Stream X-Machine - The Stream X-Machine - Relationship To X-machines

Relationship To X-machines

The Stream X-Machine is a variant of X-machine in which the fundamental data type X = Out* × Mem × In*. In the original X-machine, the φi are general relations on X. In the Stream X-Machine, these are usually restricted to functions; however the SXM is still only deterministic if (at most) one transition is enabled in each state.

A general X-machine handles input and output using a prior encoding function α: YX for input, and a posterior decoding function β: XZ for output, where Y and Z are respectively the input and output types. In a Stream X-Machine, these types are streams:

Y = In* Z = Out*

and the encoding and decoding functions are defined as:

α(ins) = (<>, mem0, ins) β(outs, memn, <>) = outs

where ins: In*, outs: Out* and memi: Mem. In other words, the machine is initialized with the whole of the input stream; and the decoded result is the whole of the output stream, provided the input stream is eventually consumed (otherwise the result is undefined).

Each processing function in a SXM is given the abbreviated type φSXM: Mem × InOut × Mem. This can be mapped onto a general X-machine relation of the type φ: X → X if we treat this as computing:

φ(outs, memi, in :: ins) = (outs :: out, memi+1, ins)

where :: denotes concatenation of an element and a sequence. In other words, the relation extracts the head of the input stream, modifies memory and appends a value to the tail of the output stream.

Read more about this topic:  Stream X-Machine, The Stream X-Machine

Famous quotes containing the words relationship to and/or relationship:

    ... the Wall became a magnet for citizens of every generation, class, race, and relationship to the war perhaps because it is the only great public monument that allows the anesthetized holes in the heart to fill with a truly national grief.
    Adrienne Rich (b. 1929)

    But the relationship of morality and power is a very subtle one. Because ultimately power without morality is no longer power.
    James Baldwin (1924–1987)