Complexity Results on Register Context-Free Grammars and Register Tree Automata

Senda, Ryoma; Takata, Yoshiaki; Seki, Hiroyuki

doi:10.1007/978-3-030-02508-3_22

Cited by 9 publications

(9 citation statements)

References 22 publications

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“…In [5], properties of RCFG were shown including the decidability of the membership and emptiness problems, and the closure properties. In our previous study [16], the membership problem for RCFG, ε-rule free RCFG and growing RCFG are shown EXPTIME-complete, PSPACE-complete and NP-complete, respectively, and the emptiness problem for these classes are shown EXPTIMEcomplete.…”

Section: Introductionmentioning

confidence: 94%

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Generalized Register Context-Free Grammars

Senda

Takata

Seki

2020

IEICE Trans. Inf. & Syst.

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Register context-free grammars (RCFG) is an extension of context-free grammars to handle data values in a restricted way. In RCFG, a certain number of data values in registers are associated with each nonterminal symbol and a production rule has the guard condition, which checks the equality between the content of a register and an input data value. This paper starts with RCFG and introduces register type, which is a finite representation of a relation among the contents of registers. By using register type, the paper provides a translation of RCFG to a normal form and ε-removal from a given RCFG. We then define a generalized RCFG (GRCFG) where an arbitrary binary relation can be specified in the guard condition. Since the membership and emptiness problems are shown to be undecidable in general, we extend register type for GRCFG and introduce two properties of GRCFG, simulation and progress, which guarantee the decidability of these problems. As a corollary, these problems are shown to be EXPTIME-complete for GRCFG with a total order over a dense set.

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Section: Introductionmentioning

confidence: 94%

“…The lower bound can be obtained from EXPTIMEcompleteness of the emptiness problem for k-GRCFG(=) [16].…”

Section: Emptiness and Membershipmentioning

confidence: 99%

Generalized Register Context-Free Grammars

Senda

Takata

Seki

2020

IEICE Trans. Inf. & Syst.

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“…For RPDS, backward and forward regularity preservation properties were shown in [20] and [26], respectively. As a related model, register context-free grammar is also studied [9], [24], [25]. First-order definable PDS (FO-PDS) is an extension of both of RPDS and FO-NFA.…”

Section: Pds and Rpdsmentioning

confidence: 99%

LTL Model Checking for Register Pushdown Systems

Senda

Takata

Seki

2021

IEICE Trans. Inf. & Syst.

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“…In [5], properties of RCFG and RPDA were shown including the equivalence in language representation power of RCFG and RPDA, the decidability of the membership and emptiness problems, and the closure properties. In [21], the computational complexity of the above decision problems for RCFG was investigated. In [22], the complexity of these problems for RPDA was also investigated but the analysis for subclasses of RPDA was not enough.…”

Section: Introductionmentioning

confidence: 99%

“…The main results of [21,22] and this paper are summarized in Table 1. The results for non-decreasing RPDA and growing RPDA are the contribution of this paper.…”

Section: Introductionmentioning

confidence: 99%

Complexity Results on Register Pushdown Automata

Senda¹,

Takata²,

Seki³

2019

Preprint

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Register pushdown automata (RPDA) is an extension of classical pushdown automata to handle data values in a restricted way. RPDA attracts attention as a model of a query language for structured documents with data values. The membership and emptiness problems for RPDA are known to be EXPTIME-complete. This paper shows the membership problem becomes PSPACE-complete and NP-complete for nondecreasing and growing RPDA, respectively, while the emptiness problem remains EXPTIME-complete for these subclasses.

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Complexity Results on Register Context-Free Grammars and Register Tree Automata

Cited by 9 publications

References 22 publications

Generalized Register Context-Free Grammars

Generalized Register Context-Free Grammars

LTL Model Checking for Register Pushdown Systems

Complexity Results on Register Pushdown Automata

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