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Deciding definability by deterministic regular expressions

Wojciech Czerwiński, Claire David, Katja Losemann, Wim Martens
2017 Journal of computer and system sciences (Print)  
We investigate the complexity of deciding whether a given regular language can be defined with a deterministic regular expression.  ...  The problem becomes EXPSPACE-complete if the language is represented as a regular expression with counters.  ...  Furthermore, Brüggemann-Klein and Wood showed that it is decidable whether a given regular language is definable by a DRE.  ... 
doi:10.1016/j.jcss.2017.03.011 fatcat:5a3o2m6qgrbhvhxkmm7dhnujuq

Deciding Definability by Deterministic Regular Expressions [chapter]

Wojciech Czerwiński, Claire David, Katja Losemann, Wim Martens
2013 Lecture Notes in Computer Science  
We investigate the complexity of deciding whether a given regular language can be defined with a deterministic regular expression.  ...  The problem becomes EXPSPACE-complete if the language is represented as a regular expression with counters.  ...  Furthermore, Brüggemann-Klein and Wood showed that it is decidable whether a given regular language is definable by a DRE.  ... 
doi:10.1007/978-3-642-37075-5_19 fatcat:7x6pko5bmravlak4s5fox7o6fy

Definability by Weakly Deterministic Regular Expressions with Counters is Decidable [chapter]

Markus Latte, Matthias Niewerth
2015 Lecture Notes in Computer Science  
We show that weakly deterministic regular expressions with counters (WDREs) -as they are used in XML Schema-are at most exponentially larger than equivalent DFAs.  ...  As a consequence, the problem, whether a given DFA is equivalent to any WDRE, is decidable in EXPSPACE.  ...  Thus, semantically, not every regular language can be defined with a deterministic regular expression.  ... 
doi:10.1007/978-3-662-48057-1_29 fatcat:johyslcrajdzjn6wrjqw47ld5i

Deterministic regular expressions with back-references

Dominik D. Freydenberger, Markus L. Schmid
2019 Journal of computer and system sciences (Print)  
By using these, deterministic regex can define non-deterministic regular languages (in particular, all unary regular languages), as well as infinite languages that are not pumpable in the usual sense.  ...  Following the original paper by Brüggemann-Klein and Wood [9], deterministic regular expressions have been studied extensively.  ...  by defining only a strict subclass of the regular languages.  ... 
doi:10.1016/j.jcss.2019.04.001 fatcat:i2dtuwp6jjc4vkso5juys4nzai

Simplifying XML schema

Geert Jan Bex, Wouter Gelade, Wim Martens, Frank Neven
2009 Proceedings of the 35th SIGMOD international conference on Management of data - SIGMOD '09  
In formal language theoretic terms, this constraint restricts content models to deterministic regular expressions.  ...  In the present paper, we therefore investigate solutions to relieve users from the burden of UPA by automatically transforming nondeterministic expressions into concise deterministic ones defining the  ...  We prove theoretical intractability for deciding whether a regular expression defines a deterministic language.  ... 
doi:10.1145/1559845.1559922 dblp:conf/sigmod/BexGMN09 fatcat:gqfcmvohebesjbzzcaw5emrrnu

Observations on the complexity of regular expression problems

H.B. Hunt
1979 Journal of computer and system sciences (Print)  
Subclasses of the regular grammars, that generate all regular sets but for which equivalence and containment are provably decidable deterministically in polynomial time, are also presented.  ...  Several observations are presented on the computational complexity of regular expression problems.  ...  are decidable deterministically in polynomial time.  ... 
doi:10.1016/0022-0000(79)90002-3 fatcat:fmynjz4tk5du3oicfvf4tk3p6q

Checking Determinism of Regular Expressions with Counting [chapter]

Haiming Chen, Ping Lu
2012 Lecture Notes in Computer Science  
As a natural result of our work we derive a characterization of weak determinism for regular expressions with counting, which leads to a new O(|ΣE||E|) time algorithm for deciding weak determinism of regular  ...  deterministic where ΣE is the set of distinct symbols in E.  ...  For a regular expression E, the language specified by E is denoted by L(E). The language of E [m,n] is defined as L(E [m,n] ) = ∪ n i=m L(E) i . Define λ(E) = true if ε ∈ L(E) and f alse otherwise.  ... 
doi:10.1007/978-3-642-31653-1_30 fatcat:cfknmddo2zgn7aucjxbrjjrho4

Unambiguous Constrained Automata [chapter]

