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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. ...##
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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*.” ...##
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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 ...##
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On a Hierarchy of Languages with Catenation and Shuffle
[chapter]

2012
*
Lecture Notes in Computer Science
*

We present basic structures, definitions, normal forms, and

doi:10.1007/978-3-642-31653-1_40
fatcat:c24ur5pauzgf5ouetn25md3il4
*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. ...##
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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. ...##
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Undecidable Problems About Timed Automata
[chapter]

2006
*
Lecture Notes in Computer Science
*

We show that in the case

doi:10.1007/11867340_14
fatcat:iveibc2i7jcfjejunt2ciebdo4
*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. ...##
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OPEN PROBLEMS ON REGULAR LANGUAGES: A HISTORICAL PERSPECTIVE

2007
*
Semigroups and Formal Languages
*

We consider successively the star-height problem, the Straubing-Thérien's concatenation

doi:10.1142/9789812708700_0004
fatcat:4nq3saewxvclho2rwkfuempmxy
*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*. ...##
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Undecidable Problems About Timed Automata
[article]

2007
*
arXiv
*
pre-print

We show that in the case

arXiv:0712.1363v1
fatcat:jtjz4sabsfh3fopmqu76vpbeou
*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. ...##
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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 ...##
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State Complexity of Permutation and Related Decision Problems on Alphabetical Pattern Constraints
[article]

2021
*
arXiv
*
pre-print

Additionally, for two subclasses, we give sharp bounds

arXiv:2006.15178v3
fatcat:u7fbbwnfljbp3cblggrdqbettm
*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 ...##
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Analytic aspects of the shuffle product
[article]

2008
*
arXiv
*
pre-print

In the search to understand how to extend these natural correspondences, we find that the

arXiv:0802.2844v1
fatcat:w4myc64xo5ev7ntufo54hzyr5q
*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. ...##
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Analytic aspects of the shuffle product

2008
*
Symposium on Theoretical Aspects of Computer Science
*

In the search to understand how to extend these natural correspondences, we find that the

doi:10.4230/lipics.stacs.2008.1317
dblp:conf/stacs/MishnaZ08
fatcat:mirxwjsyzjeetidybchfkg4bmq
*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. ...##
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Highly Undecidable Problems about Recognizability by Tiling Systems
[article]

2008
*
arXiv
*
pre-print

It is also Π^1_2-complete to determine whether

arXiv:0811.3704v1
fatcat:2qkjq4zwqnar3lyo6pu3dseave
*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. ...##
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Characterization and Complexity Results on Jumping Finite Automata
[article]

2015
*
arXiv
*
pre-print

We characterize the corresponding class

arXiv:1512.00482v1
fatcat:kmj2id4zbjgf5eramg6wf2h424
*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*...##
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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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