### 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 Σ*, a 2-tape DFA over an alphabet Σ accepts a subset of Σ* x Σ*, and therefore, it can specify a binary relation on Σ*. 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 |
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Pages (from-to) | 259-270 |

Number of pages | 12 |

Journal | Mathematical systems theory |

Volume | 29 |

Issue number | 3 |

Publication status | Published - 1996 May 1 |

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### ASJC Scopus subject areas

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

### Cite this

*Mathematical systems theory*,

*29*(3), 259-270.