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

2002 ◽  
Vol 65 (2) ◽  
pp. 393-414 ◽  
Author(s):  
Giovanni Pighizzini ◽  
Jeffrey Shallit ◽  
Ming-wei Wang
Keyword(s):  
Lower Bounds ◽  
Auxiliary Space ◽  
Descriptional Complexity ◽  
Context Free ◽  
Pushdown Automata ◽  
Context Free Grammars

ON ALTERNATING PHRASE-STRUCTURE GRAMMARS

2010 ◽  
Vol 21 (01) ◽  
pp. 1-25
Author(s):  
ETSURO MORIYA ◽  
FRIEDRICH OTTO
Keyword(s):  
Phrase Structure ◽  
Expressive Power ◽  
Context Sensitive ◽  
Leftmost Derivation ◽  
Context Free ◽  
Pushdown Automata ◽  
Context Free Grammars

The concepts of alternation and of state alternation are extended from context-free grammars to context-sensitive and arbitrary phrase-structure grammars. For the resulting classes of alternating grammars the expressive power is investigated with respect to the leftmost derivation mode and with respect to the unrestricted derivation mode. In particular new grammatical characterizations for the class of languages that are accepted by alternating pushdown automata are obtained in this way.

ON THE DESCRIPTIONAL COMPLEXITY OF METALINEAR CD GRAMMAR SYSTEMS

2005 ◽  
Vol 16 (05) ◽  
pp. 1011-1025
Author(s):  
BETTINA SUNCKEL
Keyword(s):  
Recursive Function ◽  
Trade Off ◽  
Descriptional Complexity ◽  
Grammar System ◽  
Trade Offs ◽  
Grammar Systems ◽  
Context Free ◽  
Context Free Grammars

Metalinear CD grammar systems are context-free CD grammar systems where each component consists of metalinear productions. The maximal number of nonterminals in all starting productions is referred to as the width of a CD grammar system. It is shown that between the class of CD grammar systems of width m + 1 and of width m there are savings concerning the size of the grammar system not bounded by any recursive function. This is called a non-recursive trade-off. Furthermore, it is proven that there are non-recursive trade-offs between the class of metalinear CD grammar systems of width m and the class of (2m - 1)-linear context-free grammars. In addition, some decidability results are presented.

Self-Verifying Pushdown and Queue Automata

2021 ◽  
Vol 180 (1-2) ◽  
pp. 1-28
Author(s):  
Henning Fernau ◽  
Martin Kutrib ◽  
Matthias Wendlandt
Keyword(s):  
Recursive Function ◽  
Input Word ◽  
Closure Properties ◽  
Descriptional Complexity ◽  
Trade Offs ◽  
Deterministic Automata ◽  
Context Free ◽  
Pushdown Automata ◽  
Computation Path

We study the computational and descriptional complexity of self-verifying pushdown automata (SVPDA) and self-verifying realtime queue automata (SVRQA). A self-verifying automaton is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. We show that SVPDA and SVRQA are automata characterizations of so-called complementation kernels, that is, context-free or realtime nondeterministic queue automaton languages whose complement is also context free or accepted by a realtime nondeterministic queue automaton. So, the families of languages accepted by SVPDA and SVRQA are strictly between the families of deterministic and nondeterministic languages. Closure properties and various decidability problems are considered. For example, it is shown that it is not semidecidable whether a given SVPDA or SVRQA can be made self-verifying. Moreover, we study descriptional complexity aspects of these machines. It turns out that the size trade-offs between nondeterministic and self-verifying as well as between self-verifying and deterministic automata are non-recursive. That is, one can choose an arbitrarily large recursive function f, but the gain in economy of description eventually exceeds f when changing from the former system to the latter.

scholarly journals GENERATING ALL CIRCULAR SHIFTS BY CONTEXT-FREE GRAMMARS IN GREIBACH NORMAL FORM

2007 ◽  
Vol 18 (06) ◽  
pp. 1139-1149 ◽  
Author(s):  
PETER R. J. ASVELD
Keyword(s):  
Normal Form ◽  
Complexity Measures ◽  
Descriptional Complexity ◽  
Low Degree ◽  
Cyclic Shifts ◽  
Low Degree Polynomials ◽  
Context Free ◽  
Greibach Normal Form ◽  
Context Free Grammars

For each alphabet Σn = {a1,a2,…,an}, linearly ordered by a1 < a2 < ⋯ < an, let Cn be the language of circular or cyclic shifts over Σn, i.e., Cn = {a1a2 ⋯ an-1an, a2a3 ⋯ ana1,…,ana1 ⋯ an-2an-1}. We study a few families of context-free grammars Gn (n ≥1) in Greibach normal form such that Gn generates Cn. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals ν(n), the number of rules π(n) and the number of leftmost derivations δ(n) of Gn. As in the case of Chomsky normal form, these ν, π and δ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal w. r. t. all these measures remains open.

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