Insertion-deletion systems with substitutions I

Computability ◽  
2021 ◽  
pp. 1-27
Author(s):  
Martin Vu ◽  
Henning Fernau
Keyword(s):  
Single Letter ◽  
Context Dependency ◽  
Insertions And Deletions ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Substitution Site ◽  
New Type ◽  
Left And Right ◽  
Context Free

In this paper, we discuss the addition of substitutions as a further type of operations to (in particular, context-free) insertion-deletion systems, i.e., in addition to insertions and deletions we allow single letter replacements to occur. We investigate the effect of the addition of substitution rules on the context dependency of such systems, thereby also obtaining new characterizations of and even normal forms for context-sensitive (CS) and recursively enumerable (RE) languages and their phrase-structure grammars. More specifically, we prove that for each RE language, there is a system generating this language that only inserts and deletes strings of length two without considering the context of the insertion or deletion site, but which may change symbols (by a substitution operation) by checking a single symbol to the left of the substitution site. When we allow checking left and right single-letter context in substitutions, even context-free insertions and deletions of single letters suffice to reach computational completeness. When allowing context-free insertions only, checking left and right single-letter context in substitutions gives a new characterization of CS. This clearly shows the power of this new type of rules.

scholarly journals REPRESENTATIONS AND CHARACTERIZATIONS OF LANGUAGES IN CHOMSKY HIERARCHY BY MEANS OF INSERTION-DELETION SYSTEMS

2008 ◽  
Vol 19 (04) ◽  
pp. 859-871 ◽  
Author(s):  
GHEORGHE PĂUN ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
TAKASHI YOKOMORI
Keyword(s):  
Dna Computing ◽  
Research Direction ◽  
Regular Languages ◽  
Turing Computability ◽  
Chomsky Hierarchy ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Language L ◽  
Context Free

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L = h(L(γ) ∩ D), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.

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.

Context-sensitive underspecification and the acquisition of phonemic contrasts

1996 ◽  
Vol 23 (1) ◽  
pp. 57-79 ◽  
Author(s):  
Daniel A. Dinnsen
Keyword(s):  
Free Radical ◽  
Substitution Pattern ◽  
Phonological Representations ◽  
Context Sensitive ◽  
Plausible Account ◽  
One Stage ◽  
The Status ◽  
Context Free ◽  
Phonemic Contrasts

ABSTRACTSeveral competing proposals for the (under)specification of phonological representations are evaluated against the facts of phonemic acquisition. Longitudinal evidence relating to the emergence of a voice contrast in the well-documented study of Amahl (from age 2;2 to 3;11) is reconsidered. Neither contrastive specification nor context-free radical underspecification is capable of accounting for the facts. The problem is in the characterization of the change in the status of a feature from being noncontrastive and conditioned by context at one stage to being contrastive with phonetic effects that diffuse gradually through the lexicon. Both frameworks must treat as accidental the persistence of the early substitution pattern and require the postulation of wholesale changes in underlying representations, where these changes do not accord well with the observed phonetic changes or with the facts available to the learner. Context-sensitive radical underspecification provides a plausible account of each stage and the transition between stages with minimal grammar change.

STRICT LOCAL TESTABILITY WITH CONSENSUS EQUALS REGULARITY, AND OTHER PROPERTIES

2013 ◽  
Vol 24 (06) ◽  
pp. 747-763 ◽  
Author(s):  
STEFANO CRESPI REGHIZZI ◽  
PIERLUIGI SAN PIETRO
Keyword(s):  
Regular Languages ◽  
Context Sensitive ◽  
Language Definition ◽  
Context Free

A recent language definition device named consensual is based on agreement between similar words. Considering a language over a bipartite alphabet made by pairs of unmarked/marked letters, the match relation specifies when such words agree. Thus a set (the “base”) over the bipartite alphabet consensually specifies another language that includes any terminal word such that a set of corresponding matching words is in the base. We show that all and only the regular languages are consensually generated by a strictly locally testable base; the result is based on a generalization of Medvedev's homomorphic characterization of regular languages. Consensually context-free languages strictly include the base family. The consensual and the base families collapse together if the base is context-sensitive.

scholarly journals Optimizing over subsequences generates context-sensitive languages

2021 ◽  
Vol 9 ◽  
pp. 528-537
Author(s):  
Andrew Lamont
Keyword(s):  
Optimality Theory ◽  
Generative Capacity ◽  
Context Sensitive ◽  
Finite State ◽  
Minimal Modification ◽  
Context Free

Abstract Phonological generalizations are finite-state. While Optimality Theory is a popular framework for modeling phonology, it is known to generate non-finite-state mappings and languages. This paper demonstrates that Optimality Theory is capable of generating non-context-free languages, contributing to the characterization of its generative capacity. This is achieved with minimal modification to the theory as it is standardly employed.

LANGUAGE FAMILIES DEFINED BY A CILIATE BIO-OPERATION: HIERARCHIES AND DECISION PROBLEMS

2005 ◽  
Vol 16 (04) ◽  
pp. 645-662 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
MARKUS HOLZER
Keyword(s):  
Inverted Repeat ◽  
Decision Problems ◽  
Membership Problem ◽  
Chomsky Hierarchy ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
The Status ◽  
Emptiness Problem ◽  
Context Free

We formalize the hairpin inverted repeat excision, which is known in ciliate genetics as an operation on words and languages by defining [Formula: see text] as the set of all words xαyRαRz where w = xαyαRz and the pointer α is in P. We extend this concept to language families which results in families [Formula: see text]. For [Formula: see text] and [Formula: see text] be the families of finite, regular, context-free, context-sensitive or recursively enumerable language, respectively, we determine the hierarchy of the families [Formula: see text] and compare these families with those of the Chomsky hierarchy. Furthermore, we present the status of decidability of the membership problem, emptiness problem and finiteness problem for the families [Formula: see text].

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.

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.

Use of Spelling-to-Sound Rules in Reading

1976 ◽  
Vol 43 (3_suppl) ◽  
pp. 1135-1146 ◽  
Author(s):  
Catherine G. Wolf ◽  
David Owen Robinson
Keyword(s):  
Fifth Graders ◽  
Second Graders ◽  
Single Letter ◽  
Context Sensitive ◽  
Correspondence Rules ◽  
Context Free ◽  
Novel Words

The present study investigated the use of spelling-to-sound rules by second-graders, fifth-graders, and adults in the reading of novel words. Specifically, the study was concerned with the pronunciation of the vowel of monosyllabic synthetic words. Two classes of rules were studied: context-free rules, in which the pronunciation of a single-letter vowel or vowel digraph is invariant across context, and context-sensitive rules, in which the pronunciation of the vowel is dependent upon subsequent letters of the word. The performance of children and adults on the context-free stimuli indicated that beginning as well as mature readers make use of spelling-to-sound correspondence rules in the pronunciation of novel words and that the tendency to use such rules increases with age. The context-sensitive rules were not generally used; subjects tended to give the most common pronunciation for a vowel regardless of context. However, when a pronunciation other than the most common one was used for a vowel, it tended to be used in the context predicted by the context-sensitive rules. Two models of the use of spelling-to-sound rules in reading were proposed.

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.

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