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Tiling-Recognizable Two-Dimensional Languages: From Non-Determinism to Determinism through Unambiguity
[article]

2010
*
arXiv
*
pre-print

The natural and immediate definition

arXiv:1012.0672v1
fatcat:cxs3eo56zvcnrnbb53pnr4stlu
*of**unambiguity*corresponds to*a*family UREC*of**languages*that is strictly contained in REC. ... We introduce the notion*of*line-*unambiguous*tiling recognizable*languages*and prove that it corresponds or somehow naturally introduces different notions*of*determin- ism that define*a*hierarchy inside ... Both determinism and*unambiguity*correspond to the existence*of**a*unique process*of**computation*, but while determinism is*a*"local" notion,*unambiguity*is*a*fully "global" one. ...##
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Unambiguous computations and locally definable acceptance types

1998
*
Theoretical Computer Science
*

We introduce

doi:10.1016/s0304-3975(97)00005-4
fatcat:c5mxwueohzerrhynsaihw5mmky
*a*modification*of*Hertrampf's locally definable acceptance types which allows to get*a*larger number*of*characterizable complexity*classes*. ... This sheds new light on the discussion on how to access*unambiguous**computation*. ... Acknowledgements We are grateful to Uli Hertrampf for several fruitful remarks on the conference version*of*this paper and to the anonymous referees for numerous insightful comments. ...##
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ReachFewL = ReachUL
[chapter]

2011
*
Lecture Notes in Computer Science
*

ReachFewL,

doi:10.1007/978-3-642-22685-4_23
fatcat:ctst3dfh2bfrfitng2mm2nuw7u
*a*natural generalization*of*ReachUL, is the*class**of*problems decided by nondeterministic log-space machines which on every input have at most polynomially many*computation*paths from the start ... ReachUL is the*class**of*problems decided by nondeterministic log-space machines which on every input have at most one*computation*path from the start configuration to any other configuration. ... We thank the second reviewer for pointing out*a*subtle difference between the definitions*of*ReachUL (defined in Buntrock et al. 1991) and RUSPACE(log n) (defined in Lange 1997) . ...##
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ReachFewL = ReachUL

2012
*
Computational Complexity
*

ReachFewL,

doi:10.1007/s00037-012-0050-8
fatcat:bl25fwwmivevrn4jkvwof2qswa
*a*natural generalization*of*ReachUL, is the*class**of*problems decided by nondeterministic log-space machines which on every input have at most polynomially many*computation*paths from the start ... ReachUL is the*class**of*problems decided by nondeterministic log-space machines which on every input have at most one*computation*path from the start configuration to any other configuration. ... We thank the second reviewer for pointing out*a*subtle difference between the definitions*of*ReachUL (defined in Buntrock et al. 1991) and RUSPACE(log n) (defined in Lange 1997) . ...##
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Separating Regular Languages by Piecewise Testable and Unambiguous Languages
[chapter]

2013
*
Lecture Notes in Computer Science
*

When separation is possible, we also express

doi:10.1007/978-3-642-40313-2_64
fatcat:ff7b7prouza6zcn4myahqlplji
*a*separator by saturating one*of*the original*languages*by*a*suitable congruence. ... Following the same line, we show that one can as well decide whether two regular*languages*can be separated by an*unambiguous**language*, albeit with*a*higher complexity. ... We are interested in two*classes*Sep*of*separators: the*class**of*piecewise testable*languages*, and the*class**of**unambiguous**languages*. Piecewise Testable*Languages*. ...##
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Page 516 of Mathematical Reviews Vol. , Issue 99a
[page]

1991
*
Mathematical Reviews
*

*A*regular

*language*is

*a*l|-

*unambiguous*

*language*if it is denoted by some |-

*unambiguous*regular expression. ... We give

*a*Kleene theorem for |-

*unambiguous*

*languages*and characterize |-

*unambiguous*regular

*languages*in terms

*of*structural properties

*of*the minimal deterministic au- tomata that recognize them. ...

##
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On the power of unambiguity in log-space

2012
*
Computational Complexity
*

-We revisit the

doi:10.1007/s00037-012-0047-3
fatcat:6mkpzqhcgjdiplyb3xkuvvl2fu
*class*OptL[log n] and show that ShortestPathLength -*computing*the length*of*the shortest path in*a*DAG, is complete for OptL[log n]. ... Our Results Complexity*of*ReachFewL FewL, the logspace analog*of*the polynomial time*class*FewP [All86, CH90], is the*class**of**languages*that are decided by nondeterministic logpsace machines with the ... We thank Samir Datta and Raghav Kulkarni for discussions which lead to*a*weaker version*of*Theorem 13 (namely, reachability for 4-page graphs is complete for NL). ...##
###
Page 1090 of Mathematical Reviews Vol. , Issue 89B
[page]

1989
*
Mathematical Reviews
*

*A*family L

*of*

*languages*is said to have

*a*morphic characteriza- tion if 7 =

*A*oMo---o%,(L), for some L€&, n>0, and each #, is

*a*

*class*

*of*morphisms or inverse morphisms. ... Jetty Kleijn (Leiden) 89b:68043 68Q50 Carpi, Arturo (I-NAPL-AM) On

*unambiguous*reductions

*of*monoids

*of*

*unambiguous*relations. Theoret.

