Synthesis of Macro Petri Nets into FPGA with Distributed Memories

In this paper a new method of Petri net array-based synthesis is proposed. The method is based on decomposition of colored interpreted macro Petri net into state machine subnets. Each state machine subnet is determined by one color. During the decomposition process macroplaces are expanded or replaced by doublers of macroplace. Such decomposition leads to parallel implementation of a digital system. The structured encoding of places is done by using minimal numbers of bits. Colored microoperations, which are assigned to places, are written into distributed and flexible memories. It leads to realization of a logic circuit in a two-level concurrent structure, where the combinational circuit of the first level is responsible for firing transitions, and the second level memories are used for generation of microoperations. Such an approach allows balanced usage of different kinds of resources available in modern FPGAs

FUZZY DECISIONS IN MODULAR NEURAL NETWORKS

Modular neural networks structured as associative memories are capable of processing inputs built from tensorial products of vectors. In this context, the operators of propositional and modal logic can be represented as modular distributed memories that can process not only classical Boolean but also fuzzy evaluations of truth-values of sentences. Furthermore, projecting memory outputs onto unit vectors yield discrete dynamical systems that exhibit varying degrees of complexity. As examples, we analyze outcomes of semantic evaluations in several self-referential systems including modal versions of the chaotic liar, antagonistic decisions and extended dilemmas. By studying these examples we hope to shed some light on the modeling of cognitive decisions.