Complementing Two-Way Finite Automata

Geffert, Viliam; Mereghetti, Carlo; Pighizzini, Giovanni

doi:10.1007/11505877_23

Cited by 6 publications

(14 citation statements)

References 16 publications

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“…Finally, we point out that, as proven in [GMP07], with a linear increasing in the number of the states, each 2dfas can be made halting. In particular, each n-state 2dfa can be simulated by a halting 2dfa with 4n states.…”

Section: (If Part)mentioning

confidence: 70%

Converting nondeterministic automata and context-free grammars into Parikh equivalent one-way and two-way deterministic automata

Lavado

Pighizzini

Seki

2013

Information and Computation

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We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent oneway and two-way deterministic finite automata, from a descriptional complexity point of view.We prove that for each one-way nondeterministic automaton with n states there exist Parikh equivalent one-way and two-way deterministic automata with e O( √ n·ln n) and p(n) states, respectively, where p(n) is a polynomial. Furthermore, these costs are tight. In contrast, if all the words accepted by the given automaton contain at least two different letters, then a Parikh equivalent one-way deterministic automaton with a polynomial number of states can be found.Concerning context-free grammars, we prove that for each grammar in Chomsky normal form with h variables there exist Parikh equivalent one-way and two-way deterministic automata with 2 O(h 2 ) and 2 O(h) states, respectively. Even these bounds are tight.

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Section: (If Part)mentioning

confidence: 70%

Converting nondeterministic automata and context-free grammars into Parikh equivalent one-way and two-way deterministic automata

Lavado

Pighizzini

Seki

2013

Information and Computation

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“…This, in turn, would imply the exponential gap for the trade-off between 2NFA's and 2DFA's, and also between pebble-2NFA's and pebble-2DFA's, since the complementation for the deterministic two-way machines is linear (namely, 4 · n states for 2DFA's, by [10], and at most 60 · n states for pebble-2DFA's, by Corollary 6 above).…”

Section: Resultsmentioning

confidence: 99%

“…This time we use Theorems 2(b) and 3(b), together with the fact that an n-state 2DFA can be complemented with no more than 4 · n states [10].…”

Section: Translationmentioning

confidence: 99%

Translation from classical two-way automata to pebble two-way automata

Geffert

Ištoňová

2010

RAIRO-Theor. Inf. Appl.

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We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. However, we show that these two machine models are not independent: if there exists a polynomial trade-off for the classical two-way automata, then there must also exist a polynomial trade-off for the pebble two-way automata. Thus, we have an upward collapse (or a downward separation) from the classical two-way automata to more powerful pebble automata, still staying within the class of regular languages. The same upward collapse holds for complementation of nondeterministic twoway machines.These results are obtained by showing that each pebble machine can be, by using suitable inputs, simulated by a classical two-way automaton with a linear number of states (and vice versa), despite the existing exponential blow-up between the classical and pebble two-way machines.

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“…We shall prove this statement by applying a technique developed by Sipser in [10] in order to prove that every space bounded deterministic Turing machine can be transformed into a halting deterministic Turing machine with the same space bound. Furthermore, this technique has also been used by Muscholl et al [11] in order to show a similar result for deterministic tree-walking automata and by Geffert et al [12] in order to complement deterministic two-way automata. More precisely, we show for an arbitrary IFA(k) M , how a DFA(k) M can be constructed that, on any input ¢w$, searches the backward configuration tree of M on w for a path from (q f , 0, 0, .…”

Section: This Particularly Means That Ifmentioning

confidence: 93%

On multi-head automata with restricted nondeterminism

Reidenbach

Schmid

2012

Information Processing Letters

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In this work, we consider deterministic two-way multi-head automata, the input heads of which are nondeterministically initialised, i. e., in every computation each input head is initially located at some nondeterministically chosen position of the input word. This model serves as an instrument to investigate restricted nondeterminism of two-way multi-head automata. Our result is that, in terms of expressive power, two-way multi-head automata with nondeterminism in form of nondeterministically initialising the input heads or with restricted nondeterminism in the classical way, i. e., in every accepting computation the number of nondeterministic steps is bounded by a constant, do not yield an advantage over their completely deterministic counter-parts with the same number of input heads. We conclude this paper with a brief application of this result.

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Complementing Two-Way Finite Automata

Cited by 6 publications

References 16 publications

Converting nondeterministic automata and context-free grammars into Parikh equivalent one-way and two-way deterministic automata

Converting nondeterministic automata and context-free grammars into Parikh equivalent one-way and two-way deterministic automata

Translation from classical two-way automata to pebble two-way automata

On multi-head automata with restricted nondeterminism

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