Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-09-15 , DOI: 10.1016/j.tcs.2020.09.025 Thierry Boy de la Tour; Rachid Echahed
Some computations can be elegantly presented as the parallel or simultaneous application of rules. This is the case of cellular automata and of simultaneous assignments in Python. In both cases the expected result cannot be obtained by a sequential application of rules. A general framework of attributed graph transformations is proposed where such computations can be expressed and analyzed. Determinism is achieved by an exhaustive parallel application of rules, as in cellular automata that are shown to have a straightforward representation in this framework. A more concise parallel transformation is also proposed, where some applications of rules can be ignored thanks to their symmetries, while preserving determinism. Parallel transformations are then used to characterize the property of parallel independence.