State Transition Dynamics

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 state’s 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 discrete models of computation, together with illustrative examples. The relevance of state transition systems and string dynamics is discussed from the perspective of molecular computing.

Analysing graph transformation systems through constraint handling rules

Graph transformation systems (GTS) and constraint handling rules (CHR) are non-deterministic rule-based state transition systems. CHR is well known for its powerful confluence and program equivalence analyses, for which we provide the basis in this work to apply them to GTS. We give a sound and complete embedding of GTS in CHR, investigate confluence of an embedded GTS and provide a program equivalence analysis for GTS via the embedding. The results confirm the suitability of CHR-based program analyses for other formalisms embedded in CHR.