Strong Sleptsov nets are Turing complete

Virtual Machine and Integrated Developer Environment for Sleptsov Net Computing

“…Sleptsov net computing paradigm [3,4,17,25] is based on completely graphical language of concurrent programming, with fine granulation of concurrent processes, and computing memory implementation in the form of a big, adjustable to the task structure, sparse matrix. For solving tasks with a certain spatial structure, multidimensional matrices of computing elements are applied.…”

“…The foremost peculiarity of a Sleptsov net is firing a transition at a step in a certain number of instances (multiple firing), while a Petri net fires a single transi-tion in a single instance, and Salwicki net fires the maximal set of firable transitions in a single instance each [3]. That is why an SN runs exponentially faster than a Petri net [4] opening prospects of using it as a uniform language for concurrent programming.…”

“…For convenience of drawing programs, we supply an SN with inhibitor and priority arcs though, according to the recent results [3], a strong Sleptsov net is Turingcomplete and we can use conventional arcs only. As distinct from traditional technique of programming in place-transition nets, where a control flow is represented by passage of a control token through the control flow subnet [26,27], in SN programs, we use a reversed control flow represented by passage of an empty marking (a "hole") through the control flow subnet.…”

“…Its main function consists in fast firing transitions. Combining Sleptsov strategy of maximal firing multiplicity with Salwicki strategy of maximal parallelism, we fire a maximal multiset [3] of transitions at a step. It results in mass parallel computations with fine granulation (addition, subtraction, multiplication, division within a transition) in case a Sleptsov net is perfectly mapped into the corresponding hardware structure of computing memory.…”

“…ACM Tech News [1] digest of editorial paper [2], following recent update [3] on Sleptsov net computing (SNC) [4], presents SNC as an approach that resolves modern supercomputing problems [5]. Jack Dongarra, in his ACM A.M. Turing Award lecture [5] revealed rather shocking information.…”