Christoforos Keroglou

Initial state opacity in stochastic DES

A non-deterministic finite automaton is initial-state opaque if the membership of its true initial state to a given set of secret states S remains opaque (i.e., uncertain) to an intruder who observes system activity through some natural projection map. By establishing that the verification of initial state opacity is equivalent to the language containment problem, earlier work has established that the verification of initial state opacity is a PSPACE-complete problem. In this paper, motivated by the desire to incorporate probabilistic (likelihood) information, we extend the notion of initial state opacity to stochastic discrete event systems. Specifically, we consider systems that can be modeled as probabilistic finite automata, and introduce and analyze the notions of almost initial state opacity and step-based almost initial state opacity, both of which hinge on the a priori probability that the given system generate behavior that violates initial-state opacity. We also discuss how almost initial state opacity and step-based almost initial state opacity can be verified, and analyze the complexity of the proposed verification methods.

An Approach for Preoperative Planning and Performance of MR-guided Interventions Demonstrated With a Manual Manipulator in a 1.5T MRI Scanner

PurposeThe aim of this work was to develop and test a general methodology for the planning and performance of robot-assisted, MR-guided interventions. This methodology also includes the employment of software tools with appropriately tailored routines to effectively exploit the capabilities of MRI and address the relevant spatial limitations.MethodsThe described methodology consists of: (1) patient-customized feasibility study that focuses on the geometric limitations imposed by the gantry, the robotic hardware, and interventional tools, as well as the patient; (2) stereotactic preoperative planning for initial positioning of the manipulator and alignment of its end-effector with a selected target; and (3) real-time, intraoperative tool tracking and monitoring of the actual intervention execution. Testing was performed inside a standard 1.5T MRI scanner in which the MR-compatible manipulator is deployed to provide the required access.ResultsA volunteer imaging study demonstrates the application of the feasibility stage. A phantom study on needle targeting is also presented, demonstrating the applicability and effectiveness of the proposed preoperative and intraoperative stages of the methodology. For this purpose, a manually actuated, MR-compatible robotic manipulation system was used to accurately acquire a prescribed target through alternative approaching paths.ConclusionsThe methodology presented and experimentally examined allows the effective performance of MR-guided interventions. It is suitable for, but not restricted to, needle-targeting applications assisted by a robotic manipulation system, which can be deployed inside a cylindrical scanner to provide the required access to the patient facilitating real-time guidance and monitoring.

Bounds on the probability of misclassification among hidden Markov models

Given a sequence of observations, classification among two known hidden Markov models (HMMs) can be accomplished with a classifier that minimizes the probability of error (i.e., the probability of misclassification) by enforcing the maximum a posteriori probability (MAP) rule. For this MAP classifier, we are interested in assessing the a priori probability of error (before any observations are made), something that can be obtained (as a function of the length of the sequence of observations) by summing up the probability of error over all possible observation sequences of the given length. To avoid the high complexity of computing the exact probability of error, we devise techniques for merging different observation sequences, and obtain corresponding upper bounds by summing up the probabilities of error over the merged sequences. We show that if one employs a deterministic finite automaton (DFA) to capture the merging of different sequences of observations (of the same length), then Markov chain theory can be used to efficiently determine a corresponding upper bound on the probability of misclassification. The result is a class of upper bounds that can be computed with polynomial complexity in the size of the two HMMs and the size of the DFA.

Detectability in stochastic discrete event systems

Abstract A discrete event system possesses the property of detectability if it allows an observer to perfectly estimate the current state of the system after a finite number of observed symbols, i.e., detectability captures the ability of an observer to eventually perfectly estimate the system state. In this paper we analyze detectability in stochastic discrete event systems (SDES) that can be modeled as probabilistic finite automata. More specifically, we define the notion of A-detectability, which characterizes our ability to estimate the current state of a given SDES with increasing certainty as we observe more output symbols. The notion of A-detectability is differentiated from previous notions for detectability in SDES because it takes into account the probability of problematic observation sequences (that do not allow us to perfectly deduce the system state), whereas previous notions for detectability in SDES considered each observation sequence that can be generated by the underlying system. We discuss observer-based techniques that can be used to verify A-detectability, and provide associated necessary and sufficient conditions. We also prove that A-detectability is a PSPACE-hard problem.

