On one-way Auxiliary pushdown automata

Brandenburg, Franz J.

doi:10.1007/3-540-08138-0_11

Cited by 25 publications

(16 citation statements)

References 4 publications

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“…For strong space, this question was solved by Brandenburg [4] by proving a log log n lower bound, whose optimality is witnessed by a unary language. 4 The situation in the weak case is very different. In fact, as proved by Chytil [7], for any integer k, there exists a noncontext-free language accepted in space Oðlog ðkÞ nÞ.…”

Section: Introductionmentioning

confidence: 99%

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Unary Context-Free Grammars and Pushdown Automata, Descriptional Complexity and Auxiliary Space Lower Bounds

Pighizzini¹,

Shallit²,

Wang³

2002

Journal of Computer and System Sciences

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It is well known that a context-free language defined over a one-letter alphabet is regular. This implies that unary context-free grammars and unary pushdown automata can be transformed into equivalent finite automata. In this paper, we study these transformations from a descriptional complexity point of view. In particular, we give optimal upper bounds for the number of states of nondeterministic and deterministic finite automata equivalent to unary context-free grammars in Chomsky normal form. These bounds are functions of the number of variables of the given grammars. We also give upper bounds for the number of states of finite automata simulating unary pushdown automata. As a main consequence, we are able to prove a log log n lower bound for the workspace used by one-way auxiliary pushdown automata in order to accept nonregular unary languages. The notion of space we consider is the so-called weak space concept. # 2002 Elsevier Science (USA)

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Section: Introductionmentioning

confidence: 99%

“…In Section 3, we study the cost of the simulation of unary contextfree grammars by nondeterministic finite automata. The construction used to get this 4 Actually, the space definition presented in [4] corresponds to the weak notion. However, the argument used to prove the lower bound works only for strong space.…”

mentioning

confidence: 99%

Unary Context-Free Grammars and Pushdown Automata, Descriptional Complexity and Auxiliary Space Lower Bounds

Pighizzini¹,

Shallit²,

Wang³

2002

Journal of Computer and System Sciences

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“…See also [5] and [8], The conventions regarding space bounds on the work tapes and/or oracle tape are as before. Note that there is no bound on the size of the pushdown store.…”

Section: Conversely Let L = L(m D)mentioning

confidence: 99%

“…(2)=> (5). Consider an advice function such that for each n it gives the formula corresponding to length n. It is bounded in length by a 2 polylog function.…”

Section: Sespmentioning

confidence: 99%

Nonuniform complexity classes specified by lower and upper bounds

Balcázar¹,

Gabarró²

1989

RAIRO-Theor. Inf. Appl.

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“…These automata are introduced in Brandenburg (1977), and are the one-way model of the well-known (twoway) auxiliary pushdown automata, studied by Cook (1971).…”

Section: Proofmentioning

confidence: 99%

The contextsensitivity bounds of contextsensitive grammars and languages

Brandenburg

1977

Automata, Languages and Programming

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On one-way Auxiliary pushdown automata

Cited by 25 publications

References 4 publications

Unary Context-Free Grammars and Pushdown Automata, Descriptional Complexity and Auxiliary Space Lower Bounds

Unary Context-Free Grammars and Pushdown Automata, Descriptional Complexity and Auxiliary Space Lower Bounds

Nonuniform complexity classes specified by lower and upper bounds

The contextsensitivity bounds of contextsensitive grammars and languages

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