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Nominal Regular Expressions for Languages over Infinite Alphabets. Extended Abstract [article]

Alexander Kurz and Tomoyuki Suzuki and Emilio Tuosto
2013 arXiv   pre-print
We discuss classes of such nominal regular expressions, show how such expressions have natural interpretations in terms of languages over infinite alphabets, and give Kleene theorems to characterise their  ...  Inspired by nominal techniques -- as those popular in process calculi -- we extend classical regular expressions with names (to model computational resources) and suitable operators (for allocation, deallocation  ...  Nominal regular expressions We fix a finite set S of 'letters' and a countably infinite set N of 'names' and consider languages over infinite alphabets as sets of finite words over S ∪ N .  ... 
arXiv:1310.7093v1 fatcat:rxvn5462grcwtb5tucn4wyixoa

On Learning Nominal Automata with Binders

Yi Xiao, Emilio Tuosto
2019 Electronic Proceedings in Theoretical Computer Science  
This class of automata captures nominal regular languages; analogously to the classical language theory, nominal automata have been shown to characterise nominal regular expressions with binders.  ...  These formalisms are amenable to abstract modelling resource-aware computations. We propose a learning algorithm on nominal regular languages with binders.  ...  We designed a learning algorithm for a class of languages over infinite alphabet; more precisely, we have considered nominal regular languages with binders [25, 27] .  ... 
doi:10.4204/eptcs.304.9 fatcat:3g22jydynjdxda6yrdms2gd7ty

A Characterisation of Languages on Infinite Alphabets with Nominal Regular Expressions [chapter]

Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto
2012 Lecture Notes in Computer Science  
We give a characterisation of languages on infinite alphabets in a variant of nominal regular expressions with permutations (p-NREs).  ...  Finally, we give a Kleene theorem for p-NREs and fp-automata to formally characterise languages on infinite alphabets.  ...  We would like to thank the anonymous reviewers for their valuable comments and suggestions.  ... 
doi:10.1007/978-3-642-33475-7_14 fatcat:w6hw6iq4gjb7dpo53mw3lfddhu

Preface of Special Issue on Theoretical Aspects of Computer Science

Christoph Dürr, Thomas Schwentick
2013 Theory of Computing Systems  
The first two investigate size issues for automata and (extended) regular expressions, respectively, while the third one investigates the syntactic monoids of regular languages over infinite alphabets.  ...  These extended abstracts were among the top papers of those that were chosen for presentation at STACS 2011 in a highly competitive peer-review process (after which only 54 papers out of 271 submission  ...  The article provides a version of the above mentioned theorem for regular languages over infinite words.  ... 
doi:10.1007/s00224-013-9467-y fatcat:47u6phttwjfyhmd63fuwo5mo4y

Towards Nominal Context-Free Model-Checking [chapter]

Pierpaolo Degano, Gian-Luigi Ferrari, Gianluca Mezzetti
2013 Lecture Notes in Computer Science  
Abstract. Two kinds of automata are introduced, for recognising regular and context-free nominal languages. We compare their expressive power with that of analogous proposals in the literature.  ...  Some properties of our languages are proved, in particular that emptiness of a context-free nominal language L is decidable, and that the intersection of L with a regular nominal language is still context-free  ...  The literature mainly reports on various kinds of regular languages over infinite alphabets and on their recognizers [16, 2, 7] .  ... 
doi:10.1007/978-3-642-39274-0_11 fatcat:ry3jwjhbhvgdtnl4jfvtr4nh2y

Nominal Automata for Resource Usage Control [chapter]

Pierpaolo Degano, Gian-Luigi Ferrari, Gianluca Mezzetti
2012 Lecture Notes in Computer Science  
Two classes of nominal automata, namely Usage Automata (UAs) and Variable Finite Automata (VFAs) are considered to express resource control policies over program execution traces expressed by a nominal  ...  We finally carry over to VFAs the symbolic technique for model checking Usages against UAs, so making it possible to verify the compliance of a program with a larger class of security properties.  ...  We would like to thank the anonymous referees for their comments that greatly helped us to improve the quality of our paper.  ... 
doi:10.1007/978-3-642-31606-7_11 fatcat:w2djwhhq6vfc7hrgevn4rqz5ge

On Nominal Regular Languages with Binders [chapter]

Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto
2012 Lecture Notes in Computer Science  
We investigate regular languages on infinite alphabets where words may contain binders on names. To this end, classical regular expressions and automata are extended with binders.  ...  This builds on the recent convergence of three lines of research: languages over infinite alphabets, HD-automata, and nominal sets, as we will explain now in more detail.  ...  The authors thank the reviewers for their criticisms and comments which helped to greatly improve the paper.  ... 
doi:10.1007/978-3-642-28729-9_17 fatcat:ko35ovrwkzbb7lgl7a6ezvn3tu

