The Complexity of Codiagnosability for Discrete Event and Timed Systems

In this paper we study the fault codiagnosis problem for discrete event systems given by finite automata (FA) and timed systems given by timed automata (TA). We provide a uniform characterization of codiagnosability for FA and TA which extends the necessary and sufficient condition that characterizes diagnosability. We also settle the complexity of the codiagnosability problems both for FA and TA and show that codiagnosability is PSPACE-complete in both cases. For FA this improves on the previously known bound (EXPTIME) and for TA it is a new result. Finally we address the codiagnosis problem for TA under bounded resources and show it is 2EXPTIME-complete.Comment: 24 pages

Generative Marginalization Models

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM

Synthesizing Finite-state Protocols from Scenarios and Requirements

Scenarios, or Message Sequence Charts, offer an intuitive way of describing the desired behaviors of a distributed protocol. In this paper we propose a new way of specifying finite-state protocols using scenarios: we show that it is possible to automatically derive a distributed implementation from a set of scenarios augmented with a set of safety and liveness requirements, provided the given scenarios adequately \emph{cover} all the states of the desired implementation. We first derive incomplete state machines from the given scenarios, and then synthesis corresponds to completing the transition relation of individual processes so that the global product meets the specified requirements. This completion problem, in general, has the same complexity, PSPACE, as the verification problem, but unlike the verification problem, is NP-complete for a constant number of processes. We present two algorithms for solving the completion problem, one based on a heuristic search in the space of possible completions and one based on OBDD-based symbolic fixpoint computation. We evaluate the proposed methodology for protocol specification and the effectiveness of the synthesis algorithms using the classical alternating-bit protocol.Comment: This is the working draft of a paper currently in submission. (February 10, 2014

Asynchronous Games over Tree Architectures

We consider the task of controlling in a distributed way a Zielonka asynchronous automaton. Every process of a controller has access to its causal past to determine the next set of actions it proposes to play. An action can be played only if every process controlling this action proposes to play it. We consider reachability objectives: every process should reach its set of final states. We show that this control problem is decidable for tree architectures, where every process can communicate with its parent, its children, and with the environment. The complexity of our algorithm is l-fold exponential with l being the height of the tree representing the architecture. We show that this is unavoidable by showing that even for three processes the problem is EXPTIME-complete, and that it is non-elementary in general

Communicating Processes with Data for Supervisory Coordination

We employ supervisory controllers to safely coordinate high-level discrete(-event) behavior of distributed components of complex systems. Supervisory controllers observe discrete-event system behavior, make a decision on allowed activities, and communicate the control signals to the involved parties. Models of the supervisory controllers can be automatically synthesized based on formal models of the system components and a formalization of the safe coordination (control) requirements. Based on the obtained models, code generation can be used to implement the supervisory controllers in software, on a PLC, or an embedded (micro)processor. In this article, we develop a process theory with data that supports a model-based systems engineering framework for supervisory coordination. We employ communication to distinguish between the different flows of information, i.e., observation and supervision, whereas we employ data to specify the coordination requirements more compactly, and to increase the expressivity of the framework. To illustrate the framework, we remodel an industrial case study involving coordination of maintenance procedures of a printing process of a high-tech Oce printer.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432

Centralized and distributed algorithms for on-line synthesis of maximal control policies under partial observation

This paper deals with the on-line control of partially observed discrete event systems (DES). The goal is to restrict the behavior of the system within a prefix-closed legal language while accounting for the presence of uncontrollable and unobservable events. In the spirit of recent work on the on-line control of partially observed DES (Heymann and Lin 1994) and on variable lookahead control of fully observed DES (Ben Hadj-Alouane et al. 1994c), we propose an approach where, following each observable event, a control action is computed on-line using an algorithm of linear worst-case complexity. This algorithm, called VLP-PO , has the following additional properties: (i) the resulting behavior is guaranteed to be a maximal controllable and observable sublanguage of the legal language; (ii) different maximals may be generated by varying the priorities assigned to the controllable events, a parameter of VLP-PO ; (iii) a maximal containing the supremal controllable and normal sublanguage of the legal language can be generated by a proper selection of controllable event priorities; and (iv) no off-line calculations are necessary. We also present a parallel/distributed version of the VLP-PO algorithm called DI-VLP-PO . This version uses several communicating agents that simultaneously run (on-line) identical versions of the algorithm but on possibly different parts of the system model and the legal language, according to the structural properties of the system and the specifications. While achieving the same behavior as VLO-PO, DI-VLP-PO runs at a total complexity (for computation and communication) that is significantly lower than its sequential counterpart.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45126/1/10626_2005_Article_BF01797138.pd

Visual Observation of a Moving Agent

We address the problem of observing a moving agent. In particular, we propose a system for observing a manipulation process, where a robot hand manipulates an object. A discrete event dynamic systems (DEDS) frame work is developed for the hand/object interaction over time and a stabilizing observer is constructed. Low-level modules are developed for recognizing the events that causes state transitions within the dynamic manipulation system. The work examines closely the possibilities for errors, mistakes and uncertainties in the manipulation system, observer construction process and event identification mechanisms. The system utilizes different tracking techniques in order to observe and recognize the task in an active, adaptive and goal-directed manner