Lindenmayer (L) systems form a class of interesting computational formalisms due to their parallel nature, the various circumstances under which they operate, the restrictions imposed on language acceptance, and other attributes. These systems have been extensively studied in the Formal Languages literature. In the past decade a new type of Lindenmayer system had been proposed: Watson-Crick Lindenmayer Systems. These systems are essentially a marriage between Developmental systems and DNA Computing. At their heart they are Lindenmayer systems augmented with a complementary relation amongst elements in the system just as the base pairs of DNA strands can be complementary with respect to one another. When conditions and a mechanism for 'switching' the state of a computation to it's complementary version are provided then these systems can become surprisingly more powerful than the L systems which form their backbone. This dissertation explores the computational power of new variants of Watson-Crick L systems. It is found that many of these systems are Computationally-Complete. These investigations differ from prior ones in that the systems under consideration have extended alphabets and usually Regular Triggers for complementation are considered as opposed to Context-Free Triggers investigated in previous works. / Thesis (Master, Computing) -- Queen's University, 2010-12-06 18:29:23.584

In the last decade, some researches on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the interest of the finite power property to achieve partial solutions of this problem. We prove that the star problem is decidable in some trace monoid if and only if in the same monoid, it is decidable whether a recognizable language has the finite power property. Intermediary results allow us to give a shorter proof for the decidability of the two previous problems in every trace monoid without C4-submonoid. We also deal with some earlier ideas, conjectures, and questions which have been raised in the research on the star problem and the finite power property, e.g. we show the decidability of these problems for recognizable languages which contain at most one non-connected trace.

In the last decade, some researches on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the interest of the finite power property to achieve partial solutions of this problem. We prove that the star problem is decidable in some trace monoid if and only if in the same monoid, it is decidable whether a recognizable language has the finite power property. Intermediary results allow us to give a shorter proof for the decidability of the two previous problems in every trace monoid without C4-submonoid. We also deal with some earlier ideas, conjectures, and questions which have been raised in the research on the star problem and the finite power property, e.g. we show the decidability of these problems for recognizable languages which contain at most one non-connected trace.