. This paper shows, in a realistic
road network, how repeated simulations can be used so that drivers can explore
different paths, and how macroscopic quantities such as locations of jams or
network throughput change as a result of this
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