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Is there anything that is more powerful than a finite automaton but less powerful than a deterministic push down automaton?

r.v
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  • Is this a programming question? Can you flesh out some of the acronyms and maybe add some more tags to identify the domain? – Gray Apr 02 '12 at 22:41
  • You might ask this on cs.stackexchange.com; it could receive a better answer there. – Patrick87 Apr 02 '12 at 22:49

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Sure. Let us define a UDPDA to be a DPDA which uses only one stack symbol; i.e., the stack alphabet is unary. Such a machine can recognize the language L = {a^n b^n | n > 0}, but not the language P = {w$w^R | w is any string} of simple palindromes. It can recognize any regular language by not using the stack. So L(DFA) is a subset of L(UDPDA) is a subset of L(DPDA).

You can define many other kinds of automata, much more exotic than this, which might also fit the bill. For instance, I have defined min-heap automata which are neither more nor less powerful than pushdown automata. You can find out about them by searching cs.stackexchange.com, or Google "min heap automata".

Patrick87
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