State Transition Dynamics: basic concepts and molecular computing perspectives

Classical dynamics concepts are analysed in the basic mathematical setting of state transition systems where time and space are both completely discrete and no structure is assumed on the states of the space. Interesting relationships between attractors and recurrence are identified and some features of chaos are expressed in simple set theoretic terms. String dynamics is proposed as a unifying concept for dynamical systems arising from computation models, and examples to this effect are provided. The relevance of state transition and string dynamics is discussed in the perspective of molecular computing with respect to several issues.