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Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems

Dora Giammarresi, Antonio Restivo, Sebastian Seibert, Wolfgang Thomas
1996 Information and Computation  
It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic.  ...  As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and also matches  ...  monadic second-order logic is established.  ... 
doi:10.1006/inco.1996.0018 fatcat:wftquihpyjd5jojgjhqff3tlum

Automata theory on trees and partial orders [chapter]

Wolfgang Thomas
1997 Lecture Notes in Computer Science  
Graph acceptors and their specialization for pictures, \tiling systems", are presented, and their equivalence to existential monadic second-order logic is reviewed.  ...  Other restricted versions of graph acceptors are discussed, and an intuitive exposition of the recently established monadic quanti er alternation hierarchy over graphs is given.  ...  How large is the gap between recognizability and de nability in full monadic second-order logic?  ... 
doi:10.1007/bfb0030586 fatcat:xe7c4rmzbvautdrin2igsfgurq

Uniform and nonuniform recognizability

Wolfgang Thomas
2003 Theoretical Computer Science  
, nonuniform recognizability, and monadic second-order logic.  ...  We show how this approach encompasses known models of nondeterministic automata over ÿnite words, trees, pictures, and graphs, and present some elementary metaresults connecting uniform recognizability  ...  expressions, and monadic second-order logic.  ... 
doi:10.1016/s0304-3975(01)00229-8 fatcat:4btfarn3pfdchiijplmiesg4wa

Page 7660 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
second-order logic over pictures and recognizability by tiling systems.  ...  In fact it is proved that the family of picture languages recognised by finite tiling sys- tems coincides with the family of picture languages definable in existential monadic second-order logic.  ... 

Two-Dimensional Languages [chapter]

Dora Giammarresi, Antonio Restivo
1997 Handbook of Formal Languages  
Thomas and S. Seibert for many useful discussions on the relationship between logic and tiling systems. We are grateful to M. Latteux and D.  ...  Simplot for sending us a copy of 25], and for many useful comments on domino systems, and to V. Bruyere for sending us a copy of A. Gilon's Thesis 16]. K.  ...  monadic second order logic (cf. 38] ).  ... 
doi:10.1007/978-3-642-59126-6_4 fatcat:ymevasf56jbxfkqnos6wvzlocu

Page 6559 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
[Inform. and Comput. 125 (1996), no. 1, 32-45; MR 97c:68109], regarding the expressive equivalence between existential monadic second-order logic and recognizability by tiling systems.  ...  Two results are shown: the first exhibits a class of graphs where the use of “occurrence constraints” in tiling systems can be avoided, and the second shows that over pictures (i.e., over labelled rectangular  ... 

Weighted Picture Automata and Weighted Logics [chapter]

Ina Mäurer
2006 Lecture Notes in Computer Science  
We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will be a picture series.  ...  We introduce weighted 2-dimensional on-line tessellation automata (W2OTA) and prove that for commutative semirings, the class of picture series defined by sentences of the weighted logics coincides with  ...  The author would like to thank Manfred Droste and Dietrich Kuske for their helpful discussions and comments on earlier versions of this paper.  ... 
doi:10.1007/11672142_25 fatcat:bynebp2vwfdu3e365fjuld7khi

Perfectly quilted rectangular snake tilings

Robert Brijder, Hendrik Jan Hoogeboom
2009 Theoretical Computer Science  
We introduce a particular form of snake tilings to define picture languages, and relate the obtained family to the recognizable picture languages (as defined by Wang tiles).  ...  The correspondence for substitution tilings is even closer, and hence is applicable to the Hilbert curve.  ...  Acknowledgements We are indebted to Klaus Reinhardt and Jarkko Kari for providing helpful information. We thank the referees for suggestions that improved our presentation.  ... 
doi:10.1016/j.tcs.2008.12.010 fatcat:6pwzjem2yzfllpbpa24yq3z2xq

