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.

scholarly journals Derivation "Trees" and Parallelism in Chomsky-Type Grammars

Triangle ◽  
2018 ◽  
pp. 101
Author(s):  
Benedek Nagy
Keyword(s):  
Formal Language ◽  
Phrase Structure ◽  
Formal Language Theory ◽  
Language Theory ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Rule Set ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

In this paper we discuss parallel derivations for context-free, contextsensitive and phrase-structure grammars. For regular and linear grammars only sequential derivation can be applied, but a kind of parallelism is present in linear grammars. We show that nite languages can be generated by a recursion-free rule-set. It is well-known that in context-free grammars the derivation can be in maximal (independent) parallel way. We show that in cases of context-sensitive and recursively enumerable languages the parallel branches of the derivation have some synchronization points. In the case of context-sensitive grammars this synchronization can only be local, but in a derivation of an arbitrary grammar we cannot make this restriction. We present a framework to show how the concept of parallelism can be t to the derivations in formal language theory using tokens.

scholarly journals A Pumping Lemma for Permitting Semi-Conditional Languages

2019 ◽  
Vol 30 (01) ◽  
pp. 73-92
Author(s):  
Zsolt Gazdag ◽  
Krisztián Tichler ◽  
Erzsébet Csuhaj-Varjú
Keyword(s):  
Open Problem ◽  
Generative Power ◽  
Context Sensitive ◽  
Sentential Form ◽  
Pumping Lemma ◽  
Context Free ◽  
Context Free Grammars

Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word [Formula: see text] and such a rule can be applied to a sentential form [Formula: see text] only if [Formula: see text] is a subword of [Formula: see text]. We consider permitting generalized SCGs (pgSCGs) where each rule [Formula: see text] is associated with a set of words [Formula: see text] and [Formula: see text] is applicable only if every word in [Formula: see text] occurs in [Formula: see text]. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.

A Multi-level Refinement Approach for Structural Synthesis of Optimal Probabilistic Models

2021 ◽  
Vol 179 (1) ◽  
pp. 1-33
Author(s):  
Toufik Benouhiba
Keyword(s):  
Probabilistic Models ◽  
Probability Distributions ◽  
Search Space ◽  
Optimization Techniques ◽  
Context Sensitive ◽  
Multi Level ◽  
Two Stages ◽  
Abstraction Levels ◽  
Context Free ◽  
Context Free Grammars

Probabilistic models play an important role in many fields such as distributed systems and simulations. Like non-probabilistic systems, they can be synthesized using classical refinement-based techniques, but they also require identifying the probability distributions to be used and their parameters. Since a fully automated and blind refinement is generally undecidable, many works tried to synthesize them by looking for the parameters of the distributions. Syntax-guided synthesizing approaches are more powerful, they try to synthesize models structurally by using context-free grammars. However, many problems arise like huge search space, the complexity of generated models, and the limitation of context-free grammars to define constraints over the structure. In this paper, we propose a multi-step refinement approach, based on meta-models, offering several abstraction levels to reduce the size of the search space. More specifically, each refinement step is divided into two stages in which the desired shape of models is first described by context-sensitive constraints. In the second stage, model templates are instantiated by using global optimization techniques. We use our approach to a synthesize a set of optimal probabilistic models and show that context-sensitive constraints coupled with the multi-level abilities of the approach make the synthesis task more effective.

scholarly journals Context-Free Grammars with Graph Controlled Tables

1975 ◽  
Vol 4 (43) ◽  
Author(s):  
Grzegorz Rozenberg ◽  
Arto Salomaa
Keyword(s):  
Context Free Grammar ◽  
Context Sensitive ◽  
Context Free ◽  
Context Free Grammars

It is shown that every context-sensitive language can be generated by a context-free grammar with graph control over sets of productions. This can be done in two different ways, corresponding to unconditional transfer programmed grammars and programmed grammars with empty failure fields. Also some results concerning ordinary programmed grammars are established.

scholarly journals Prediction of RNA Pseudoknotted Secondary Structure using Stochastic Context Free Grammars (SCFG)1

2006 ◽  
Vol 9 (2) ◽  
Author(s):  
Rafael García
Keyword(s):  
Secondary Structure ◽  
Computational Linguistics ◽  
Rna Structure ◽  
Maximum Length ◽  
Context Sensitive ◽  
Complexity Cost ◽  
Stochastic Context Free Grammars ◽  
Matching Techniques ◽  
Context Free ◽  
Context Free Grammars

Pseudoknots are a frequent RNA structure that assumes essential roles for varied biocatalyst cell’s functions. One of the most challenging fields in bioinformatics is the prediction of this secondary structure based on the base-pair sequence that dictates it. Previously, a model adapted from computational linguistics – Stochastic Context Free Grammars (SCFG) – has been used to predict RNA secondary structure. However, to this date the SCFG approach impose a prohibitive complexity cost [O(n4)] when they are applied to the prediction of pseudoknots, mainly because a context-sensitive grammar is formally required to analyze them. Other hybrids approaches (energy maximization) give a O(n3)complexity in the best case, besides having several restrictions in the maximum length of the sequence for practical analysis. Here we introduce a novel algorithm, based on pattern matching techniques, that uses a sequential approximation strategy to solve the original problem. This algorithm not only reduces the complexity to O(n2logn), but also widens the maximum length of the sequence, as well as the capacity of analyzing several pseudoknots simultaneously.

ON THE LEFTMOST DERVIATION IN MATRIX GRAMMARS

1999 ◽  
Vol 10 (01) ◽  
pp. 61-79 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
HENNING FERNAU ◽  
GHEORGHE PĂUN
Keyword(s):  
Systematic Study ◽  
Regular Language ◽  
Formal Languages ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Leftmost Derivation ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

Matrix grammars are one of the classical topics of formal languages, more specifically, regulated rewriting. Although this type of control on the work of context-free grammars is one of the earliest, matrix grammars still raise interesting questions (not to speak about old open problems in this area). One such class of problems concerns the leftmost derivation (in grammars without appearance checking). The main point of this paper is the systematic study of all possibilities of defining leftmost derivation in matrix grammars. Twelve types of such a restriction are defined, only four of which being discussed in literature. For seven of them, we find a proof of a characterization of recursively enumerable languages (by matrix grammars with arbitrary context-free rules but without appearance checking). Other three cases characterize the recursively enumerable languages modulo a morphism and an intersection with a regular language. In this way, we solve nearly all problems listed as open on page 67 of the monograph [7], which can be seen as the main contribution of this paper. Moreover, we find a characterization of the recursively enumerable languages for matrix grammars with the leftmost restriction defined on classes of a given partition of the nonterminal alphabet.

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