*Comput*. Sci. 51 (1987), no. 1-2, 215-220. ...

##
###
Page 6953 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

This is

*a*consequence*of*the following results: (i) an FTR*language**of**unambiguous*star height one is*unambiguous*renewal; (ii) there exist renewal*languages*which are not*unambiguous*renewal. ... It is well known that over*a*finite alphabet and*a**class**A**of*regular*languages*, context-free*languages*are obtained as solutions*of*such equation systems. ...##
###
Unambiguity of circuits

1993
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(93)90255-r
fatcat:hafq2x7k4vdyhledp7wuklmnpm
*Unambiguity**of*circuits, Theoretical*Computer*Science 107 (1993) 77-94. The concept*of**unambiguity**of*circuits is considered. ... Several*classes**of**unambiguous*circuit families within the NC-hierarchy are introduced and related to*unambiguous*automata and to PRAMS with exclusive write access. ... By XRYW-TIME(f(n)) we denote the*class**of*all*languages*recognizable in timef by XR YW-PRAMS with*a*polynomial number*of*processors. ...##
###
Making Nondeterminism Unambiguous

2000
*
SIAM journal on computing (Print)
*

An analogous result holds for the

doi:10.1137/s0097539798339041
fatcat:6blrh74y5ran5cgij2w3r42vtu
*class**of*problems reducible to context-free*languages*. ... We show that in the context*of*nonuniform complexity, nondeterministic logarithmic space bounded*computation*can be made*unambiguous*. ... Acknowledgment: We thank Klaus-Jörn Lange for helpful comments, and for drawing our attention to min-unique graphs, and for arranging for the second author to spend some*of*his sabbatical time in Tübingen ...##
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RUSPACE(log n ) $\subseteq$ DSPACE(log 2 n /log log n )

1998
*
Theory of Computing Systems
*

We present

doi:10.1007/s002240000102
fatcat:rfzq32x2dzfzxbtk4ztr4vptwu
*a*deterministic algorithm running in space O , log 2 n= loglogn solving the connectivity problem on strongly*unambiguous*graphs. ... In addition, we present*a*n Olog n time-bounded algorithm for this problem running on*a*parallel pointer machine. ... Acknowledgments We thank DIMACS for the use*of*o ce space where much*of*this work was done while the second author visited Rutgers University. ...##
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Unambiguous Auxiliary Pushdown Automata and Semi-unbounded Fan-in Circuits

1995
*
Information and Computation
*

Moreover, an improved simulation

doi:10.1006/inco.1995.1064
fatcat:34pihqia5jendaizmtujfzewpm
*of*LOGUCFL (the*class**of**languages*logspace many-one reducible to*unambiguous*context-free*languages*) by*unambiguous*circuits and AuxPDAs is developed. ...*A*cost-free simulation*of*polynomially ambiguity bounded AuxPDAs by*unambiguous*ones is given. ... We are particularly indebted to Klaus-J orn Lange for making us familiar with the considered problems, for his support and encouragement, and for allowing us to include results*of*(Lange and Rossmanith ...##
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On the Power of Unambiguity in Logspace
[article]

2010
*
arXiv
*
pre-print

We revisit the

arXiv:1001.2034v1
fatcat:hwqnxnubwrgvjofu7lmqizggxy
*class*[ n] and show that ShortestPathLength -*computing*the length*of*the shortest path in*a*DAG, is complete for [ n]. ... We introduce [ n], an*unambiguous*version*of*[ n], and show that (*a*) = if and only if [ n] = [ n], (b) ≤[ n] ≤. [-] We show that the reachability problem over graphs embedded on 3 pages is complete for ... We thank Samir Datta and Raghav Kulkarni for discussions which lead to*a*weaker version*of*Theorem 13 (namely, reachability for 4-page graphs is complete for NL). ...##
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A Note on Unambiguity, Finite Ambiguity and Complementation in Recognizable Two-Dimensional Languages
[chapter]

2009
*
Lecture Notes in Computer Science
*

We give partial answers based on the introduction

doi:10.1007/978-3-642-03564-7_9
fatcat:hcoftre3jnf2jc3gy2seldspoi
*of*special*classes**of**languages**of*"high complexity", in*a*sense specified in the paper and motivated by some necessary conditions holding for recognizable ... and*unambiguous**languages*. ... We will introduce*a**class*HP ⊆ co-REC \ REC*of*not-recognizable*languages*and*a**class*HK ⊆ REC \ UREC*of*ambiguous*languages*, whose*languages*are "hard" with respect to some complexity functions. ...
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