We propose and evaluate a new technique for learning hybrid automata automatically by observing the runtime behavior of a dynamical system. Working from a sequence of continuous state values and predicates about the environment, CHARDA recovers the distinct dynamic modes, learns a model for each mode from a given set of templates, and postulates causal guard conditions which trigger transitions between modes. Our main contribution is the use of information-theoretic measures (1) as a cost function for data segmentation and model selection to penalize over-fitting and (2) to determine the likely causes of each transition. CHARDA is easily extended with different classes of model templates, fitting methods, or predicates. In our experiments on a complex videogame character, CHARDA successfully discovers a reasonable over-approximation of the character's true behaviors. Our results also compare favorably against recent work in automatically learning probabilistic timed automata in an aircraft domain: CHARDA exactly learns the modes of these simpler automata.
Despite the general undecidability of many HA properties, it is possible to constrain models or carefully choose semantics to obtain different analysis characteristics: discretizing time or variable values evades undecidability by approximating the true dynamics @cite_10 ; keeping these continuous but constraining the allowed flow and guard conditions admits geometric analysis @cite_19 ; and one can always merge states together to yield an over-approximation, producing smaller and simpler models. There are also composable variations of hybrid automata that admit compositional analysis @cite_3 as well as a logical axiomatization @cite_9 , not to mention the body of tools and research that already exist for synthesizing control policies, ensuring safety, characterizing reachable areas, et cetera.
@cite_19 @cite_9 @cite_10 @cite_3
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Over the last years there has been an increasing research effort directed towards the automatic verification of infinite state systems, such as timed automata, hybrid automata, data-independent systems, relational automata, Petri nets, lossy channel systems, context-free and push-down processes. We present a method for deciding reachability properties of networks of timed processes. Such a network consists of an arbitrary set of identical timed automata, each with a single real-valued clock. Using a standard reduction from safety properties to reachability properties, we can use our algorithm to decide general safety properties of timed networks. To our knowledge, this is the first decidability result concerning verification of systems that are infinite-state in "two dimensions": they contain an arbitrary set of (identical) processes, and they use infinite data-structures, viz real-valued clocks. We illustrate our method by showing how it can be used to automatically verify Fischer's protocol, a timer-based protocol for enforcing mutual exclusion among an arbitrary number of processes.Finally, we show undecidability of the recurrent state problem: given a state in a timed network, check whether there is a computation of the network visiting the state infinitely often. This implies undecidability of model checking for any temporal logic which is sufficiently expressive to encode the recurrent state problem, such as PTL, CTL, etc. Abstract We present an approximation technique, that can render real-time model checking of safety and universal path properties more efficient. It is beneficial, when loops lead to repetition of control situations. Basically we augment a timed automata model with carefully selected extra transitions. This increases the size of the state-space, but potentially decreases the number of symbolic states to be explored by orders of magnitude. We give a formal definition of a timed automata formalism, enriched with basic data types, hand-shake synchronization, urgency, and committed locations. We prove by means of a trace semantics, that if a safety property can be established in the augmented model, it also holds for the original model. We extend our technique to a richer set of properties, that can be decided via a set of traces (universal path properties). In order for universal path properties to carry over to the original model, the semantics of the timed automata formalism is formulated relative to the applied augmentation. Our technique is particularly useful in systems, where a scheduler dictates repetition of control over elapsing time. As a typical example we mention translations of LEGO® RCX™ programs to U ppaal models, where the Round-Robin scheduler is a static entity. We allow scheduler and associated tasks to “park”, until some timing or environmental conditions are met. We apply our technique on a brick-sorter model for a safety property and report run-time data. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. Controlling concurrent systems to impose some global invariant is an undecidable problem. One can gain decidability at the expense of reducing concurrency. Even under this flexible design assumption, the synthesis problem remains highly intractable. One practical method for designing controllers is based on checking knowledge properties upon which the processes can make their decisions whether to allow or block transitions. A major deficiency of this synthesis method lies in calculating the knowledge based on the system that we want to control, and not on the resulted system. The original system has less knowledge, and as a result, we may introduce far more synchronization than needed. In this paper we show techniques to reduce this overhead.