Complementing two-way finite automata

Geffert, Viliam; Mereghetti, Carlo; Pighizzini, Giovanni

doi:10.1016/j.ic.2007.01.008

Cited by 53 publications

(33 citation statements)

References 17 publications

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“…For instance, the divide-and-conquere technique used to prove Theorem 5.2 derives from a similar argument used by Savitch to prove his famous theorem concerning the removal of nondeterminism in space bounded Turing machines [42]. The inductive counting technique used in [14] to obtain the polynomial complementation of 2NFAs, was introduced independently by Immerman [21] and Szelepcsényi [47] to prove the closure under complementation of nondeterministic space. The state polynomial conversion of unary 2NFAs into equivalent unambiguous 2NFAs, uses a result by Reinhardt and Allender [40], which, in the context of nonuniform complexity, shows that nondeterministic logspace bounded machines can be made unambiguous keeping the space bound.…”

Section: Discussionmentioning

confidence: 99%

“…(i) Each unary n-state 2NFA accepting a language L can be transformed into a 2NFA with O(n 8 ) states accepting the complement of L [14].…”

Section: Normal Forms For Unary Nondeterministic Automatamentioning

confidence: 99%

“…In particular, concerning the simulation by 2DFAs, the following result has been proved: While the proof of Theorem 5.2 strongly relies on the normal form for unary 2NFAs presented in Theorem 5.1, the construction obtained to prove Theorem 5.3 uses a procedure which, essentially, is able to detect infinite loops in outer nondeterministic automata. This procedure is derived from an algorithm, presented in [14], to make two-way deterministic automata halting, which, in turns, is derived by a complementation technique for space bounded deterministic Turing machines discovered by Sipser [45].…”

Section: Normal Forms For Unary Nondeterministic Automatamentioning

confidence: 99%

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Two-Way Finite Automata: Old and Recent Results

Pighizzini

2013

Fundamenta Informaticae

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The notion of two-way automata was introduced at the very beginning of automata theory. In 1959, Rabin and Scott and, independently, Shepherdson, proved that these models, both in the deterministic and in the nondeterministic versions, have the same power of one-way automata, namely, they characterize the class of regular languages. In 1978, Sakoda and Sipser posed the question of the costs, in the number of the states, of the simulations of one-way and two-way nondeterministic automata by two-way deterministic automata. They conjectured that these costs are exponential. In spite of all attempts to solve it, this question is still open. In the last ten years the problem of Sakoda and Sipser was widely reconsidered and many new results related to it have been obtained. In this work we discuss some of them. In particular, we focus on the restriction to the unary case, namely the case of automata defined over the one letter input alphabet, and on the connections with open questions in space complexity.

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Section: Discussionmentioning

confidence: 99%

“…(i) Each unary n-state 2NFA accepting a language L can be transformed into a 2NFA with O(n 8 ) states accepting the complement of L [14].…”

Section: Normal Forms For Unary Nondeterministic Automatamentioning

confidence: 99%

Section: Normal Forms For Unary Nondeterministic Automatamentioning

confidence: 99%

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Two-Way Finite Automata: Old and Recent Results

Pighizzini

2013

Fundamenta Informaticae

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“…For instance, the divide-and-conquere technique used to prove Theorem 5.2 derives from the proof of the famous Savitch Theorem [33]. The inductive counting tecnique used in [10] to obtain the polynomial complementation of 2NFAs derives from the argument used to prove the closure under complementation of nondeterministic space, the famous result independently proved in 1988 by Immerman [14] and Szelepcsényi [37]. Actually, the complexity theory for finite automata can be developed as a part of standard complexity theory for Turing machines, with classes, reductions, complete problems and so on.…”

Section: Discussionmentioning

confidence: 99%

Two-Way Finite Automata: Old and Recent Results

Pighizzini

2012

Electron. Proc. Theor. Comput. Sci.

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The notion of two-way automata was introduced at the very beginning of automata theory. In 1959, Rabin and Scott and, independently, Shepherdson, proved that these models, both in the deterministic and in the nondeterministic versions, have the same power of one-way automata, namely, they characterize the class of regular languages. In 1978, Sakoda and Sipser posed the question of the cost, in the number of the states, of the simulation of one-way and two-way nondeterministic automata by two-way deterministic automata. They conjectured that these costs are exponential. In spite of all attempts to solve it, this question is still open. In the last ten years the problem of Sakoda and Sipser was widely reconsidered and many new results related to it have been obtained. In this work we discuss some of them. In particular, we focus on the restriction to the unary case and on the connections with open questions in space complexity

show abstract

“…There are two classes of finite automata: deterministic finite automata (DFA) and nondeterministic finite automata (NFA). In contrast to NFA, each pair of state and input symbols in DFA will lead to one and only one transition to the next state (Geffert et al, 2007).…”

Section: Modeling Strategies In Finite Automatamentioning

confidence: 99%

Adaptive automata model for learning opponent behavior based on genetic algorithms

Almanasra¹,

Suwais²,

Arshad³

2012

Sci. Res. Essays

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The purpose of this research is to study how genetic algorithms (GA's) are applied in the field of Game Theory. GA's are effective approaches for machine learning and optimization problems. In this work, genetic algorithm is utilized to determine the behavior of an opponent in Prisoners' Dilemma. The opponent behavior will be modeled by means of adaptive automaton. The basic problem of this study is the well-known Prisoner Dilemma. The primary purpose of this research is to determine the opponent behavior towards finding a better strategy to be followed by the player, since the best strategy to be followed depends on the opponent behavior. The results of our proposed model showed the capability of our model to identify the opponent model efficiently. Based on the provided knowledge about the opponent model, the dynamic strategy showed better results when compared to other well-known strategies.

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Complementing two-way finite automata

Cited by 53 publications

References 17 publications

Two-Way Finite Automata: Old and Recent Results

Two-Way Finite Automata: Old and Recent Results

Two-Way Finite Automata: Old and Recent Results

Adaptive automata model for learning opponent behavior based on genetic algorithms

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