Finite automata with external storage

Perceptions of this chapter: The Finite automata with external storage of un-bounded capacity, subject to different access restrictions which limit the automa’s power of computation. The counter automata (or CA), pushdown automata (or PDA), non-equivalence of deterministic (or DPDA) and non-deterministic PDAs (or DPDA) and linear bounded automata (or LBA). Various access restrictions naturally lead to the automata of different power, stated by the relationship: CA < DPDA < NPDA < LBA. Remarkably, an additional relaxation of access restrictions rapidly leads to a universal model of computation, that is, one as powerful as any other model (that is, of discrete computation). We generally refer to the 2-PDA (that is, a PDA with 2 stacks), the QM or Post machine (that is, a finite state machine and a queue), and the Turing machine (or TM).

Finite automata with external storage - concepts, conventions and notation

FSM M controls the access to an input tape T (if any) and the storage device S. The general form of transition:

(Current state of M, currently scanned symbol on T, presently scanned symbol on S)
-> (New state of M, newly written symbol on S, motion of the read or write head on S)

The two significant parameters are:

a) Size of storage device (that is, un-bounded, except for LBA, where storage size based on the size of input).

b) Access operations (example: read, write, motion of the read or write head and test for empty).

Details might vary greatly, example:

There might be no input tape T. Input to be processed is written in a designated region of the storage device.

The structure of storage device, example: one or more tapes (that is, single-ended or double-ended), 2-d grid and so on.

Acceptance: By accepting the state or by designated content of the storage device (example: empty).

Tape T and storage S might have separate alphabets that we call A, B.

We will employ various conventions selected to make each illustration simple.

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