Abstract
Rational transductions are defined by rational relations, i.e. rational subsets of the product of two free monoids. The chapter therefore begins with two sections concerned with recognizable and rational subsets of an arbitrary monoid. The next two sections contain the definition and basic properties of rational relations and rational transductions. Examples of rational transductions are given in Section 5. Then the machines realizing rational transductions are introduced. Matrix representations of rational transductions are investigated in Section 7. In the last section we show that most of the usual decision problems are unsolvable for rational transductions.
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