Consideration of geometric constraints regarding MR-compatible interventional robotic devices

The design of MR-compatible robotic systems is a challenging task given the magnetic nature of the scanning environment but also the limitations imposed by the geometric characteristics of the imaging modality. The latter issue is often referred to as geometric MR-compatibility and was treated through image-based analyses as part of the design of a new interventional robotic device. Examinations on geometric MR-compatibility focused on ways to quantify the available space inside a cylindrical scanner, considerations regarding the effective field-of-view of an MR scanner, representations of the attainable anatomical region as defined for needle targeting applications, and computer simulations using three-dimensional digital models representing the patient. Geometric considerations are relevant both to the design of an MR-compatible robotic device but also its operation, as for example when using patient-specific data for intervention planning purposes. A preoperative planning procedure developed for the new robotic device will also be described.

Revised Test for Stochastic Diagnosability of Discrete-Event Systems

This paper provides revisions to the algorithms presented by Chen et al., 2013 for testing diagnosability of stochastic discrete-event systems. Additional new contributions include PSPACE-hardness of verifying strong stochastic diagnosability (referred as A-Diagnosability in Thorsley et al., 2005) and a necessary and sufficient condition for testing stochastic diagnosability (referred as AA-Diagnosability in Thorsley et al., 2005) that involves a new notion of probabilistic equivalence.Note to Practitioners—Detecting system failures is essential prior to fault mitigation. For stochastic discrete-event systems, the property of stochastic diagnosability (S-Diagnosability) allows one to detect any system failure with arbitrarily small error bound and within bounded delay. This paper contributes by revising and extending the results in the previous work by Chen et al., 2013, regarding the verification of S-Diagnosability.

Distributed diagnosis using predetermined synchronization strategies in the presence of communication constraints

We consider distributed fault diagnosis in a discrete event system modeled as a nondeterministic finite automaton that is observed at multiple observation sites through distinct natural projection maps. The majority of previous work in this setting has focused on local observers (diagnosers) that are separately implemented at each observation site, i.e., these diagnosers do not attempt at any point to refine their diagnostic information by exchanging information among themselves, and typically rely exclusively on communicating their decision (fault or no fault) to a coordinator that is responsible for making the ultimate diagnosis decision (e.g., co-diagnosability). In our previous work, we extended these techniques to allow local observers/diagnosers to communicate their state estimates along with diagnostic information (normal or fault condition) to a coordinator that fuses local diagnostic information and subsequently provides this refined information to the different observation sites (to aid them in taking immediate or future diagnostic decisions). In this work, we extend these synchronization strategies to cases where a coordinator is not present and there may exist communication constraints between the exchange of information among local sites (i.e., each local diagnoser may only exchange information with a subset of the local diagnosers). We verify diagnosability in this setting via the construction of an appropriate composition of local diagnosers, which is able to capture the refinement of information under the given synchronization strategy and communication constraints.

Opacity formulations and verification in discrete event systems

In many emerging security applications, a property of a system, that may reveal important details about its behaviour, needs to be kept secret (opaque) to outside observers (intruders). Motivated by such applications, several authors have formalized, analyzed, and described methods to verify notions of opacity in discrete event systems of interest. This paper offers a review of various definitions of opacity, along with methodologies for their verification and complexity analysis. We review state-based notions of opacity (namely, current-state opacity and initial-state opacity) in non-deterministic finite automata, as well as their extensions to stochastic settings. Specifically, we discuss these notions of opacity and methods to verify them in discrete event systems modeled by non-deterministic finite automata (NFAs) or probabilistic finite automata (PFAs).

Design of MR-compatible robotic devices: magnetic and geometric compatibility aspects

Specially designed robotic manipulators have been proposed for the performance of minimally invasive interventions under real-time magnetic resonance imaging (MRI) guidance. The design of MR-compatible robotic systems is a challenging task given the limitations imposed by the magnetic nature of the scanning environment but also the geometry of a high-field cylindrical scanner. These issues are discussed with special emphasis on geometric MR-compatibility. Acquired MR images are used for the analysis of the available space inside the scanner in order to provide the necessary input for the design of interventional devices.

Probabilistic system opacity in discrete event systems

In many emerging security applications, a system designer frequently needs to ensure that a certain property of a given system (that may reveal important details about the system’s operation) be kept secret (opaque) to outside observers (eavesdroppers). Motivated by such applications, several researchers have formalized, analyzed, and described methods to verify notions of opacity in discrete event systems of interest. This paper introduces and analyzes a notion of opacity in systems that can be modeled as probabilistic finite automata or hidden Markov models. We consider a setting where a user needs to choose a specific hidden Markov model (HMM) out of m possible (different) HMMs, but would like to “hide” the true system from eavesdroppers, by not allowing them to have an arbitrary level of confidence as to which system has been chosen. We describe necessary and sufficient conditions (that can be checked with polynomial complexity), under which the intruder cannot distinguish the true HMM, namely, the intruder cannot achieve a level of certainty about its decision, which is above a certain threshold that we can a priori compute.