The Von Neumann model is as used in a desktop computer - executes instructions sequentially
Von Neumann computations are a class of computer programs ideally suited to sequential processing.
Turing machines are very similar
Other examples are Analog Computers, Optical Computers, Quantum Computers, Cell Processors, DNA, Neural Nets (in Silicon).
Most Non Von Neumann models distributes the computation amongst processing units - for example FPGA or neural networks.
Typical naturally inspired examples are Genetic, DNA and Neural Nets.
They can be thought of as a class of computer programs ideally suited for parallel computation.
In principle any Non Von Neumann representation is Turing Complete, and can perform arbitrary computations.
If would be very difficult . though in principle possible . to write Microsoft Word on a large enough FPGA; it.s even possible on DNA
The trade-off is between parallelism and programmability.
In a NVM machine, the computational nodes act in parallel: this often gives huge speed increases.
The problem is, we don.t know how to program them to very well.
Konrad Zuse.s Plankalkül: The First
High-Level, "non von Neumann"
Konrad Zuse was the first person in history to build a working digital computer, a fact that is still not generally acknowledged. Even less known is that in the years 1943.1945, Zuse developed a high-level programming model and, based on it, an algorithmic programming language called Plankalkül (plan calculus).
The first non-Von Neumann computer.
John Backus Can Programming Be Liberated from the von Neumann Style?
Enumera The First Cell Processor Design.
The von Neumann Architecture of Computer Systems by H. Norton Riley
Celoxica The Technology Leader in C Based Electronic Design , create Parrallel FPGA using the Handel-C language. A variant of C, handel-c is a behavioral language for FPGA design.
SystemC is also a C variant for direct VHDL or Verilog creation of FPGA or Silicon Design code.
Zero Instruction Set Computer jointly developed by IBM in Paris and by Guy Paillet. Neural Net chip for image recognition.
From CISC to RISC to ZISC
The term von Neumann language refers to those programming languages that are high-level abstract isomorphisms of von Neumann architectures. As of 2004, most current programming languages fit into this description, likely as a consequence of the extensive domination of the von Neumann computer architecture during the past 50 years.
The differences between FORTRAN, C, and even Java, although considerable, are ultimately constrained by the fact that all three are based on the programming style of the von Neumann computer (if, for example, Java objects were all executed in parallel with asynchronous message passing and attribute-based declarative addressing, then Java would not be in the group).
The isomorphism between von Neumann programming languages and architectures is in the following manner:
Using a metaphor from Backus, assignment statements in von Neumann languages split programming into two worlds: the right side and left side of assignment statements. The right side consists of expressions, an orderly mathematical space with potentially useful algebraic properties: most computation takes place here. The left side consists of statements, a disorderly mathematical space with few useful mathematical properties (structured programming can be seen as a limited heuristic that does apply in this space, though).
Backus claimed that there exists now in computer science a vicious cycle where the long standing emphasis on von Neumann languages has continued the primacy of the von Neumann computer architecture... and our dependency on it has made non-von Neumann languages uneconomical and thus limited their further development: the lack of widely available and effective non-von Neumann languages has deprived computer designers of the motivation and the intellectual foundation necessary to develop new computer architectures.