Distinguishing Hidden Markov Chains

Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HMCs are called distinguishable if for every $\varepsilon > 0$ there is a distinguishing algorithm whose error probability is less than $\varepsilon$. We show that one can decide in polynomial time whether two HMCs are distinguishable. Further, we present and analyze two distinguishing algorithms for distinguishable HMCs. The first algorithm makes a decision after processing a fixed number of observations, and it exhibits two-sided error. The second algorithm processes an unbounded number of observations, but the algorithm has only one-sided error. The error probability, for both algorithms, decays exponentially with the number of processed observations. We also provide an algorithm for distinguishing multiple HMCs. Finally, we discuss an application in stochastic runtime verification.Comment: This is the full version of a LICS'16 pape

Fault-ignorant Quantum Search

We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand. We prove lower bounds on the runtime of such algorithms and thereby find that the quadratic speedup is necessarily lost (in our noise models). However, for low but constant noise levels the algorithms we provide (based on Grover's algorithm) still outperform the best noiseless classical search algorithm.Comment: v1: 15+8 pages, 4 figures; v2: 19+8 pages, 4 figures, published version (Introduction section significantly expanded, presentation clarified, results and order unchanged

Specifying Reusable Components

Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal verification of reusable components. Model-based contracts conservatively extend the classic Design by Contract with a notion of model, which underpins the precise definitions of such concepts as abstract equivalence and specification completeness. Experiments applying model-based contracts to libraries of data structures suggest that the method enables accurate specification of practical software

Using Taint Analysis and Reinforcement Learning (TARL) to Repair Autonomous Robot Software

It is important to be able to establish formal performance bounds for autonomous systems. However, formal verification techniques require a model of the environment in which the system operates; a challenge for autonomous systems, especially those expected to operate over longer timescales. This paper describes work in progress to automate the monitor and repair of ROS-based autonomous robot software written for an a-priori partially known and possibly incorrect environment model. A taint analysis method is used to automatically extract the data-flow sequence from input topic to publish topic, and instrument that code. A unique reinforcement learning approximation of MDP utility is calculated, an empirical and non-invasive characterization of the inherent objectives of the software designers. By comparing off-line (a-priori) utility with on-line (deployed system) utility, we show, using a small but real ROS example, that it's possible to monitor a performance criterion and relate violations of the criterion to parts of the software. The software is then patched using automated software repair techniques and evaluated against the original off-line utility.Comment: IEEE Workshop on Assured IEEE Workshop on Assured Autonomous Systems, May, 202

Runtime verification for stochastic systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 97-101).We desire a capability for the safety monitoring of complex, mixed hardware/software systems, such as a semi-autonomous car. The field of runtime verification has developed many tools for monitoring the safety of software systems in real time. However, these tools do not allow for uncertainty in the system's state or failure, both of which are essential for the problems we care about. In this thesis I propose a capability for monitoring the safety criteria of mixed hardware/software systems that is robust to uncertainty and hardware failure. I start by framing the problem as runtime verification of stochastic, faulty, hidden-state systems. I solve this problem by performing belief state estimation over a novel set of models that combine Büchi automata, for modeling safety requirements, with probabilistic hierarchical constraint automata, for modeling mixed hardware/software systems. This method is innovative in its melding of safety monitoring techniques from the runtime verification community with probabilistic mode estimation techniques from the field of model-based diagnosis. I have verified my approach by testing it on automotive safety requirements for a model of an actuator component. My approach shows promise as a real-time safety monitoring tool for such systems.by Cristina M. Wilcox.S.M