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 BOND-FREE LANGUAGES: FORMALIZATIONS, MAXIMALITY AND CONSTRUCTION METHODS

2005 ◽  
Vol 16 (05) ◽  
pp. 1039-1070 ◽  
Author(s):  
LILA KARI ◽  
STAVROS KONSTANTINIDIS ◽  
PETR SOSÍK
Keyword(s):  
Polynomial Time ◽  
Structural Characterization ◽  
Regular Languages ◽  
Important Case ◽  
Similarity Relation ◽  
Construction Methods ◽  
Large Sets ◽  
Code Property ◽  
Context Free

The problem of negative design of DNA languages is addressed, that is, properties and construction methods of large sets of words that prevent undesired bonds when used in DNA computations. We recall a few existing formalizations of the problem and then define the property of sim-bond-freedom, where sim is a similarity relation between words. We show that this property is decidable for context-free languages and polynomial-time decidable for regular languages. The maximality of this property also turns out to be decidable for regular languages and polynomial-time decidable for an important case of the Hamming similarity. Then we consider various construction methods for Hamming bond-free languages, including the recently introduced method of templates, and obtain a complete structural characterization of all maximal Hamming bond-free languages. This result is applicable to the θ-k-code property introduced by Jonoska and Mahalingam.

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.

A FORMAL STUDY OF PRACTICAL REGULAR EXPRESSIONS

2003 ◽  
Vol 14 (06) ◽  
pp. 1007-1018 ◽  
Author(s):  
CEZAR CÂMPEANU ◽  
KAI SALOMAA ◽  
SHENG YU
Keyword(s):  
Regular Languages ◽  
Proper Subset ◽  
Regular Expressions ◽  
Formal Treatment ◽  
Practical Applications ◽  
Context Sensitive ◽  
Formal Study ◽  
Pumping Lemma ◽  
Context Free

Regular expressions are used in many practical applications. Practical regular expressions are commonly called "regex". It is known that regex are different from regular expressions. In this paper, we give regex a formal treatment. We make a distinction between regex and extended regex; while regex represent regular languages, extended regex represent a family of languages larger than regular languages. We prove a pumping lemma for the languages expressed by extended regex. We show that the languages represented by extended regex are incomparable with context-free languages and a proper subset of context-sensitive languages. Other properties of the languages represented by extended regex are also studied.

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.

scholarly journals Formal language theory: refining the Chomsky hierarchy

2012 ◽  
Vol 367 (1598) ◽  
pp. 1956-1970 ◽  
Author(s):  
Gerhard Jäger ◽  
James Rogers
Keyword(s):  
Natural Language ◽  
Formal Language ◽  
Regular Languages ◽  
Language Theory ◽  
Context Free Grammar ◽  
Chomsky Hierarchy ◽  
Context Sensitive ◽  
Four Levels ◽  
Context Free ◽  
Natural Language Syntax

The first part of this article gives a brief overview of the four levels of the Chomsky hierarchy, with a special emphasis on context-free and regular languages. It then recapitulates the arguments why neither regular nor context-free grammar is sufficiently expressive to capture all phenomena in the natural language syntax. In the second part, two refinements of the Chomsky hierarchy are reviewed, which are both relevant to the extant research in cognitive science: the mildly context-sensitive languages (which are located between context-free and context-sensitive languages), and the sub-regular hierarchy (which distinguishes several levels of complexity within the class of regular languages).

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.

Nondeterministic Ordered Restarting Automata

2018 ◽  
Vol 29 (04) ◽  
pp. 663-685 ◽  
Author(s):  
Kent Kwee ◽  
Friedrich Otto
Keyword(s):  
Regular Languages ◽  
Context Sensitive ◽  
Finite State ◽  
Emptiness Problem ◽  
Context Free

While (stateless) deterministic ordered restarting automata accept exactly the regular languages, it has been observed that nondeterministic ordered restarting automata (ORWW-automata for short) are more expressive. Here we show that the class of languages accepted by the latter automata is an abstract family of languages that is incomparable to the linear, the context-free, and the growing context-sensitive languages with respect to inclusion, and that the emptiness problem is decidable for these languages. In addition, we give a construction that turns a stateless ORWW-automaton into a nondeterministic finite-state acceptor for the same language.

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.

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.

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