EMSO-logic and automata related to homogeneous flow event structures

K Shahbazyan, Yu Shoukourian
2004 Theoretical Computer Science  
In this paper we study the recognizability and deÿnability on existential monadic second order (EMSO) logic of languages related to homogeneous ow event structures (HFES), i.e., the languages of conÿgurations  ...  If G is the domain of linear order or binary tree then the recognizability and EMSO-deÿnability of conÿgurations of HFES hold.  ...  The binary tree t is represented by the tree model t = (dom(t); S t 1 ; S t 2 ; ¡ t ; In logical formulas we use ÿrst-order variables x; y; z; : : : for positions, and monadic second-order variables X;  ... 
doi:10.1016/j.tcs.2004.03.030 fatcat:z7e5hjqdjnaf5dikcyzfzm6oty

Bisimulation-invariant PTIME and higher-dimensional μ-calculus

Martin Otto
1999 Theoretical Computer Science  
Biichi-Elgot-Trakhtenbrot Theorem (the automaton-recognizable properties of finite words are those that are definable in monadic second-order logic), or the Immerman-Vardi Theorem (the PTIME properties  ...  Paradigmatic results in this area are, for instance, Fagin's Theorem (the NP-recognizable properties of finite structures are exactly those that can be formalized in existential second-order logic), the  ...  second-order logic.  ... 
doi:10.1016/s0304-3975(98)00314-4 fatcat:klwctsikb5fhpm45567db6vn6y

Characterizations of recognizable picture series

Ina Mäurer
2007 Theoretical Computer Science  
the families of series characterized by weighted tiling or weighted domino systems.  ...  We assign weights to different devices, ranging from picture automata to tiling systems.  ...  Acknowledgements The author would like to thank Manfred Droste and Paul Gastin for their helpful discussions and comments on earlier versions of this paper, as well as the work of the unknown referees  ... 
doi:10.1016/j.tcs.2007.01.019 fatcat:wopdjrx7wbcefiamcdr2opra4m

Weighted Automata and Logics on Graphs [chapter]

Manfred Droste, Stefan Dück
2015 Lecture Notes in Computer Science  
Weighted automata model quantitative features of the behavior of systems and have been investigated for various structures like words, trees, traces, pictures, and nested words.  ...  As a consequence, we obtain corresponding Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words.  ...  Conclusion We introduced a weighted generalization of Thomas' graph acceptors [33, 34] and a suitable weighted logic in the sense of Droste and Gastin [9] .  ... 
doi:10.1007/978-3-662-48057-1_15 fatcat:d53kbssbsbhozbxyh6yhxjc6cy

On some recognizable picture-languages [chapter]

Klaus Reinhardt
1998 Lecture Notes in Computer Science  
We show that the language of pictures over fa; bg, where all occurring b's are connected is recognizable, which solves an open problem in Mat98].  ...  Furthermore we show that the language of pictures over fa; bg, where the number of a's is equal to the number of b's is nonuniformly recognizable.  ...  A set (language) of pictures is called recognizable if it is recognized by a nite tiling system.  ... 
doi:10.1007/bfb0055827 fatcat:jkoijn4tdne6lkpo53pumcwqqa

Unambiguous recognizable two-dimensional languages

Marcella Anselmo, Dora Giammarresi, Maria Madonia, Antonio Restivo
2006 RAIRO - Theoretical Informatics and Applications  
Some closure and non-closure properties of UREC are presented. Finally we show that it is undecidable whether a given tiling system is unambiguous.  ...  Further UREC family coincides with the class of picture languages defined by unambiguous 2OTA and it strictly contains its deterministic counterpart.  ...  Moreover finite tiling systems have also a natural logic meaning: in [11, 12] it is shown that the family REC and the family of languages defined by existential monadic second order formulas coincide  ... 
doi:10.1051/ita:2006008 fatcat:6ad3fsdvzfesbeanox4kenvwny

Weighted Automata and Logics on Infinite Graphs [chapter]

Stefan Dück
2016 Lecture Notes in Computer Science  
This gives us the first general results connecting automata and logics over infinite graphs in the qualitative and the quantitative setting.  ...  We show a Büchi-like connection between graph automata and logics for infinite graphs.  ...  Acknowledgments: I want to thank Manfred Droste and Tobias Weihrauch for helpful discussions and insightful remarks on earlier drafts of this paper.  ... 
doi:10.1007/978-3-662-53132-7_13 fatcat:jkr7qckpq5fnnk53qf26mybqgy
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