Computability of Recursive Functions
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Formal languages and their relation to automata
Formal languages and their relation to automata
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We define a finite-state machine called a circular automata (CA) which processes information in a queue; we show that any function computed (or any language recognized) by such a machine is computable (recognizable) by a Turing machine and vice versa. Space and time bounds are given for the needed simulations. Furthermore, the class of languages recognized by (non-) deterministic linear bounded automata is equal to the class of languages recognized by (non-) deterministic CA which don't expand the length of the contents of the queue. Whether every language recognized by such a non-expanding CA is recognized by a deterministic one is equivalent to the famous LBA problem.CA can be viewed as generalizations of ordinary finite automata and as a Shepherdson-Sturgis single register machine programming language. An interesting model of a non-expanding CA is that of a finite-state machine which process tapes in the form of a loop. This appears to be a very natural way to process magnetic tape which circles back on itself.