Michaël Cadilhac, Alain Finkel, Pierre McKenzie
2012 Lecture Notes in Computer Science  
Problems decidable for deterministic CA are nonetheless shown to remain decidable for unambiguous CA, and testing for regularity is added to this set of decidable problems.  ...  Unambiguous CA are then shown incomparable with deterministic reversal-bounded machines in terms of expressivity, and a deterministic model equivalent to unambiguous CA is identified.  ...  This amounts to deciding, by Lemma 2, whether L(A, C) is regular. L(A, C) ) ∩ Run(A) is crucial to the proof of Lemma 4 and to the decidability of regularity for UnCA.  ... 
doi:10.1007/978-3-642-31653-1_22 fatcat:ke64zflzgbes5hn4jljqdhag2i

UNAMBIGUOUS CONSTRAINED AUTOMATA

MICHAËL CADILHAC, ALAIN FINKEL, PIERRE MCKENZIE
2013 International Journal of Foundations of Computer Science  
Problems decidable for deterministic CA are nonetheless shown to remain decidable for unambiguous CA, and testing for regularity is added to this set of decidable problems.  ...  Unambiguous CA are then shown incomparable with deterministic reversal-bounded machines in terms of expressivity, and a deterministic model equivalent to unambiguous CA is identified.  ...  This amounts to deciding, by Lemma 2, whether L(A, C) is regular. L(A, C) ) ∩ Run(A) is crucial to the proof of Lemma 4 and to the decidability of regularity for UnCA.  ... 
doi:10.1142/s0129054113400339 fatcat:m6hixrt42ra65c5ivugqrtgcui

Regular Expressions with Numerical Constraints and Automata with Counters [chapter]

Dag Hovland
2009 Lecture Notes in Computer Science  
We define a class of finite automata with counters and a deterministic subclass of these. Deterministic finite automata with counters can recognize words in linear time.  ...  Regular expressions with numerical constraints are an extension of regular expressions, allowing to bound numerically the number of times that a subexpression should be matched.  ...  With matching we mean the problem of deciding whether a given word is in the language defined by the regular expression.  ... 
doi:10.1007/978-3-642-03466-4_15 fatcat:xdxtrppn4za7dcv52rltgdgwwy

Beyond omega-Regular Languages

Mikolaj Bojanczyk, Marc Herbstritt
2010 Symposium on Theoretical Aspects of Computer Science  
It can be described using a form of regular expressions, namely by ω-regular expressions.  ...  It can be described using automata, namely by nondeterministic Büchi automata, or the equivalent deterministic Muller automata.  ...  Above, we have described several classes of languages of ω-words, defined by: the logics with new quantifiers and automata with counters.  ... 
doi:10.4230/lipics.stacs.2010.2440 dblp:conf/stacs/Bojanczyk10 fatcat:6oaslsh6kndxzixfk6zzpwqj7m

Formal Methods of Transformations (Dagstuhl Seminar 17142)

Emmanuel Filiot, Sebastian Maneth, Helmut Seidl, Marc Herbstritt
2017 Dagstuhl Reports  
This seminar was motivated by recent advances and breakthrough results, both in the settings of words and trees.  ...  The goal of this Dagstuhl seminar was to gather researchers working on the theory and practice of transformations (also know as transductions) of word and tree structures, which are realised by transducers  ...  Deterministic two-way transducers define the robust class of regular functions which, among other good properties, is closed under composition.  ... 
doi:10.4230/dagrep.7.4.23 dblp:journals/dagstuhl-reports/FiliotMS17 fatcat:2kwm6o7h2banfjp5y5nb4wimvm

Deterministic Regular Expressions With Back-References [article]

Dominik D. Freydenberger, Markus L. Schmid
2018 arXiv   pre-print
problem and some decidable problems in static analysis), while, at the same time, their expressive power exceeds that of deterministic regular expressions without back-references.  ...  We demonstrate that, compared to their non-deterministic superclass, these deterministic regular expressions with back-references have desirable algorithmic properties (i.e., efficiently solvable membership  ...  We can decide in time O(|Σ||α|k), whether a regex α with k variables and over alphabet Σ is deterministic (if so, we can construct its Glushkov-automaton in the same time). 2.  ... 
arXiv:1802.01508v1 fatcat:hxy7h2jyj5dz5ie7mi3t3ds7ca

Matching Trace Patterns with Regular Policies [chapter]

Franz Baader, Andreas Bauer, Alwen Tiu
2009 Lecture Notes in Computer Science  
We consider policies that are described by regular expressions, finite automata, or formulae of linear temporal logic (LTL).  ...  of finite words to express policies means that we only monitor safety properties [11] .  ...  A policy is a regular language over Σ. We assume that such a policy is given either by a regular expression or by a (non-deterministic) finite automaton.  ... 
doi:10.1007/978-3-642-00982-2_9 fatcat:kf67vtpcvfey5kb5envmdfm3tq

Page 2665 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
Summary: “Regular expressions define regular languages, so there are algorithms that can solve some important problems concern- ing regular languages such as finite automata synthesis or analysis by using  ...  regular expressions.  ... 
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