Learning Nominal Automata [article]

Joshua Moerman and Matteo Sammartino and Alexandra Silva and Bartek Klin and Michał Szynwelski
2016 arXiv   pre-print
We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets.  ...  The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata.  ...  We thank Frits Vaandrager and Gerco van Heerdt for useful comments and discussions. We also thank the anonymous reviewers.  ... 
arXiv:1607.06268v2 fatcat:wrwbdhm425er5fogem3opmnj2e

Learning nominal automata

Joshua Moerman, Matteo Sammartino, Alexandra Silva, Bartek Klin, Michał Szynwelski
2017 SIGPLAN notices  
We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets.  ...  The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata.  ...  We thank Frits Vaandrager and Gerco van Heerdt for useful comments and discussions. We also thank the anonymous reviewers.  ... 
doi:10.1145/3093333.3009879 fatcat:i36tyni3ezbuxbztgp33hqzabi

Automata with Group Actions

Mikolaj Bojanczyk, Bartek Klin, Slawomir Lasota
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
Our motivating question is a Myhill-Nerode theorem for infinite alphabets.  ...  This framework builds on the idea of nominal sets of Gabbay and Pitts; nominal sets are the special case of our framework where letters can be only compared for equality.  ...  The following result is an abstract counterpart of the Myhill-Nerode theorem for infinite alphabets: Theorem 3 Let L be a G-language.  ... 
doi:10.1109/lics.2011.48 dblp:conf/lics/BojanczykKL11 fatcat:nrrsy7qxojflzf2jkm2aloesfe

Nominal Monoids

Mikołaj Bojańczyk
2013 Theory of Computing Systems  
We develop an algebraic theory for languages of data words.  ...  The first field is the algebraic theory of regular languages. In this theory, a regular language is represented by its syntactic monoid, which is a finite monoid.  ...  Acknowledgements I would like to thank Clemens Ley for introducing me to the subject. I would like to thank Sławomir Lasota and Bartek Klin for many stimulating discussions.  ... 
doi:10.1007/s00224-013-9464-1 fatcat:mx6v6dan3zcy5pnnxupulm7qvm

Symbolic Model Checking of Tense Logics on Rational Kripke Models [chapter]

Wilmari Bekker, Valentin Goranko
2009 Lecture Notes in Computer Science  
Rational Kripke models are based on (generally infinite) rational graphs, with vertices labeled by the words in some regular language and transitions recognized by asynchronous two-head finite automata  ...  If Y is a regular language over an alphabet Γ then Y | γ is a regular language over the alphabet Γ − {γ}. Proof.  ...  Extended star-free regular expressions over an alphabet Σ are defined as follows: E := a | ¬E | E 1 ∪ E 2 | E 1 ; E 2 , where a ∈ Σ.  ... 
doi:10.1007/978-3-642-03092-5_2 fatcat:meg6lzhf4baohjbvf337o5nld4

Nominal Büchi Automata with Name Allocation [article]

Henning Urbat and Daniel Hausmann and Stefan Milius and Lutz Schröder
2021 arXiv   pre-print
We introduce regular nominal nondeterministic B\"uchi automata (B\"uchi RNNAs), an automata model for languages of infinite bar strings, repurposing the previously introduced RNNAs over finite bar strings  ...  We approach omega-languages over infinite alphabets in the setting of nominal sets, and study languages of infinite bar strings, i.e. infinite sequences of names that feature binding of fresh names; binding  ...  Conclusions and Future Work We have introduced Büchi regular nondeterministic nominal automata (Büchi RNNAs), an automaton model for languages of infinite words over infinite alphabets.  ... 
arXiv:2107.03213v2 fatcat:axrni5h2brbcvpqeoqqcdao5zm

Varieties of Data Languages

Henning Urbat, Stefan Milius, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
We establish an Eilenberg-type correspondence for data languages, i.e. languages over an infinite alphabet.  ...  This is the first result of this kind for data languages.  ...  language over the alphabet Σ.  ... 
doi:10.4230/lipics.icalp.2019.130 dblp:conf/icalp/UrbatM19 fatcat:grw5knn6uvf2he3zyqu2yuijki

Symbolic model checking of tense logics on rational Kripke models [article]

Wilmari Bekker, Valentin Goranko
2008 arXiv   pre-print
Rational Kripke models are based on (generally infinite) rational graphs, with vertices labeled by the words in some regular language and transitions recognized by asynchronous two-head finite automata  ...  Every atomic proposition in a rational Kripke model is evaluated in a regular set of states.  ...  We wish to thank Arnaud Carayol, Balder ten Cate, Carlos Areces, Christophe Morvan, and Stéphane Demri, for various useful comments and suggestions.  ... 
arXiv:0810.5516v1 fatcat:gnpsz54nnve5zh6ztcid3kmpxa
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