## Conway's Problem and the commutation of languages (2001)

Venue: | Bulletin of EATCS |

Citations: | 8 - 5 self |

### BibTeX

@ARTICLE{Karhumäki01conway'sproblem,

author = {Juhani Karhumäki and Ion Petre},

title = {Conway's Problem and the commutation of languages},

journal = {Bulletin of EATCS},

year = {2001},

volume = {74},

pages = {171--177}

}

### OpenURL

### Abstract

We survey the known results on two old open problems on commutation of languages. The first problem, raised by Conway in 1971, is asking if the centralizer of a rational language must be rational as well – the centralizer of a language is the largest set of words commuting with that language. The second problem, proposed by Ratoandromanana in 1989, is asking for a characterization of those languages commuting with a given code – the conjecture is that the commutation with codes may be characterized as in free monoids. We present here simple proofs for the known results on these two problems. 1