# Inferring finite automata with stochastic output functions and an application to map learning

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## Abstract

It is often useful for a robot to construct a spatial representation of its environment from experiments and observations, in other words, to learn a map of its environment by exploration. In addition, robots, like people, make occasional errors in perceiving the spatial features of their environments. We formulate map learning as the problem of inferring from noisy observations the structure of a reduced deterministic finite automaton. We assume that the automaton to be learned has a distinguishing sequence. Observation noise is modeled by treating the observed output at each state as a random variable, where each visit to the state is an independent trial and the correct output is observed with probability exceeding 1/2. We assume no errors in the state transition function.

Using this framework, we provide an exploration algorithm to learn the correct structure of such an automaton with probability 1−δ, given as inputs δ, an upper bound*m* on the number of states, a distinguishing sequence*s*, and a lower bound α>1/2 on the probability of observing the correct output at any state. The running time and the number of basic actions executed by the learning algorithm are bounded by a polynomial in δ^{−1},*m*, |*s*|, and (1/2−α)^{−1}.

We discuss the assumption that a distinguishing sequence is given, and present a method of using a weaker assumption. We also present and discuss simulation results for the algorithm learning several automata derived from office environments.

### Keywords

Automata inference noisy outputs distinguishing sequences map learning spatial representation### References

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