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We show that Sleptsov place–transition nets (that allow transition firing in multiple instances at a step) run fast by implementing multiplication and division operations in polynomial time. In comparison, Petri nets (PNs) implement the mentioned operations in exponential time. Moreover, PNs are obtained as a special case of Sleptsov nets (SNs) using loops with places having unit marking attached to each transition. In addition, we develop basics of an SN programming technology including basic operations and program composition rules. We provide examples of programs written in SN language for encryption/decryption with the RSA algorithm, calculation of fuzzy logic functions, and parallel calculation of the solutions to Laplace equations. SN computers promise hyper-performance because of a concurrent programming style consisting of a concise graphical language and small granulation of parallel processes on the level of separate events. [ABSTRACT FROM PUBLISHER]