Families of languages defined by ciliate bio-operations

We investigate families of languages de%ned by closure under operations generalized from models of gene descrambling in stichotrichous ciliates. We speci%cally consider languages that are closed under the synchronized insertion and deletion operations as well as languages closed under the hairpin inversion (hi) operation. Biologically, this studies sets of genes that cannot be further descrambled. In addition, we show that every trio closed under hairpin inversion is also closed under the double loop with alternating direct pointers (dlad)-excision/reinsertion bio-operation. c © 2004 Elsevier B.V. All rights reserved.