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2 2006

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Synchronized Shuffle on Backbones

Manea F., Mitrana V., Voinescu D-C.

Fundamenta Informaticae

2006

Vol. 73, nr 1-2

191-202

In this paper we continue the study on synchronized shuffle started in [5] by introducing the condition that the two words which are to be shuffled have to synchronize on a predefined set of backbones. As far as the language-theoretic properties of this operation are concerned, we prove that in a trio the closure under shuffle is equivalent to the closure under synchronized shuffle on a regular set of backbones. Based on this result we show that a set of backbones is regular if and only if the synchronized shuffle of every two regular languages on that set is also regular. Some relationships between this operation and the synchronized shuffle operations introduced in [5] are presented and some open problem are finally discussed.

Routes and Products of Monoids

Mateescu A., Freund R.

Fundamenta Informaticae

2006

Vol. 73, nr 1-2

205-211

We investigate the problem of finding monoids that recognize languages of the form L1\JoinTL2 where T is an arbitrary set of routes. We present a uniform method based on routes to find such monoids. Many classical operations from the theory of formal languages, such as catenation, bi-catenation, simple splicing, shuffle, literal shuffle, and insertion are shown to be just particular instances of the operation T.