Finite strings can map to finite strings {automata theory}.
symbols
Systems have finite symbol sets, such as 0 or no symbol and 1.
strings
Finite tape has segments, each with one symbol. Segment series make symbol series.
read and write
Tape reader reads one tape segment. Tape writer writes one tape segment. Tape mover moves tape one segment forward or backward.
tape
Tape has input symbols and starts at initial position.
state
Automaton starts in initial internal state. Automaton changes state in response to rules. Controller has a finite number of possible states.
rules
Given current state and symbol, functions {transition function} {next-output function} tell which symbol to write and where, functions {next-state function} tell what next controller state is, and functions {next-move function} tell whether to move tape, read tape, or write on tape.
processing
Controller decides what tape mover, tape writer, and tape reader do at next step, based on symbol reading, controller state, and rules. When automaton stops, original string has become new string.
algorithm
Automatons can represent any computer program or algorithm.
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Date Modified: 2022.0224