Flip-pushdown automata are pushdown automata with the additional power to flip or reverse its pushdown, and were recently introduced by Sarkar [13]. We solve most of Sarkar's open problems. In particular, we show that k+1 pushdown reversals are better than k for both deterministic and nondeterministic flip-pushdown automata, i.e., there are languages which can be recognized by a deterministic flip-pushdown automaton with k+1 pushdown reversals but which cannot be recognized by a k-flip-pushdown (deterministic or nondeterministic). Furthermore, we investigate closure and non-closure properties as well as computational complexity problems such as fixed and general membership.

/pdf/flip-pushdown-automata-k-1-pushdown-reversals-are-better-29n6osa539.pdf

Pushdown Automaton with the Ability to Flip its Stack

Flip-pushdown automata: k + 1 pushdown reversals are better than k

Flip-pushdown automata are pushdown automata with the additional ability to flip or reverse its pushdown. We investigate deterministic and nondeterministic flip-pushdown automata accepting by final state or empty pushdown. In particular, for nondeterministic flip-pushdown automata both acceptance criterion are equally powerful, while for determinism, acceptance by empty pushdown is strictly weaker. This nicely fits into the well-known results on ordinary pushdown automata. Moreover, we consider hierarchies of flip-pushdown automata w.r.t. the number of pushdown reversals. There we show that nondeterminism is better than determinism. Moreover, since there are languages which can be recognized by a deterministic flip-pushdown automaton with k + 1 pushdown reversals but which cannot be recognized by a k-flip-pushdown (deterministic or nondeterministic) as shown in [9] we are able to complete our investigations with incomparabiiity results on different levels of the hierarchies under consideration.

Flip-pushdown automata: Nondeterminism is better than determinism

Flip-pushdown automata are pushdown automata with the additional ability to flip or reverse its pushdown We investigate deterministic and nondeterministic flip-pushdown automata accepting by final state or empty pushdown In particular, for nondeterministic flip-pushdown automata both acceptance criterion are equally powerful, while for determinism, acceptance by empty pushdown is strictly weaker This nicely fits into the well-known results on ordinary pushdown automata Moreover, we consider hierarchies of flip-pushdown automata wrt the number of pushdown reversals There we show that nondeterminism is better than determinism Moreover, since there are languages which can be recognized by a deterministic flip-pushdown automaton with k + 1 pushdown reversals but which cannot be recognized by a k-flip-pushdown (deterministic or nondeterministic) as shown in [9] we are able to complete our investigations with incomparability results on different levels of the hierarchies under consideration

/pdf/flip-pushdown-automata-nondeterminism-is-better-than-24x3stpv2e.pdf

Flip-pushdown automata: nondeterminism is better than determinism

The class of growing context-sensitive languages (GCSL) was proposed as a naturally defined subclass of context-sensitive languages whose membership problem is solvable in polynomial time. Growing context-sensitive languages and their deterministic counterpart called Church-Rosser languages (CRL) complement the Chomsky hierarchy in a natural way, as the classes filling the gap between context-free languages and context-sensitive languages. They possess characterizations by a natural machine model, length-reducing two-pushdown automata (lrTPDA). We introduce a lower bound technique for lrTPDAs. Using this technique, we prove the conjecture of McNaughton, Narendran and Otto that the set of palindromes is not in CRL. As a consequence we obtain that CFL∩coCFL as well as UCFL∩coUCFL are not included in CRL, where UCFL denotes the class of unambiguous context-free languages; this solves an open problem posed by Beaudry, Holzer, Niemann and Otto. Another corollary is that CRL is a strict subset of GCSL∩coGCSL.

/pdf/lower-bound-technique-for-length-reducing-automata-1dhq5z546z.pdf

Pushdown Automaton with the Ability to Flip its Stack

Citations

Flip-pushdown automata: k + 1 pushdown reversals are better than k

Flip-pushdown automata: Nondeterminism is better than determinism

Flip-pushdown automata: nondeterminism is better than determinism

Lower bound technique for length-reducing automata

Modern Language Models and Computation

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