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.

ON THE DESCRIPTIONAL COMPLEXITY OF THE WINDOW SIZE FOR DELETING RESTARTING AUTOMATA

2013 ◽  
Vol 24 (06) ◽  
pp. 831-846 ◽  
Author(s):  
MARTIN KUTRIB ◽  
FRIEDRICH OTTO
Keyword(s):  
Upper Bound ◽  
Recursive Function ◽  
Window Size ◽  
Input Word ◽  
Trade Off ◽  
Descriptional Complexity ◽  
The Impact ◽  
Current Word ◽  
Restarting Automaton

The restarting automaton was inspired by the technique of ‘analysis by reduction’ from linguistics. A restarting automaton processes a given input word through a sequence of cycles. In each cycle the current word on the tape is scanned from left to right and a single local simplification (a rewrite) is executed. One of the essential parameters of a restarting automaton is the size of its read/write window. Here we study the impact of the window size on the descriptional complexity of several types of deterministic and nondeterministic restarting automata. For all k ≥ 4, we show that the savings in the economy of descriptions of restarting automata that can only delete symbols but not rewrite them (that is, the so-called R- and RR-automata) cannot be bounded by any recursive function, when changing from window size k to window size k + 1. This holds for deterministic as well as for nondeterministic automata, and for k ≥ 5, it even holds for the stateless variants of these automata. However, the trade-off between window sizes two and one is recursive for deterministic devices. In addition, a polynomial upper bound is given for the trade-off between RRWW-automata with window sizes k + 1 and k for all k ≥ 2.

ON METALINEAR PARALLEL COMMUNICATING GRAMMAR SYSTEMS

2007 ◽  
Vol 18 (06) ◽  
pp. 1313-1322
Author(s):  
ANDREAS MALCHER ◽  
BETTINA SUNCKEL
Keyword(s):  
Intermediate Model ◽  
Grammar System ◽  
Grammar Systems ◽  
Context Free ◽  
Parallel Communicating Grammar Systems

A generalization of centralized and returning parallel communicating grammar systems with linear components (linear CPC grammar systems) is studied. It is known that linear CPC grammar systems are more powerful than regular CPC grammar systems and that CPC grammar systems with context-free components are more powerful than linear CPC grammar systems. Here, the intermediate model of metalinear CPC grammar systems is studied. This is a CPC grammar system where the master is allowed to use metalinear rules whereas the remaining components are restricted to use linear rules only. It turns out that metalinear CPC grammar systems are more powerful than linear CPC grammar systems and less powerful than CPC grammar systems with context-free components. Furthermore, it is shown that all languages generated by metalinear CPC grammar systems are semilinear.

Limitations of Coverability Trees for Context-Free Parallel Communicating Grammar Systems and Why these Grammar Systems are not Linear Space

2016 ◽  
Vol 26 (03) ◽  
pp. 1650012
Author(s):  
Stefan D. Bruda ◽  
Mary Sarah Ruth Wilkin
Keyword(s):  
Linear Space ◽  
Decision Problems ◽  
Analysis Tool ◽  
Context Sensitive ◽  
Grammar System ◽  
Grammar Systems ◽  
Context Free ◽  
Parallel Communicating Grammar Systems

Coverability trees offer a finite characterization of all the derivations of a context-free parallel grammar system (CF-PCGS). Their finite nature implies that they necessarily omit some information about these derivations. We demonstrate that the omitted information is most if not all of the time too much, and so coverability trees are not useful as an analysis tool except for their limited use already considered in the paper that introduces them (namely, determining the decidability of certain decision problems over PCGS). We establish this result by invalidating an existing proof that synchronized CF-PCGS are less expressive than context-sensitive grammars. Indeed, we discover that this proof relies on coverability trees for CF-PCGS, but that such coverability trees do not in fact contain enough information to support the proof.

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.

scholarly journals Splicing Context-Free Matrix Grammars using Parallel Communicating Grammar Systems

2019 ◽  
Vol 8 (12) ◽  
pp. 1281-1283
Keyword(s):  
Dna Computing ◽  
Computational Theory ◽  
Generative Power ◽  
Grammar System ◽  
Grammar Systems ◽  
Context Free ◽  
Theoretical Results ◽  
Parallel Communicating Grammar Systems

Extensive research on splicing of strings in DNA computing has established important theoretical results in computational theory. Further, splicing on strings has been extended to arrays in[2]. In this context, we propose, a grammar system, using queries to splice context-free matrix grammars and show that the language generated by this grammar system is incomparable to the language given in [3] and has more generative power than in [2].

ON THE TERMINATING DERIVATION MODE IN COOPERATING DISTRIBUTED GRAMMAR SYSTEMS WITH FORBIDDING COMPONENTS

2009 ◽  
Vol 20 (02) ◽  
pp. 331-340 ◽  
Author(s):  
TOMÁŠ MASOPUST
Keyword(s):  
Generative Power ◽  
Context Sensitive ◽  
Grammar Systems ◽  
Context Free ◽  
Context Free Grammars

This paper discusses the terminating derivation mode in cooperating distributed grammar systems where components are forbidding grammars instead of context-free grammars. Such systems are called forbidding cooperating distributed grammar systems, and it is demonstrated that the number of their components can be reduced to two without changing the generative power and that these systems are computationally complete. Without erasing productions, however, these systems are less powerful than context-sensitive grammars.

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