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The problem of combinatorial filter reduction arises from questions of resource optimization in robots; it is one specific way in which automation can help to achieve minimalism, to build better, simpler robots. This paper contributes a new…
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the `canonical boolean representation' of the syntactic monoid. Equivalently, it is the least number of…
What is the minimal information that a robot must retain to achieve its task? To design economical robots, the literature dealing with reduction of combinatorial filters approaches this problem algorithmically. As lossless state compression…
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
Deterministic and nondeterministic finite automata with translucent letters were introduced by Nagy and Otto more than a decade ago as Cooperative Distributed systems of a kind of stateless restarting automata with window size one. These…
An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
Deterministic models are approximations of reality that are easy to interpret and often easier to build than stochastic alternatives. Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic…
Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the…
Discrete time control systems whose dynamics and observations are described by stochastic equations are common in engineering, operations research, health care, and economics. For example, stochastic filtering problems are usually defined…
Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
Markovian processes have long been used to model stochastic environments. Reinforcement learning has emerged as a framework to solve sequential planning and decision-making problems in such environments. In recent years, attempts were made…
History-deterministic automata are those in which nondeterministic choices can be correctly resolved stepwise: there is a strategy to select a continuation of a run given the next input letter so that if the overall input word admits some…
Bayesian filtering is a key tool in many problems that involve the online processing of data, including data assimilation, optimal control, nonlinear tracking and others. Unfortunately, the implementation of filters for nonlinear, possibly…
The unknown inputs in a dynamical system may represent unknown external drivers, input uncertainty, state uncertainty, or instrument faults and thus unknown-input reconstruction has several wide-spread applications. In this paper we…