scholarly journals PC grammar systems with five context-free components generate all recursively enumerable languages

2003 ◽  
Vol 299 (1-3) ◽  
pp. 785-794 ◽  
Author(s):  
Erzsébet Csuhaj-Varjú ◽  
Gheorghe Păun ◽  
György Vaszil
Keyword(s):  
Recursively Enumerable ◽  
Grammar Systems ◽  
Context Free ◽  
Recursively Enumerable Languages

scholarly journals REMARKS ON CONTEXT-FREE PARALLEL COMMUNICATING GRAMMAR SYSTEMS GENERATING CROSSED AGREEMENTS

2008 ◽  
Vol 19 (04) ◽  
pp. 873-886
Author(s):  
BIANCA TRUTHE
Keyword(s):  
Natural Languages ◽  
Context Free Grammar ◽  
Recursively Enumerable ◽  
Grammar Systems ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Parallel Communicating Grammar Systems

Parallel communicating grammar systems are language generating devices consisting of several grammars which derive synchronously their sentential forms and communicate with each other by sending their sentential forms to another component on request. Due to collaboration, grammar systems with context-free components are more powerful than a single context-free grammar; they even can generate all recursively enumerable languages. In natural languages, there occur constructions that cannot be modelled by context-free languages. Three important phenomena are the so-called multiple agreements, crossed agreements and replication which are represented by the three non-context-free languages K1 = { anbncn | n ≥ 1 }, K2 = { anbmcndm | m ≥ 1, n ≥ 1 }, and K3 = { ww | w ∈ { a, b }+}, respectively. In the present paper, we give parallel communicating grammar systems (PC grammar systems) that are context-free and that generate the language K2, working in different modes. In two cases, the results are optimal.

PC GRAMMAR SYSTEMS WITH CLUSTERS OF COMPONENTS

2011 ◽  
Vol 22 (01) ◽  
pp. 203-212 ◽  
Author(s):  
ERZSÉBET CSUHAJ-VARJÚ ◽  
MARION OSWALD ◽  
GYÖRGY VASZIL
Keyword(s):  
Future Research ◽  
Open Problems ◽  
Recursively Enumerable Language ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Grammar Systems ◽  
Context Free

We introduce PC grammar systems where the components form clusters and the query symbols refer to clusters not individual grammars, i.e., the addressee of the query is not precisely identified. We prove that if the same component replies to all queries issued to a cluster in a rewriting step, then non-returning PC grammar systems with 3 clusters and 7 context-free components are able to generate any recursively enumerable language. We also provide open problems and directions for future research.

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.

MORPHIC CHARACTERIZATIONS OF LANGUAGE FAMILIES IN TERMS OF INSERTION SYSTEMS AND STAR LANGUAGES

2011 ◽  
Vol 22 (01) ◽  
pp. 247-260 ◽  
Author(s):  
FUMIYA OKUBO ◽  
TAKASHI YOKOMORI
Keyword(s):  
Unique Feature ◽  
Recursively Enumerable ◽  
Context Free Language ◽  
Similar Characterization ◽  
Language L ◽  
Finite Set ◽  
Context Free ◽  
String Rewriting ◽  
Free Language ◽  
Recursively Enumerable Languages

Insertion systems have a unique feature in that only string insertions are allowed, which is in marked contrast to a variety of the conventional computing devices based on string rewriting. This paper will mainly focus on those systems whose insertion operations are performed in a context-free fashion, called context-free insertion systems, and obtain several characterizations of language families with the help of other primitive languages (like star languages) as well as simple operations (like projections, weak-codings). For each k ≥ 1, a language L is a k-star language if L = F+ for some finite set F with the length of each string in F is no more than k. The results of this kind have already been presented in [10] by Păun et al., while the purpose of this paper is to prove enhanced versions of them. Specifically, we show that each context-free language L can be represented in the form L = h(L(γ)∩F+), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context-free manner), h is a projection, and F+ is a 2-star language. A similar characterization can be obtained for recursively enumerable languages, where insertion systems of weight (3, 3) and 2-star languages are involved.

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.

