Rethinking Computer Science Part 3: A Sequential Interpreter.

Part 3 presents the logical structures of a memory, a configurable oscillation and a sequential interpreter ring forming a traditional universal sequential processor.

Memory: Stopping a Data Wavefront
In the flow model of computation successive wavefronts of data spontaneously propagate through the flow paths of networks of linked oscillations. A memory would entail stopping a data wavefront from flowing, holding it for an indefinite period, then allowing it to flow again. This can be accomplished with a ring.

 A Memory Ring
An oscillation link maintains a wavefront until it is accepted by the following oscillation. A ring can be arranged with an added dual-rail control path that indefinitely delays acceptance at a specific link, C, in the ring effectively stopping and storing a data wavefront.

The read rail transitioning to data enables the stored data wavefront to the output of the ring. The wavefront flows both out of the ring and back into the ring through B to be restored at C allowing multiple reads of the same wavefront.

The write rail transitioning to data enables the stored data wavefront to a consume path, D2, removing it from the ring and allowing a data wavefront presented on the input path, also enabled by the write rail, to flow into the ring and to C replacing the previous wavefront with the input wavefront.

A data wavefront is maintained indefinitely at C until a dual rail read/write command wavefront allows it to flow.

 A Randomly Addressable Memory
Memory rings can be stacked with a write bus and a read bus and individual read/write controls to form an arbitrarily large random access memory.

The memory operates as a complex conditional oscillation which is a consume oscillation for write and a produce oscillation for read. Each oscillation only one memory element is addressed and enabled to accept an input from the write bus or to present an output to the read bus.

The entire memory structure is a network of dual threshold elements.

A Configurable Oscillation

All flow is characterized in terms of two input one output operations and in terms of a common flow path structure (32 dual-rail bits for instance). The behaviors of all oscillations are characterized in terms of a common set of operations on the common flow path structure. An oscillation is defined that conditionally realizes each operation by steering the input through the specified operation to the output.

A computation can now realized as a network of identical configurable oscillations each behaving according to its configuration code.

Symbolically Specifying the Network
Each arc of the network is assigned a unique name which associates an output of one node to one or more inputs of other nodes. The network can now be expressed as a collection of statements each of which associates the names of the input arcs and the name of the output arc with a configuration code such as below.

opcode, inAname, inBname outname

The collection of statements, specifying the network structure by name correspondence, can be placed in an environment in which the name correspondence relations can be conveniently realized. If the unique names are unique memory addresses then the statements become linked by reference through memory locations. Since each memory location will maintain a data wavefront indefinitely the statements can be performed one at a time in any ordering that preserves the dependency relations of the original flow network. In particular, the statements can be placed linearly in a memory and with the assistance of conditional branching the statements can be performed one at a time in sequence in an appropriate order. Data wavefronts flowing haltingly through memory ultimately realize the computation specified by the original flow network.

 An Interpreting Pipeline Ring
A pipeline ring containing a configurable oscillation performs operations in sequence by fetching a statement from memory, fetching its input wavefronts from memory performing the operation and sending the result wavefront to memory, then doing it again, and again.

The ring and the memory are realized entirely in terms of a spontaneously behaving, network of linked oscillations composed entirely of dual threshold operations. No clock, no critical timing issues, no state machine, no DQ flip flops.

The sequential interpreter delivers, “universal”, computation as a coherent structure of logical relations in contrast to a heterogeneous structure of clock, Boolean logic and DQ flip flops or of abstract state machine, mechanical read/write head and paper tape. Universality is attained by mapping dependency networks into the tabula rasa of single memory and sequence. Is this the only road to universality or might there be a universal interpreter that directly interprets flow networks preserving their structure and behavior?

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