by Ronald L. Rivest, Robert E. Schapire
http://theory.lcs.mit.edu/~rivest/RivestSchapire-DiversityBasedInferenceOfFiniteAutomata.ps
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Abstract:
We present new procedures for inferring the structure of a finite-state automaton (FSA) from its input/output behavior, using access to the automaton to perform experiments. Our procedures use a new representation for finite automata, based on the notion of equivalence between tests. We call the number of such equivalence classes the diversity of the automaton; the diversity may be as small as the logarithm of the number of states of the automaton. For the special class of permutation automata, we describe an inference procedure that runs in time polynomial in the diversity and log(1=ffi), where ffi is a given upper bound on the probability that our procedure returns an incorrect result. (Since our procedure uses randomization to perform experiments, there is a certain controllable chance that it will return an erroneous result.) We also discuss techniques for handling more general automata. We present evidence for the practical efficiency of our approach. For example, our procedure is able to infer the structure of an automaton based on Rubik's Cube (which has approximately 10
Citations
|
5825
|
Introduction to Algorithms
– Cormen, Leiserson, et al.
- 1992
|
|
627
|
Language identification in the limit
– Gold
|
|
370
|
Learning regular sets from queries and counterexamples
– Angluin
- 1987
|
|
255
|
Cryptographic limitations on learning boolean formulae and finite automata
– Kearns, Valiant
- 1994
|
|
254
|
Switching and Finite Automata Theory
– Kohavi
- 1978
|
|
184
|
Combinatorial Problems and Exercises
– Lovász
- 1993
|
|
176
|
Efficiency of a Good But Not Linear Set Union Algorithm
– Tarjan
- 1975
|
|
175
|
Complexity of automaton identification from given data
– Gold
- 1978
|
|
129
|
Inference of Finite Automata Using Homing Sequences
– Rivest, Schapire
- 1993
|
|
124
|
Inference of reversible languages
– Angluin
- 1982
|
|
86
|
On the complexity of minimum inference of regular sets
– Angluin
- 1978
|
|
82
|
Algebraic Structure Theory of Sequential Machines
– Hartmanis, Stearns
- 1966
|
|
71
|
Inductive inference, dfas, and computational complexity
– Pitt
- 1989
|
|
68
|
The minimum consistent DFA problem cannot be approximated within any polynomial
– Pitt, Warmuth
- 1993
|
|
64
|
The Design and Analysis of Efficient Learning Algorithms
– Schapire
- 1992
|
|
55
|
Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process,” The Annals of Applied Probability
– Fill
- 1991
|
|
31
|
Prediction-preserving reducibility
– Pitt, Warmuth
- 1990
|
|
20
|
Matrix Theory
– Franklin
- 1968
|
|
20
|
Language identi cation in the limit
– Gold
- 1967
|
|
19
|
System identification via state characterization. Aulomatico
– Gold
- 1972
|
|
18
|
Inference of nite automata using homing sequences
– Rivest, Schapire
- 1993
|
|
16
|
Complexity of automaton identi cation from given data
– Gold
- 1978
|
|
13
|
Evangelos Kokkevis, and Oded Maron. Inferring finite automata with stochastic output functions and an application to map learning
– Dean, Angluin, et al.
- 1992
|
|
10
|
private communication
– Young
- 1994
|
|
8
|
Bounds for eigenvalues of doubly stochastic matrices
– Fiedler
- 1972
|
|
6
|
The design and analysis of e cient learning algorithms
– Schapire
- 1992
|
|
5
|
A mechanism for early Piagetian learning
– Drescher
- 1987
|
|
4
|
Brazdin'. Finite Automata: Behavior and Synthesis
– unknown authors
- 1973
|
|
4
|
System identi cation via state characterization
– Gold
- 1972
|
|
3
|
Evangelos Kokkevis, and Oded Maron. Inferring nite automata with stochastic output functions and an application to map learning
– Dean, Angluin, et al.
- 1992
|
|
2
|
Genetic AI --- translating Piaget into Lisp
– Drescher
- 1986
|
|
1
|
A note on diversity
– Angluin
- 1987
|
|
1
|
The fundamental duality of system theory
– Bainbridge
- 1977
|