PARALLEL FINITE AUTOMATA SYSTEMS COMMUNICATING BY STATES

2002 ◽  
Vol 13 (05) ◽  
pp. 733-749 ◽  
Author(s):  
CARLOS MARTÍN-VIDE ◽  
ALEXANDRU MATEESCU ◽  
VICTOR MITRANA
Keyword(s):  
Finite Automata ◽  
Point Of View ◽  
Computational Power ◽  
Open Problems ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Power Point ◽  
Grammar Systems ◽  
Recursively Enumerable Languages ◽  
Parallel Communicating Grammar Systems

An accepting device based on the communication between finite automata working in parallel is introduced. It consists of several finite automata working independently but communicating states to each other by request. Several variants of parallel communicating finite automata systems are investigated from their computational power point of view. We prove that all of them are at most as powerful as multi-head finite automata. Homomorphical characterizations of recursively enumerable languages are obtained starting from languages recognized by all variants of parallel communicating finite automata systems having at most three components. We present a brief comparison with the parallel communicating grammar systems. Some remarks suggesting that these devices might be mildly context-sensitive ones as well as a few open problems and directions for further research are also discussed.

On describing the regular closure of the linear languages with graph-controlled insertion-deletion systems

2018 ◽  
Vol 52 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Henning Fernau ◽  
Lakshmanan Kuppusamy ◽  
Indhumathi Raman
Keyword(s):  
Target Component ◽  
Language Family ◽  
Current Component ◽  
Descriptional Complexity ◽  
Recursively Enumerable ◽  
Language Classes ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Kleene Closure

A graph-controlled insertion-deletion (GCID) system has several components and each component contains some insertion-deletion rules. A transition is performed by any applicable rule in the current component on a string and the resultant string is then moved to the target component specified in the rule. The language of the system is the set of all terminal strings collected in the final component. When resources are very limited (especially, when deletion is demanded to be context-free and insertion to be one-sided only), then GCID systems are not known to describe the class of recursively enumerable languages. Hence, it becomes interesting to explore the descriptional complexity of such GCID systems of small sizes with respect to language classes below RE and even below CF. To this end, we consider so-called closure classes of linear languages defined over the operations concatenation, Kleene star and union. We show that whenever GCID systems (with certain syntactical restrictions) describe all linear languages (LIN) with t components, we can extend this to GCID systems with just one more component to describe, for instance, the concatenation of two languages from the language family that can be described as the Kleene closure of linear languages. With further addition of one more component, we can extend the construction to GCID systems that describe the regular closure of LIN.

Jumping Grammars

2015 ◽  
Vol 26 (06) ◽  
pp. 709-731 ◽  
Author(s):  
Zbyněk Křivka ◽  
Alexander Meduna
Keyword(s):  
Finite Index ◽  
Open Problems ◽  
Generative Power ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

This paper introduces and studies jumping grammars, which represent a grammatical counterpart to the recently introduced jumping automata. These grammars are conceptualized just like classical grammars except that during the applications of their productions, they can jump over symbols in either direction within the rewritten strings. More precisely, a jumping grammar rewrites a string z according to a rule x → y in such a way that it selects an occurrence of x in z, erases it, and inserts y anywhere in the rewritten string, so this insertion may occur at a different position than the erasure of x. The paper concentrates its attention on investigating the generative power of jumping grammars. More specifically, it compares this power with that of jumping automata and that of classical grammars. A special attention is paid to various context-free versions of jumping grammars, such as regular, right-linear, linear, and context-free grammars of finite index. In addition, we study the semilinearity of context-free, context-sensitive, and monotonous jumping grammars. We also demonstrate that the general versions of jumping grammars characterize the family of recursively enumerable languages. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

CD GRAMMAR SYSTEMS WITH REGULAR START CONDITIONS

2008 ◽  
Vol 19 (04) ◽  
pp. 767-779
Author(s):  
RUDOLF FREUND ◽  
MARION OSWALD
Keyword(s):  
Finite Index ◽  
Hybrid Mode ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
The Family ◽  
Grammar Systems ◽  
Regular Sets ◽  
Classical Derivation ◽  
Recursively Enumerable Languages

We consider cooperating distributed grammar systems with the components working in different derivation modes as well as with regular sets as additional start conditions for the components. With the classical derivation modes ≤ k and = k as well as with the internally hybrid mode (≥ ℓ∧ ≤ k) we obtain a characterization of the family of recursively enumerable languages even with only one component, with the derivation modes *, t, and ≥ k as well as with the internally hybrid mode (t∧ ≥ k) two components working in the same mode and only one common regular set for both components yield computational completeness. For the internally hybrid modes (t∧ ≤ k) and (t∧ = k) we only obtain languages of finite index, but combining one component working in one of these modes (t∧ ≤ k) and (t∧ = k) with a component working in one of the modes * and ≥ k we again obtain a characterization of the family of recursively enumerable languages.

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