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Page 5698 of Mathematical Reviews Vol. , Issue 89J [page]

1989 Mathematical Reviews  
This proves that the @- hierarchy over an infinite alphabet is infinite.  ...  The author establishes that for every n there exists a language L,, over a finite alphabet S, such that each shuffle expression generating L, contains at least n nested @-operators.  ... 

Page 511 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
We also give a temporal logic characterization of shuffle ideals and we study its expressive power over infinite words.  ...  Summary: “We prove an effective characterization of level 5/2 of the Straubing-Thérien hierarchy for the restricted case of languages defined over a two-letter alphabet.”  ... 

Page 5650 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
{For the entire collection see MR 91h:68011.} 91j:68068 68Q45 Jedrzejowicz, Joanna (PL-GDAN) Infinite hierarchy of shuffle expressions over a finite alphabet. Inform. Process.  ...  J. 10 (1963), 385-397; MR 28 #1069] proved that the +-hierarchy over an infinite alphabet is infinite, that is, for each n there exists a language generated by an expression which contains exactly n nested  ... 

On a Hierarchy of Languages with Catenation and Shuffle [chapter]

Nils Erik Flick, Manfred Kudlek
2012 Lecture Notes in Computer Science  
We present basic structures, definitions, normal forms, and a hierarchy of languages based on catenation, shuffle and their iterations, defined by algebraic closure or least fix point solution of systems  ...  of equations.  ...  Definitions and Basic Structures Formal language theory normally deals with subsets of Σ * , all words over a finite alphabet, using as basic binary operator catenation, denoted by in the sequel.  ... 
doi:10.1007/978-3-642-31653-1_40 fatcat:c24ur5pauzgf5ouetn25md3il4

Page 3064 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
They take trees over an arbitrary ranked alphabet of input symbols rather than derivation trees as arguments, and the values of the attributes are also trees over a ranked alphabet of out- put symbols.  ...  This paper introduces the notion of 2-star height. The principal result is that the 2-star hierarchy is infinite when the alphabet contains at least two symbols. J.  ... 

Undecidable Problems About Timed Automata [chapter]

Olivier Finkel
2006 Lecture Notes in Computer Science  
We show that in the case of timed Büchi automata accepting infinite timed words some of these problems are Π 1 1 -hard, hence highly undecidable (located beyond the arithmetical hierarchy). 1  ...  We show that the problem of the minimization of the number of clocks of a timed automaton is undecidable. It is also undecidable whether the shuffle of two timed regular languages is timed regular.  ...  Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
doi:10.1007/11867340_14 fatcat:iveibc2i7jcfjejunt2ciebdo4

OPEN PROBLEMS ON REGULAR LANGUAGES: A HISTORICAL PERSPECTIVE

LAURA CHAUBARD, JEAN-ÉRIC PIN
2007 Semigroups and Formal Languages  
We consider successively the star-height problem, the Straubing-Thérien's concatenation hierarchy and the shuffle operation.  ...  On the algebraic side, we present Eilenberg's variety theory and its successive improvements, including the recent notion of C-variety.  ...  Operations on languages Let A be a finite alphabet and let A * be the free monoid on A.  ... 
doi:10.1142/9789812708700_0004 fatcat:4nq3saewxvclho2rwkfuempmxy

Undecidable Problems About Timed Automata [article]

Olivier Finkel
2007 arXiv   pre-print
We show that in the case of timed B\"uchi automata accepting infinite timed words some of these problems are Pi^1_1-hard, hence highly undecidable (located beyond the arithmetical hierarchy).  ...  We show that the problem of the minimization of the number of clocks of a timed automaton is undecidable. It is also undecidable whether the shuffle of two timed regular languages is timed regular.  ...  Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
arXiv:0712.1363v1 fatcat:jtjz4sabsfh3fopmqu76vpbeou

Page 4218 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
Thus Ry = {A | 68 COMPUTER SCIENCE 4218 A <pa Aa} (a < w”) forms the fine hierarchy of w-regular lan- guages over X.  ...  For the shuffle product case, surprisingly, ao Q is a regular language, where a is a letter of the alphabet Y.” 99f:68128 68Q50 68Q10 68Q45 Mihalache, Valeria (R-BUCHM; Bucharest) Terminal versus non-terminal  ... 

State Complexity of Permutation and Related Decision Problems on Alphabetical Pattern Constraints [article]

Stefan Hoffmann
2021 arXiv   pre-print
Additionally, for two subclasses, we give sharp bounds expressed in terms of the size of a recognizing input automaton and the size of the alphabet.  ...  We give a sharp state complexity bound expressed in terms of the longest strings in the unary projection languages of an associated finite language and which is already sharp for the subclass of finite  ...  I thank the anonymous reviewers for careful reading, noticing a reoccurring typo in the proof of Theorem 1 that was luckily spotted and fixed and helping me identifying some unclear formulations throughout  ... 
arXiv:2006.15178v3 fatcat:u7fbbwnfljbp3cblggrdqbettm

Analytic aspects of the shuffle product [article]

Marni Mishna, Mike Zabrocki
2008 arXiv   pre-print
In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of D-finite generating functions, a class which contains algebraic.  ...  In the process, we define a grammar class that models D-finite generating functions.  ...  We wish to also acknowledge the financial support of NSERC.  ... 
arXiv:0802.2844v1 fatcat:w4myc64xo5ev7ntufo54hzyr5q

Analytic aspects of the shuffle product

Marni Mishna, Mike Zabrocki, Marc Herbstritt
2008 Symposium on Theoretical Aspects of Computer Science  
In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of D-finite generating functions, a class which contains algebraic.  ...  In the process, we define a grammar class that models D-finite generating functions.  ...  We wish to also acknowledge the financial support of NSERC.  ... 
doi:10.4230/lipics.stacs.2008.1317 dblp:conf/stacs/MishnaZ08 fatcat:mirxwjsyzjeetidybchfkg4bmq

Highly Undecidable Problems about Recognizability by Tiling Systems [article]

Olivier Finkel
2008 arXiv   pre-print
It is also Π^1_2-complete to determine whether a given Büchi recognizable language of infinite pictures can be accepted row by row using an automaton model over ordinal words of length ω^2.  ...  Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the Büchi  ...  Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
arXiv:0811.3704v1 fatcat:2qkjq4zwqnar3lyo6pu3dseave

Characterization and Complexity Results on Jumping Finite Automata [article]

Henning Fernau, Meenakshi Paramasivan, Markus L. Schmid, Vojtěch Vorel
2015 arXiv   pre-print
We characterize the corresponding class of languages in terms of special shuffle expressions and survey other equivalent notions from the existing literature.  ...  In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol.  ...  Jumping Finite Automata and Shuffle Expressions Following Meduna and Zemek [65, 66] , we denote a general finite machine as M = (Q, Σ, R, s, F ), where Q is a finite set of states, Σ is the input alphabet  ... 
arXiv:1512.00482v1 fatcat:kmj2id4zbjgf5eramg6wf2h424

Page 758 of Mathematical Reviews Vol. , Issue 84b [page]

1984 Mathematical Reviews  
He also generalises similarly the model of a pushdown automaton, and characterises the behaviour of R-automata in terms of power series over the input alphabet X with coefficients in R [see A.  ...  The author defines a finite-state R-automaton as a generalisation of both stochastic and nondeterministic automata, having a behavior with values in a semiring R.  ... 
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