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

Dora Giammarresi
2010 arXiv   pre-print
The natural and immediate definition 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.  ... 
arXiv:1012.0672v1 fatcat:cxs3eo56zvcnrnbb53pnr4stlu

Unambiguous computations and locally definable acceptance types

Rolf Niedermeier, Peter Rossmanith
1998 Theoretical Computer Science  
We introduce 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.  ... 
doi:10.1016/s0304-3975(97)00005-4 fatcat:c5mxwueohzerrhynsaihw5mmky

ReachFewL = ReachUL [chapter]

Brady Garvin, Derrick Stolee, Raghunath Tewari, N. V. Vinodchandran
2011 Lecture Notes in Computer Science  
ReachFewL, 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) .  ... 
doi:10.1007/978-3-642-22685-4_23 fatcat:ctst3dfh2bfrfitng2mm2nuw7u

ReachFewL = ReachUL

Brady Garvin, Derrick Stolee, Raghunath Tewari, N. V. Vinodchandran
2012 Computational Complexity  
ReachFewL, 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) .  ... 
doi:10.1007/s00037-012-0050-8 fatcat:bl25fwwmivevrn4jkvwof2qswa

Separating Regular Languages by Piecewise Testable and Unambiguous Languages [chapter]

Thomas Place, Lorijn van Rooijen, Marc Zeitoun
2013 Lecture Notes in Computer Science  
When separation is possible, we also express 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.  ... 
doi:10.1007/978-3-642-40313-2_64 fatcat:ff7b7prouza6zcn4myahqlplji

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.  ... 

On the power of unambiguity in log-space

A. Pavan, Raghunath Tewari, N. V. Vinodchandran
2012 Computational Complexity  
-We revisit the 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).  ... 
doi:10.1007/s00037-012-0047-3 fatcat:6mkpzqhcgjdiplyb3xkuvvl2fu

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

Klaus-Jörn Lange
1993 Theoretical Computer Science  
., 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.  ... 
doi:10.1016/0304-3975(93)90255-r fatcat:hafq2x7k4vdyhledp7wuklmnpm

Making Nondeterminism Unambiguous

Klaus Reinhardt, Eric Allender
2000 SIAM journal on computing (Print)  
An analogous result holds for the 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  ... 
doi:10.1137/s0097539798339041 fatcat:6blrh74y5ran5cgij2w3r42vtu

RUSPACE(log n ) $\subseteq$ DSPACE(log 2 n /log log n )

E. Allender
1998 Theory of Computing Systems  
We present 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.  ... 
doi:10.1007/s002240000102 fatcat:rfzq32x2dzfzxbtk4ztr4vptwu

Unambiguous Auxiliary Pushdown Automata and Semi-unbounded Fan-in Circuits

R. Niedermeier, P. Rossmanith
1995 Information and Computation  
Moreover, an improved simulation 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  ... 
doi:10.1006/inco.1995.1064 fatcat:34pihqia5jendaizmtujfzewpm

On the Power of Unambiguity in Logspace [article]

Aduri Pavan and Raghunath Tewari and N. V. Vinodchandran
2010 arXiv   pre-print
We revisit the 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).  ... 
arXiv:1001.2034v1 fatcat:hwqnxnubwrgvjofu7lmqizggxy

A Note on Unambiguity, Finite Ambiguity and Complementation in Recognizable Two-Dimensional Languages [chapter]

Marcella Anselmo, Maria Madonia
2009 Lecture Notes in Computer Science  
We give partial answers based on the introduction 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.  ... 
doi:10.1007/978-3-642-03564-7_9 fatcat:hcoftre3jnf2jc3gy2seldspoi
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