Probabilistic Automaton Model Research Articles

Undecidability results for probabilistic automata

The model of probabilistic automata was introduced by Rabin in 1963. Ever since, undecidability results were obtained for this model, showing that although simple, it is very expressive. This paper provides streamlined constructions implying the most important negative results, including the celebrated inapproximability result of Condon and Lipton.

Probabilistic Automata Model of a Soft Robot for the Planning of Manipulation Tasks

Soft robots must be able to structure an automation problem into a sequence of actions that lead to a desired state, before they can fulfill a meaningful role in automation applications. This, however, can only be successful if the robot can predict the outcome of an action. The theory of rigid industrial robots is not applicable without major changes, because kinematic chains do not adequately describe the continuous deformation of the complex, often biologically inspired shapes of soft robots. Analytic solutions have not been found yet. Numerical solutions based on finite elements are slow, technically challenging, and only suitable for one specific robot. It is, however, possible to observe the outcome of an action, and use these observations to plan a sequence of actions that let the robot accomplish an automation task. In this paper, we analyze a probabilistic automaton that computes the optimal sequence of actions to bring the robot into a desired state. An earlier article explained the functioning of the method in a toy example. In this paper, we analyze if it is feasible to apply the method to a planning problem inspired by a real soft robot. We show the results and document the planning process. We identify the analog of an impulse response, although it is not closed form due to the nonparametric nature of the method. Note to Practitioners —A soft robotic sorting table has a computer-controlled soft surface that can move delicate objects without damaging them. There are currently no closed-loop control systems for such robots, because it is unclear how to relate the control signals to the behavior of the table, or which actions to choose in order to solve a manipulation task. In this paper, we propose a probabilistic automaton to plan the best action sequence on average. The sequence brings the workpieces on top of a soft table into a desired condition. It is a machine learning solution that is based on observations of the input signals and their effect, rather than a detailed analytical or numerical modeling of the robot. We show that it is feasible to model an existing soft robotic table. We demonstrate that the planning is successful by solving complex maze tasks. Our results are based on experiments and simulations.

Probabilistic-automaton modeling in soils migration processes research

Structural-functional systems stochastic approach to the study and analysis of the process of migration accumulation of substances in the soil was presented in the paper. The purpose of the model investigation of the considered system is to study stochastic flow patterns of substances, which in some discrete time points come in the studied type of soil. The feasibility of the approach to solving a given problem is caused by dynamic process of migration accumulation of substances, as well as a large number of probabilistic factors of influence. The proposed approach is founded on the theory of probabilistic-automaton modeling of dynamic processes, which is based on the selected Moore automaton. The authors have synthesized probabilistic-automaton model of migration accumulation of certain substances in specific-type soil subsystems. The input parameters of this model are statistical data, relating to the time points of substances arrival in the soil and the amount of certain substances arrival at fixed, sufficiently large time intervals. Depending on the accumulation intensity of anthropogenic changes and conditional intensity of equilibrium transitions of ecosystem, expressions for the probability of system stable functioning take different forms. According to examples of using the synthesized model, this approach allows to conduct research, analysis and forecasting of processes of migration accumulation of pollutants under anthropogenic load and is one of the most suitable for environmental studies.

Formal Verification of Differential Privacy for Interactive Systems (Extended Abstract)

Differential privacy is a promising approach to privacy preserving data analysis with a well-developed theory for functions. Despite recent work on implementing systems that aim to provide differential privacy, the problem of formally verifying that these systems have differential privacy has not been adequately addressed. We develop a formal probabilistic automaton model of differential privacy for systems by adapting prior work on differential privacy for functions. We present the first sound verification technique for proving differential privacy of interactive systems. The technique is based on a form of probabilistic bisimulation relation. The novelty lies in the way we track quantitative privacy leakage bounds using a relation family instead of a single relation. We illustrate the proof technique on a representative automaton motivated by PINQ, an implemented system that is intended to provide differential privacy. Surprisingly, our analysis yields a privacy leakage bound of (2t⁎ϵ) rather than (t⁎ϵ) when ϵ-differentially private functions are called t times. The extra leakage arises from accounting for bounded memory constraints of real computers.

How Should Prey Animals Respond to Uncertain Threats?

A prey animal surveying its environment must decide whether there is a dangerous predator present or not. If there is, it may flee. Flight has an associated cost, so the animal should not flee if there is no danger. However, the prey animal cannot know the state of its environment with certainty, and is thus bound to make some errors. We formulate a probabilistic automaton model of a prey animal's life and use it to compute the optimal escape decision strategy, subject to the animal's uncertainty. The uncertainty is a major factor in determining the decision strategy: only in the presence of uncertainty do economic factors (like mating opportunities lost due to flight) influence the decision. We performed computer simulations and found that in silico populations of animals subject to predation evolve to display the strategies predicted by our model, confirming our choice of objective function for our analytic calculations. To the best of our knowledge, this is the first theoretical study of escape decisions to incorporate the effects of uncertainty, and to demonstrate the correctness of the objective function used in the model.

MODELLING OF COMPUTER COMMUNICATION NETWORKS VIA PROBABILISTIC AUTOMATA

An interdisciplinary approach for computing the point‐to‐point message delay, a measure of congestion in a computer communication network, is derived by the inclusion of a queueing theory result in a probabilistic automaton model. This network model is structurally composed of the interconnection of two distinct repetitive probabilistic automatons. The formulation of the solution is based on the network probability transition matrix which represents the state transitions for the number of customers in the GI/G/1 queue at each computer node and the intranode and internode port routing.

Toward a probabilistic automata model of some aspects of code-switching

As Kolers (1972) has pointed out, the study of bilingualism offers a distinctive way to study some of the mental activities underlying the way that people use language. Code-switching (the introduction into the context of one language stretches of speech which exhibit primarily the other language's phonological and morphological features) offers a unique opportunity for studying some of the more complicated aspects of bilingual speech, particularly regarding the momentary choice of language. Researchers whose work has influenced this paper include Haugen, Weinreich, Mackey, Fishman, Rayfleld, Clyne, Hasselmo, Gumperz, Diebold, Lance, Valdés-Fallis, Pfaff, and Timm. Among the list of poorly understood phenomena in code-switching are (I) seemingly unpredictable switching, and (2) the possibility of formal, complex rules underlying different code-switching patterns. It is these open questions which modelling might illuminate.