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.

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.

scholarly journals Generative Power and Closure Properties of Watson-Crick Grammars

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Nurul Liyana Mohamad Zulkufli ◽  
Sherzod Turaev ◽  
Mohd Izzuddin Mohd Tamrin ◽  
Azeddine Messikh
Keyword(s):  
Proper Subset ◽  
Computational Power ◽  
Closure Properties ◽  
Generative Power ◽  
Context Sensitive ◽  
Closure Operations ◽  
The Family ◽  
Grammar Rules ◽  
Almost All ◽  
Context Free

We defineWK linear grammars, as an extension of WK regular grammars with linear grammar rules, andWK context-free grammars, thus investigating their computational power and closure properties. We show that WK linear grammars can generate some context-sensitive languages. Moreover, we demonstrate that the family of WK regular languages is the proper subset of the family of WK linear languages, but it is not comparable with the family of linear languages. We also establish that the Watson-Crick regular grammars are closed under almost all of the main closure operations.

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 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).

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.

scholarly journals COMPRESSED MEMBERSHIP PROBLEMS FOR REGULAR EXPRESSIONS AND HIERARCHICAL AUTOMATA

2010 ◽  
Vol 21 (05) ◽  
pp. 817-841 ◽  
Author(s):  
MARKUS LOHREY
Keyword(s):  
Open Problem ◽  
Regular Languages ◽  
Regular Expressions ◽  
Membership Problem ◽  
Complexity Bounds ◽  
Straight Line ◽  
Membership Problems ◽  
Context Free ◽  
Straight Line Programs ◽  
Extended Regular Expressions

Membership problems for compressed strings in regular languages are investigated. Strings are represented by straight-line programs, i.e., context-free grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g., suitably extended regular expressions, hierarchical automata) are considered. Precise complexity bounds are derived. Among other results, it is shown that the compressed membership problem for regular expressions with intersection is PSPACE-complete. This solves an open problem of Plandowski and Rytter.

Learning Nonregular Languages: A Comparison of Simple Recurrent Networks and LSTM

2002 ◽  
Vol 14 (9) ◽  
pp. 2039-2041 ◽  
Author(s):  
J. Schmidhuber ◽  
F. Gers ◽  
D. Eck
Keyword(s):  
Recent Article ◽  
Short Term Memory ◽  
Recurrent Networks ◽  
Short Term ◽  
Term Memory ◽  
Context Sensitive ◽  
Simple Recurrent Networks ◽  
Long Short Term Memory ◽  
Context Free

In response to Rodriguez's recent article (2001), we compare the performance of simple recurrent nets and long short-term memory recurrent nets on context-free and context-sensitive languages.

RESTRICTED SETS OF TRAJECTORIES AND DECIDABILITY OF SHUFFLE DECOMPOSITIONS

2005 ◽  
Vol 16 (05) ◽  
pp. 897-912 ◽  
Author(s):  
MICHAEL DOMARATZKI ◽  
KAI SALOMAA
Keyword(s):  
Regular Languages ◽  
Decomposition Problem ◽  
Open Question ◽  
Free Set ◽  
Context Free ◽  
Undecidability Result

The decidability of the shuffle decomposition problem for regular languages is a long standing open question. We consider decompositions of regular languages with respect to shuffle along a regular set of trajectories and obtain positive decidability results for restricted classes of trajectories. Also we consider decompositions of unary regular languages. Finally, we establish in the spirit of the Dassow-Hinz undecidability result an undecidability result for regular languages shuffled along a fixed linear context-free set of trajectories.

Context-sensitivity in conversation: Eye gaze and the German repair initiatorbitte?

1996 ◽  
Vol 25 (4) ◽  
pp. 587-612 ◽  
Author(s):  
Maria M. Egbert
Keyword(s):  
Conversation Analysis ◽  
Eye Gaze ◽  
Linguistic Analysis ◽  
Social Situations ◽  
Telephone Conversation ◽  
Context Sensitive ◽  
Mutual Gaze ◽  
Course Of Action ◽  
Context Free ◽  
Selection Of

ABSTRACTJust as turn-taking has been found to be both context-free and context-sensitive (Sacks, Schegloff & Jefferson 1974), the organization of repair is also shown here to be both context-free and context-sensitive. In a comparison of American and German conversation, repair can be shown to be context-free in that, basically, the same mechanism can be found across these two languages. However, repair is also sensitive to the linguistic inventory of a given language; in German, morphological marking, syntactic constraints, and grammatical congruity across turns are used as interactional resources. In addition, repair is sensitive to certain characteristics of social situations. The selection of a particular repair initiator, Germanbitte?‘pardon?’, indexes that there is no mutual gaze between interlocutors; i.e., there is no common course of action. The selection ofbitte?not only initiates repair; it also spurs establishment of mutual gaze, and thus displays that there is attention to a common focus. (Conversation analysis, context, cross-linguistic analysis, repair, gaze, telephone conversation, co-present interaction, grammar and interaction)

scholarly journals Representation and Reasoning about Strategic Abilities with ω-Regular Properties

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3052
Author(s):  
Liping Xiong ◽  
Sumei Guo
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Dynamic Logic ◽  
Research Area ◽  
Regular Expressions ◽  
Multi Agent Systems ◽  
Practical Applications ◽  
Multi Agent ◽  
Strategy Logic ◽  
Active Research

Specification and verification of coalitional strategic abilities have been an active research area in multi-agent systems, artificial intelligence, and game theory. Recently, many strategic logics, e.g., Strategy Logic (SL) and alternating-time temporal logic (ATL*), have been proposed based on classical temporal logics, e.g., linear-time temporal logic (LTL) and computational tree logic (CTL*), respectively. However, these logics cannot express general ω-regular properties, the need for which are considered compelling from practical applications, especially in industry. To remedy this problem, in this paper, based on linear dynamic logic (LDL), proposed by Moshe Y. Vardi, we propose LDL-based Strategy Logic (LDL-SL). Interpreted on concurrent game structures, LDL-SL extends SL, which contains existential/universal quantification operators about regular expressions. Here we adopt a branching-time version. This logic can express general ω-regular properties and describe more programmed constraints about individual/group strategies. Then we study three types of fragments (i.e., one-goal, ATL-like, star-free) of LDL-SL. Furthermore, we show that prevalent strategic logics based on LTL/CTL*, such as SL/ATL*, are exactly equivalent with those corresponding star-free strategic logics, where only star-free regular expressions are considered. Moreover, results show that reasoning complexity about the model-checking problems for these new logics, including one-goal and ATL-like fragments, is not harder than those of corresponding SL or ATL*.

Sign in / Sign up

Export Citation Format

Share Document