### Abstract

We investigate the learning problem of two-tape deterministic finite automata (2-tape DFAs) from queries and counterexamples. Instead of accepting a subset of ∑*, a 2-tape DFA over an alphabet ∑ accepts a subset of ∑* × ∑*, and therefore, it can specify a binary relation on ∑*. In [3] Angluin showed that the class of deterministic finite automata (DFAs) is learnable in polynomial time from membership queries and equivalence queries, namely, from a minimally adequate teacher (MAT). In this article we show that the class of 2-tape DFAs is learnable in polynomial time from MAT. More specifically, we show an algorithm that, given any language L accepted by an unknown 2-tape DFA M, learns from MAT a two-tape nondeterministic finite automaton (2-tape NFA) M' accepting L in time polynomial in n and l, where n is the size of M and l is the maximum length of any counterexample provided during the learning process.

Original language | English |
---|---|

Pages (from-to) | 259-270 |

Number of pages | 12 |

Journal | Theory of Computing Systems |

Volume | 29 |

Issue number | 3 |

Publication status | Published - 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)

### Cite this

*Theory of Computing Systems*,

*29*(3), 259-270.

**Learning two-tape automata from queries and counterexamples.** / Yokomori, Takashi.

Research output: Contribution to journal › Article

*Theory of Computing Systems*, vol. 29, no. 3, pp. 259-270.

}

TY - JOUR

T1 - Learning two-tape automata from queries and counterexamples

AU - Yokomori, Takashi

PY - 1996

Y1 - 1996

N2 - We investigate the learning problem of two-tape deterministic finite automata (2-tape DFAs) from queries and counterexamples. Instead of accepting a subset of ∑*, a 2-tape DFA over an alphabet ∑ accepts a subset of ∑* × ∑*, and therefore, it can specify a binary relation on ∑*. In [3] Angluin showed that the class of deterministic finite automata (DFAs) is learnable in polynomial time from membership queries and equivalence queries, namely, from a minimally adequate teacher (MAT). In this article we show that the class of 2-tape DFAs is learnable in polynomial time from MAT. More specifically, we show an algorithm that, given any language L accepted by an unknown 2-tape DFA M, learns from MAT a two-tape nondeterministic finite automaton (2-tape NFA) M' accepting L in time polynomial in n and l, where n is the size of M and l is the maximum length of any counterexample provided during the learning process.

AB - We investigate the learning problem of two-tape deterministic finite automata (2-tape DFAs) from queries and counterexamples. Instead of accepting a subset of ∑*, a 2-tape DFA over an alphabet ∑ accepts a subset of ∑* × ∑*, and therefore, it can specify a binary relation on ∑*. In [3] Angluin showed that the class of deterministic finite automata (DFAs) is learnable in polynomial time from membership queries and equivalence queries, namely, from a minimally adequate teacher (MAT). In this article we show that the class of 2-tape DFAs is learnable in polynomial time from MAT. More specifically, we show an algorithm that, given any language L accepted by an unknown 2-tape DFA M, learns from MAT a two-tape nondeterministic finite automaton (2-tape NFA) M' accepting L in time polynomial in n and l, where n is the size of M and l is the maximum length of any counterexample provided during the learning process.

UR - http://www.scopus.com/inward/record.url?scp=0010600364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010600364&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0010600364

VL - 29

SP - 259

EP - 270

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 3

ER -